Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for University Physics Volume 2
Check Your Understanding Is the efficiency of the various light bulbs the only consideration when comparing the various light bulbs?Can a wire cany a current and still be neutral—that is, have a total charge of zero? Explain.Car batteries are rated in ampere-hours (Ah). To what physical quantity do ampere-hours correspond (voltage, current, charge, energy; power,...)?When working with high-power electric circuits, it is advised that whenever possible, you work "one-handed” or “keep one hand in your pocket." Why is this a sensible suggestion?Incandescent light bulbs are being replaced with more efficient LED and CFL light bulbs. Is there any obvious evidence that incandescent light bulbs might not be that energy efficient? Is energy converted into anything but visible light?It was stated that the motion of an electron appears nearly random when an electrical field is applied to the conductor. What makes the motion nearly random and differentiates it from the random motion of molecules in a gas?Electric circuits are sometimes explained using a conceptual model of water flowing through a pipe. In this conceptual model, the voltage source is represented as a pump that pumps water through pipes and the pipes connect components in the circuit. Is a conceptual model of water flowing through a pipe an adequate representation of the circuit? How are electrons and wires similar to water molecules and pipes? How are they different?An incandescent light bulb is partially evacuated. Why you suppose that is?The [R drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.Do impurities in semiconducting materials listed in Table 9.1 supply free charges? (Hint Examine the range of resistivity for each and determine whether die pure semiconductor has the higher or lower conductivity.)Does the resistance of an object depend on the path current takes through it? Consider, for example, arectangular bar—is its resistance the same along its lengthas across its width?If aluminum and copper wires of the same length have the same resistance, which has the larger diameter? Why?In Determining Field from Potential, resistance was defined as R=VI . In this section, we presentedOhm’s law, which is commonly expressed as V = IR.The equations look exactly alike. What is the difference between Ohm’s law and the definition of resistance?Shown below are the results of an experiment where four devices were connected across a variable voltage source. The voltage is increased and the current is measured. Which device, if any, is an ohmic device?The current I is measured through a sample of an ohmic material as a voltage V is applied, (a) What is the current when the voltage is doubled to 2V (assume the change in temperature of the material is negligible)? (b) What is the voltage applied is the current measured is 0.27 (assume the change in temperature of the material is negligible)? What will happen to the current if the material if the voltage remains constant, but the temperature of the material increases significantly?Common household appliances are rated at 110 V, but power companies deliver voltage in the kilovolt range and then step the voltage down using transformers to 110 V to be used in homes. You will learn in later chapters that transformers consist of many turns of wire, which warm up as current flows through them, wasting some of the energy that is given off as heat. This sounds inefficient. Why do the power companies transport electric power using this method?Your electric bill gives your consumption in units of kilowatt-hour (kW h). Does this unit represent the amount of charge, current, voltage, power, or energy you buy?Resistors are commonly rated at 18W,14W,12W ,1 W and 2 W for use in electrical circuits. If a current of1 = 2.00 A is accidentally passed through a R=1.00 resistor rated at 1 W, what would be the most probable outcome? Is there anything that can be done to prevent such an accident?Ail immersion heater is a small appliance used to heat a cup of water for tea by passing current through a resistor. If the voltage applied to the appliance is doubled, will the time required to heat the water change? By how much? Is this a good Idea?What requirement for superconductivity7 makes current superconducting devices expensive to operate?Name two applications for superconductivity listed in this section and explain how superconductivity is used in the application. Can you think of a use for superconductivity that is not listed?A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like protons or electrons. You may have seen it used to make human hair stand on end or produce large sparks. One application of the Van de Graaff generator is to create X-rays by bombarding a hard metal target with the beam. Consider a beam of protons at 1.00 keV and a current of 5.00 mA produced by the generator, (a) What is the speed of the protons? (b) How many protons are produced each second?A cathode ray tube (CRT) is a device that produces a focused beam of electrons in a vacuum. The electrons strike a phosphor-coated glass screen at the end of the tube, which produces a blight spot of light. The position of the bright spot of light on the screen can be adjusted by deflecting the electrons with electrical fields, magnetic fields, or both. Although the CRT tube was once commonly found in televisions, computer displays, and oscilloscopes, newer appliances use a liquid crystal display (LCD) or plasma screen. You still may come across a CRT in your study of science. Consider a CRT with an electron beam average current of 25.00A . How many electrons strike the screen every minute?How many electrons flow through a point in a wire in 3.00s if there is a constant current of I= 4.00 AA conductor carries a current that is decreasing exponentially with time. The current is modeled as I=I0et/ , where I0= 3.00 A is the current at timet = 0.00 s and =0.50 s is the time constant. How much charge flows through the conductor between t = 0.00 s and =3 ?The quantity of charge through a conductor is modeledas Q=4.00Cs4t41.00Cst+6.00mc .What is the current at time t = 3.00 s?The current through a conductor is modeled as I(t)=Imsin(2[60Hz]t) . Write an equation for the charge as a function of time.The charge on a capacitor in a circuit is modeled as Q(t)=Qmaxcos(+) . What is the current through the circuit as a function of time?An aluminum wire 1.628 mm in diameter (14-gauge) carries a current of 3.00 amps, (a) What is the absolute value of the charge density in the wire? (b) What is the drift velocity of the electrons? (c) What would be the drift velocity if the same gauge copper were used instead of aluminum? The density of copper is 8.96 g/cm3 and thedensity of aluminum is 2.70 g/cm3. The molar mass ofaluminum is 26.98 g/mol and the molar mass of copper is 63.5 g/mol. Assume each atom of metal contributes one free electron.The current of an election beam has a measuredcurrent of I=50.00A with a radius of 1.00 mm2. What is the magnitude of the current density of the beam?A high-energy proton accelerator produces a proton beam with a radius of r - 0,90 mm. The beam current is I=9.00A and is constant. The charge density ofthe beam is n = 6.001011 protons per cubic meter, (a)What is the current density of the beam? (b) What is the drift velocity of the beam? (c) How much time does it take for 1.0010 m protons to be emitted by the accelerator?Consider a wire of a circular cross-section with a radius of R = 3.00mm. The magnitude of the currentdensity is modeled as J=cr2=5.00106Am4r2 . Whatis the current through the inner section of the wire from the center to r = 0.5R?The current of an electron beam has a measured current of I=50.00A with a radius of 1,00 mm2. What is the magnitude of the current density of the beam?The current supplied to an ail conditioner unit is 4.00 amps. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density is n=8.481028electronsm3 Find magnitude of (a) current density and (b) the drift velocity.What current flows through the bulb of a 3.00-V flashlight when its hot resistance is 3.60 ?Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.How many volts are supplied to operate an indicator light on a DVD player that has a resistance of 140 , given that 25.0 mA passes through it?What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.If the 0. 10.0-mm-diameter tungsten filament in a light bulb is to have a resistance of 0.200 at 20.0C , how long should it be?A lead rod has a length of 30.00 cm and a resistance of 5.00. What is the radius of the rod?Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance pet- unit length (as they might in household wiring).What current flows through a 2.54-cm-diameter rod of Pure silicon that is 20.0 cm long, when 1.00103 V is applied to it? (Such a rod may be used to make nuclear- particle detectors, for example.)(a) To what temperature must you raise a copper wire,originally at 20.0C , to double its resistance, neglectingany changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?A resistor made of nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at 20.0C . Over what temperature range can it be used?Of what material is a resistor made if its resistance is 40.0% greater at 100.0C than at 20.0C ?An electronic device designed to operate at any temperature in the range from 10.0C to 55.0C contains pure carbon resistors. By what factor does their resistance increase over this range?(a) Of what material is a wire made, if it is 25.0 m long with a diameter of 0.100 mm and has a resistance of 77.7 at 20.0C ? (b) What is its resistance at 150.0C ?Assuming a constant temperature coefficient of resistivity what is the maximum percent decrease in the resistance of a constantan wire starting at 20.0C ?A copper wire has a resistance of 0.500 at 20.0°C and an iron wire has a resistance of 0.525 at the same temperature. At what temperature are their resistances equal?A 2.2-k resistor is connected across a D cell battery (1.5 V). What is the current through the resistor?A resistor rated at 250 k is connected across two D cell batteries (each 1.50 V) in series, with a total voltage of 3.00 V. Tire manufacturer advertises that their resistors are within 5% of the rated value. What are the possible minimum current and maximum current through the resistor?A resistor is connected in series with a power supply of 20.00 V. The current measure is 0.50 A. What is the resistance of the resistor?A resistor is placed in a circuit with an adjustable voltage source. The voltage across and the current through the resistor and the measurements are shown below. Estimate the resistance of the resistor.The following table show the measurements of a current through and the voltage across a sample of material. Plot the data, and assuming the object is an ohmic device, estimate the resistance.A 20.00-V battery is used to supply current to a 10-k resistor. Assume the voltage drop across any wires used for connections is negligible, (a) What is the current through the resistor? (b) What is the power dissipated by the resistor? (c) What is the power input from the battery; assuming all the electrical power is dissipated by the resistor? (d) What happens to the energy dissipated by the resistor?What is the maximum voltage that can be applied to a 10k resistor rated at 14W?A heater is being designed that uses a coil of 14-gauge nichrome wire to generate 300 W using a voltage of y= 110V. How long should the engineer make the wire?An alternative to CFL bulbs and incandescent bulbs are light-emitting diode (LED) bulbs. A 100-W incandescent bulb can be replaced by a 16-W LED bulb. Both produce 1600 lumens of light. Assuming the cost of electricity is $0.10 per kilowatt-hour, how much does it cost to run die bulb for one year if it runs for four hours a day?The power dissipated by a resistor with a resistance of R=100 is P = 2.0 W . What are the current through and the voltage drop across the resistor?Running late to catch a plane, a driver accidentally leaves the headlights on after parking the car in the airport parking lot. During takeoff, the driver realizes the mistake. Having just replaced the battery, the driver knows that the battery is a 12-V automobile battery, rated at 100Ah . The driver, knowing there is nothing that can be done, estimates how long the lights will shine, assuming there are two 12-V headlights, each rated at 40 W. What did the driver conclude?SI. A physics student has a single-occupancy dorm loom. The student lias a small refrigerator that runs with a current of 3.00 A and a voltage of 110 V, a lamp that contains a 100-YV bulb, an overhead light with a 60-W bulb, and various other small devices adding up to 3.00 W. (a) Assuming the power plant that supplies 110 V electricity to the dorm is 10 km away and the two aluminum transmission cables use 0-gauge wire with a diameter of 8.252 mm, estimate the percentage of the total power supplied by the power company that is lost in the transmission, (b) What would be the result is the power company delivered the electric power at 110 kV?A 0.50-W, 220- resistor carries the maximumcurrent possible without damaging the resistor. If the current were reduced to half the value, what would be the power consumed?Consider a power plant is located 60 km away from a residential area uses Q-gauge (A=42.40mm2) wire ofcopper to transmit power at a current of I = 100.00 A.How much more power is dissipated in the copper wires than it would be in superconducting wires?A wire is drawn through a die, stretching it to four times its original length. By what factor does its resistance increase?Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has a=0.06/C ) when it isat the same temperature as the patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is 82.0% of its value at 37C (normal bodytemperature)?Electrical power generators are sometimes "load tested” by passing current through a large vat of water. A similar method can be used to test the heat output of a resistor. A R = 30 resistor is connected to a 9.0-V battery and the resistor leads are water proofed and the resistor is placed in 1.0 kg of room temperature water (T=20C) . Current runs through the resistor for 20 minutes. Assuming all the electrical energy dissipated by the resistor is converted to heat, what is the final temperature of the water?A 12-guage gold wire has a length of 1 meter. (a) What would be the length of a silver 12-gauge wire with the same resistance? (b) What are their respective resistances at the temperature of boiling water?What is the change in temperature required to decrease the resistance for a carbon resistor by 10%?A coaxial cable consists of an inner conductor with radius r1=0.25cm and an outer radius of r0=0.5cm and has a length of 10 meters. Plastic, with a resistivityof =2.001013m m, separates the two conductors. What is the resistance of the cable?A 10.00-meter long wire cable that is made of copper has a resistance of 0.051 ohms, (a) What is the weight if the wire was made of copper? (b) What is the weight of a 10.00-meter-long wire of the same gauge made of aluminum? (c)What is the resistance of the aluminum wire? The density of copper is 8960 kg/m3 and the density of aluminum is 2760 kg/m3.A nichrome rod that is 3.00 mm long with a cross sectional area of 1.00 mm2 is used for a digital thermometer, (a)What is the resistance at room temperature? (b)What is the resistance at body temperature?The temperature in Philadelphia, PA can vary between 68.00F and 100.00F in one summer day. By what percentage will an aluminum wire’s resistance change during the day?When 100.0 V is applied across a 5-gauge (diameter 4.621 mm) wire that is 10 m long, the magnitude of the current density is 2.0X108A/m2 . What is die resistivity of the wire?A wire with a resistance of 5.0 is drawn out through a die so that its new Length is twice times its original length. Find the resistance of the longer wire. You may assume that the resistivity and density of the material are unchanged.What is the resistivity of a wire of 5-gauge wire (A=16.8106m2) , 5.00 m length, and 5.10 m resistance?Coils are often used in electrical and electronic circuits. Consider a coil which is formed by winding 1000 turns of insulated 20-gauge copper wire (area 0.52 mm2 ) in a single layer on a cylindrical non-conducting core of radius 2.0 mm. What is the resistance of the coil? Neglect the thickness of the insulation.Currents of approximately 0.06 A can be potentially fatal. Currents in that range can make the heart fibrillate (beat in an uncontrolled manner). The resistance of a dry human body can be approximately 100 k . (a) What voltage can cause 0.06 A through a dry human body? (b) When a human body is wet, the resistance can fall to 100 . What voltage can cause harm to a wet body?A 20.00-ohm; 5.00-watt resistor is placed in series with a power supply, (a) What is the maxim tun voltage that can be applied to the resistor without hanniug the resistor? (b) What would be the current through the resistor?A battery with an emf of 24.00 V delivers a constant current of 2.00 mA to an appliance. Haw much work does the battery do in three minutes?A 12.00-V battery has an internal resistance of a tenth of an ohm. (a) What is the current if the battery terminals are momentarily shorted together? (b) What is the terminal voltage if the battery delivers 0.25 amps to a circuit?A 10-gauge copper wire has a cross-sectional area A=5.26mm2 and carries a current of I=5.00A . The adensity of copper is =89.50g/cm2 . One mole ofcopper atoms (6.021023atoms) has a mass ofapproximately 63.50 g. What is the magnitude of the drift velocity of the elections, assuming that each copper atom contributes one free electron to the current?The current through a 12-gauge wire is given as I(t)=(5.00A)sin(260Hzt)). What is the current density at time 15.00 ms?A particle accelerator produces a beam with a radius of 1.25 mm with a current of 2.00 mA. Each proton has a kinetic energy of 10.00 MeV. (a) What is the velocity of the protons? (b) What is the number (n) of protons per unit volume? (b) How many electrons pass a cross sectional area each second?In this chapter, most examples and problems involved direct current (DC). DC circuits have the current flowing in one direction, from positive to negative. When the current was changing, it was changed linearly from I=ImaxtoI=+Imax and the voltage changed linearly from V=Vmax to V=+Vmax where Vmax=ImaxR .Suppose a voltage source is placed in series with a resistor of R = 10 that supplied a current that alternated as a sine wave, for example, I(t)=(3.00A)sin(24.00st) . (a) What would a graph of the voltage drop across the resistor V(t) versus time look like? (b) What would a plot of V(t) versus I(t) for one period look like? (Hint: If you are not sure, try plotting V(t) versus I(t) using a spreadsheet.)A current of I= 25A is drawn from a 100-V batteryfor 30 seconds. By how much is the chemical energy reduced?Consider a square rod of material with sides of length L = 3.00 cm with a current density of J=J0eaxk=(0.35Am2)e(2.1103m1)xk as shown below. Find the current that passes through the face of the rod.A resistor of an unknown resistance is placed in an insulated container filled with 0.75 kg of water. A voltage source is connected in series with the resistor and a current of 1.2 amps flows through the resistor for 10 minutes. During this time, the temperature of the water is measured and the temperature change during this time is T10.00C . (a) What is the resistance of the resistor? (b) What is the voltage supplied by the power supply?The charge that flows through a point in a wire as a function of time is modeled as q(t)=q0et/T=10.0Cet/5s . (a) What is the initial current through the wire at time t = 0.00 s? (b) Find the current at time t=12T . (c) At what time t will the current be reduced by one-half I=12I0 ?Consider a resistor made from a hollow cylinder of carbon as shown below. The inner radius of the cylinder is Ri= 0.20 mm and the outer radius is R0 = 0.30 mm. The length of the resistor is L = 0.90 mm. The resistivity of the carbon is =3.5105 m. (a) Prove that theresistance perpendicular from the axis is R=2L1n(R0Ri) . (b) What is the resistance?What is the current through a cylindrical wire of radiusR = 0.1 mm if the current density is J=J0Rr where J0=32000Am2?A student uses a 100.00-W, 115.00-V radiant heater to heat the student’s dorm room, dining the hours between sunset and sunrise, 6:00 p.m. to 7:00 a m. (a) What current does the heater operate at? (b) How many electrons move through the heater? (c) What is the resistance of the heater? (d) How much heat was added to the dorm room?A 12-V car battery is used to power a 20.00-W, 12.00-V lamp during the physics club camping trip/star party. The cable to the lamp is 2.00 meters long, 14-gauge copper wire with a charge density of n=9.501028m3 . (a) What is the current draw by the lamp? (b) How long would it take an electron to get from the battery to the lamp?A physics student uses a 115.00-V immersion heater to heat 400.00 grams (almost two cups) of water for herbal tea. During the two minutes it takes the water to heat, the physics student becomes bored and decides to figure our the resistance of the heater. The student starts with the assumption that the water is initially at the temperature of the room Ti=25.00C and reaches Tf=100.00C . The specific heat of the water is c=4180JkgK What is the resistance of the heater?Check Your Understanding If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Wiry do you suppose this happens?Check Your Understanding Some strings of miniature holiday lights are made to short out when a bulb bums out. The device that causes the short is called a shunt, which allows current to flow around the open circuit. A “short” is like putting a piece of wire across the component. The bulbs are usually grouped in series of nine bulbs. If too many bulbs bum out, the shunts eventually open. What causes this?Check Your Understanding Consider the same potential difference (V = 3.00 V) applied to the same three resistors connected in series. Would the equivalent resistance of the series circuit be higher, lower, or equal to the three resistor in parallel? Would the current through the series circuit be higher, lower, or equal to the current provided by the same voltage applied to the parallel circuit? How would the power dissipated by the resistor in series compare to the power dissipated by the resistors in parallel?Check Your Understanding How would you use a river and two waterfalls to model a parallel configuration of two resistors? How does this analogy break down?Check Your Understanding Consider the electrical circuits in your home. Give at least two of circuits that must use a combination of series and parallel circuits to operate efficiently.Check Your Understanding In considering the following schematic and the power supplied and consumed by a circuit, will a voltage source always provide power to the circuit, or can a voltage source consume power?Check Your Understanding When using Kirchhoff’s laws, you need to decide which loops to use and the direction of current flow through each loop. In analyzing the circuit in Example 10.7, the direction of current flow was chosen to be clockwise, from point a to point b. How would the results change if the direction of the current was chosen to be counterclockwise, from point b to point a?Check Your Understanding Digital meters are able to detect smaller currents than analog meters employing galvanometers. How does this explain their ability to measure voltage and current more accurately than analog meters?What effect will the internal resistance of a rechargeable battery have on the energy being used to recharge the battery?A battery with an internal resistance of r and an emf of 10.00 V is connected to a load resistor R = r. As the battery ages, die internal resistance triples. How much is the current through the load resistor reduced?Show that the power dissipated by the load resistor is maximum when the resistance of the load resistor is equal to the internal resistance of the battery.A voltage occurs across an open switch. What is the power dissipated by the open switch?The severity of a shock depends on die magnitude of the current through your body. Would you prefer to be in series or in parallel with a resistance, such as the heating element of a toaster, if you were shocked by it? Explain.Suppose you are doing a physics lab that asks you to put a resistor into a circuit, but all the resistors supplied have a larger resistance than the requested value. How would you connect the available resistances to attempt to get the smaller value asked for?Some light bulbs have three power settings (not including zero), obtained from multiple filaments that are individually switched and wired in parallel. What is the minimum number of filaments needed for three power settings?Can all of die currents going into the junction shown below be positive? Explain.Consider the circuit shown below. Does the analysis of the circuit require Kirchhoff’s method, or can it be redrawn to simplify die circuit? If it is a circuit of series and parallel connections, what is the equivalent resistance?Do batteries in a circuit always supply power to a circuit, or can they absorb power in a circuit? Give an example.What are the advantages and disadvantages of connecting batteries in series? In parallel?Semi-truck or trucks use four large 12-V batteries. The starter systemrequires 24 V, while normal operation of the truck’s other electrical components utilizes 12 V. How could the four batteries be connected to produce 24 V? To produce 12 V? Why is 24 V better than 12 V for starting the truck’s engine (a very heavy load)?What would happen if you placed a voltmeter in series with a component to be tested?What is die basic operation of an ohmmeter as it measures a resistor?Why should you not connect an ammeter directly across a voltage source as shown below?A battery, switch, capacitor, and lamp are connected in series. Describe what happens to the Lamp when the switch is closed.When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit—it is not possible to measure time variations shorter than RC. How would you manipulate ft and C in the circuit to allow the necessary measurements?Why isn’t a short circuit necessarily a shock hazard?We are often advised to not flick electric switches with wet hands, dry your hand first. We are also advised to never throw water on an electric fire. Why?A car battery with a 12-V emf and an internal resistance of 0.050 is being charged with a current of 60 A. Note that in this process, the battery is being charged. (a)What is the potential difference across its terminals? (b)At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted into chemical energy?The label on a battery-powered radio recommends the use of a rechargeable nickel-cadmium cell (nicads), although it has a 1.25-V emf, whereas an alkaline cell has a 1.58-V emf. The radio has a 3.20 resistance.(a) Draw a circuit diagram of the radio and its battery. Now, calculate the power delivered to the radio (b) when using a nicad cells, each having an internal resistance of 0.0400 , and (c) when using an alkaline cell, having an internal resistance of 0.200 . (d) Does this differenceseem significant, considering that the radio's effective resistance is lowered when its volume is aimed up?An automobile starter motor has an equivalent resistance of 0.0500 and is supplied by a 12.0-V battery with a 0.0100- internal resistance, (a) What is thecurrent to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add 0.0900 to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)(a) What is the internal resistance of a voltage source if its terminal potential drops by 2.00 V when the current supplied increases by 5.00 A? (b) Can the emf of the voltage source be found with the information supplied?A person with body resistance between his hands of 10.0k accidentally grasps the terminals of a20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation, (b) If the internal resistance of the power supply is 2000 , what is thecurrent through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low- resistance devices? Explain your reasoning.A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in °C/min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300 kcal/kg • °C, assuming no heat escapes?(a) What is the resistance of a 1.00102 , a 2.50k , and a 4.00k resistor connected in series? (b) In parallel?What are the largest and smallest resistances yon can obtain by connecting a 36.0- , a 50.0- , and a 700- resistor together?An 1800-W toaster, a 1400-W speaker, and a 75-W lamp are plugged into the same outlet in a 15-A fuse and 120-V circuit. (The three devices are in parallel when plugged into the same socket.) (a) What current is drawn by each device? (b) Will this combination blow the 15-A fuse?Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.O-V system. What power would one headlight and the starter consume if connected in series to a 12.O-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)(a) Given a 48.0-V battery and 24.0- and 96.0- resistors,find die current and power for each when connected in series. (b) Repeat when the resistances are in parallel.Referring to the example combining series and parallel circuits and Figure 10.16, calculate in the followingtwo different ways: (a) from the known values of Iand I2 (b) using Ohm’s law for R2 In both parts, explicitlyshow how you follow the steps in the Problem-Solving Strategy: Series and Parallel Resistors.Referring to Figure 10.16, (a) Calculate P3and notehow it compares with P3found in the first two exampleproblems in this module, (b) Find the total power supplied by the source and compare it with the sum of the powers dissipated by the resistors.Refer to Figure 10.17 and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is 0.800 and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligible change in bulb resistance, (b) What power is consumed by the motor?Show that if two resistors R1 and R2 are combined and one is much greater than the other (R1R2) (a) their series resistance is very n early equal to the greater resistance R1 and (b) their parallel resistance is very nearly equal to smaller resistance R2 .Consider the circuit shown below. The terminal voltage of the battery is V = 18.00 V. (a) Find the equivalent resistance of the circuit, (b) Find the current through each resistor, (c) Find the potential drop across each resistor, (d) Find the power dissipated by each resistor, (e) Find the power supplied by the battery.Consider the circuit shown below, (a) Find the voltage across each resistor. (b)What is the power supplied to the circuit and the power dissipated or consumed by the circuit?Consider the circuits shown below, (a) What is the current through each resistor in part (a)? (b) What is the current through each resistor in part (b)? (c) What is the power dissipated or consumed by each circuit? (d) What is the power supplied to each circuit?Consider the circuit shown below. Find V1,I2, and I3.Consider the circuit shown below. Find V1, V2, and R4.Consider the circuit shown below. Find I1, I2,and I3.Consider the circuit shown below, (a) I1,I2,I3,I4,andI5 (b) Find the power supplied by thevoltage sources, (c) Find the power dissipated by the resistors.Consider the circuit shown below. Write the three loop equations for the loops shown.Consider the circuit shown below. Write equations for the three currents in terms of R and V.Consider the circuit shown in the preceding problem. Write equations for the power supplied by the voltage sources and the power dissipated by the resistors in termsA child's electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of 0.0200 inseries with a 1.53-V carbon-zinc dry cell having a 0.100- internal resistance. The load resistance is 10.0 . (a) Draw a circuit diagram of the toy and itsbatteries, (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?Apply the junction rule to Junction b shown below. Is any new information gained by applying the junction rule at e?Apply the loop rule to Loop afedcba in die preceding problem.Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of 0.100 by placing a 1.00-k voltmeter across its terminals (see below), (a) What current flows? (b) Find the terminal voltage, (c) To see how close the measured terminal voltage is to die emf, calculate their ratio.The timing device in an automobile's intermittent wiper system is based on an RC rime constant and utilizes a 0.500F capacitor and a variable resistor. Over whatrange must R be made to vary to achieve time constants from 2.00 to 15.0 s?A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?The duration of a photographic flash is related to an RC time constant, which is 0.100F for a certain camera, (a) If the resistance of the flash lamp is 0.0400 duringdischarge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800 k ?A 2.00- and a 7.50F capacitor can be connected in series or parallel, as can a 25.0- and a 100k resistor.Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.A 500 resistor, an uncharged 1.50F capacitor,and a 6.16-V emf are connected in series, (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator, (a) If the defibrillator has a capacitance of 8.00F , what is theresistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to 6.00102V ?An ECG monitor must have an KC time constant lessthan 1.00102s to be able to measure variations involtage oversmall time intervals, (a) If the resistance of the circuit (duemostly to that of the patient's chest) is 1.00kTwhat is the maximum capacitance of the circuit?(b) Would It be difficult in practice to limit the capacitance to less than the value found in (a)?Using the exact exponential treatment, determine how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-M resistor to 90.0% of its final voltage.If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an EC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one EC constant is acceptable, and given that the flash is driven by a 600F capacitor, what is the resistance in the flash tube?(a) How much power is dissipated in a short circuit of 240-V ac through a resistance of 0.250 ? (b) What current flows?What voltage is involved in a 1.44-kW short circuit through a 0.100- resistance?Find the current through a person and identify the likely effect on her if she touches a 120-V ac source: (a) if she is standing on a rubber mat and offers a total resistance of 300 k (b) if she is standing barefoot on wet grass and has a resistance of only 4000 k .While taking a bath, a person touches the metal case of a radio. The path through the person to the drainpipe and ground has a resistance of 4000- . What is the smallest voltage on the case of the radio that could cause ventricular fibrillation?A man foolishly tries to fish a burning piece of bread from a toaster with a metal butter knife and comes into contact with 120-V ac. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path tire current follows through the person?(a) During surgery, a current as small as 20.0A applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is 300 what is the smallest voltage that poses thisdanger? (b) Does your answer imply that special electrical safetyprecautions are needed?(a) What is the resistance of a 220-V ac short circuit that generates a peak power of 96.8 kW? (b) What would the average power be if the voltage were 120 V ac?A heart defibrillator passes 10.0 A through a patient’s torso for 5.00 ms in an attempt to restore normal beating, (a) How much charge passed? (b) What voltage was applied if 500 J of energy was dissipated? (c) What was the path’s resistance? (d) Find the temperature increase caused in the 8.00 kg of affected tissue.A short circuit in a 120-V appliance cord has a0.500- resistance. Calculate the temperature rise of the2.00 g of surrounding materials, assuming their specific heat capacity is 0.200cal/gC and that it takes 0.0500 sfor a circuit breaker to interrupt the current. Is this likely to be damaging?A circuit contains a D cell battery, a switch, a 20- resistor, and four 20-mF capacitors connected in series, (a) What is the equivalent capacitance of the circuit? (b) What is the fiC time constant? (c) How long before the current decreases to 50% of the initial value once the switch is closed?A circuit contains a D-cell battery, a switch, a 20- resistor, and three 20-mF capacitors. The capacitors are connected in parallel, and the parallel connection of capacitors are connected in series with the switch, the resistor and the battery, (a) What is die equivalent capacitance of the circuit? (b) What is the KC time constant? (c) How long before the current decreases to 50% of the initial value once the switch is closed?Consider the circuit below. The battery has an emf of = 30.00 V and an internal resistance of r = 1,00 . (a) Find the equivalent resistance of the circuit and the current out of the battery. (b) Find the current through each resistor, (c) Find die potential drop across each resistor, (d) Find the power dissipated by each resistor, (e) Find the total power supplied by the batteries.A homemade capacitor is constructed of 2 sheets of aluminum foil with an area of 2.00 square meters, separated by paper, 0.05 mm thick, of the same area and a dielectric constant of 3.7. The homemade capacitor is connected in series with a 100,00- resistor, a switch, and a 6.00-V voltage source, (a) What is the RC time constant of the circuit? (b) What is the initial current through the circuit, when the switch is closed? (c) How long does it take the current to reach one third of its initial value?A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0.05 mm indiameter. The resistivity of the graphite is =1.38102/m . The homemade resistor is place inseries with a switch, a 10.00-mF capacitor and a 0.50-V power source, (a) What is the BC time constant of the circuit? (b) What is the potential drop across the pencil 1.00 s after the switch is closed?The rather simple circuit shown below is known as a voltage divider. The symbol consisting of three horizontal lines is represents “ground” and can be defined as the point where the potential is zero. The voltage divider is widely used in circuits and a single voltage source can be used to provide reduced voltage to a load resistor as shown in the second part of the figure, (a) What is the output voltage Vout of circuit (a) in terms of R1,R2,andVin (b) What is the output voltage Vout of circuit (b) in terms of R1,R2,RLandVinThree 300- resistors areconnect in series with anAAA battery with a rating of 3 AmpHours. (a) How long can the battery supply the resistors with power? (b) If the resistors are connected in parallel, how long can the battery last?Consider a circuit that consists of a real battery with an emf and an internal resistance of r connected to a variable resistor R. (a) In order for the terminal voltage of the battery to be equal to the emf of the battery, what should the resistance of the variable resistor be adjusted to? (b) In older to get the maximum current from the battery, what should the resistance variable resistor be adjusted to? (c) In order for the maximum power output of the battery to be reached, what should the resistance of the variable resistor be set to?Consider the circuit shown below. What is the energy Stored in each capacitor after the switch has been closed for a very long time?Consider a circuit consisting of a battery with an emf l and an internal resistance of r connected in series with a resistor R and a capacitor C. Show that the total energy supplied by the battery while charging the battery is equal to l 2 C.Consider the circuit shown below. The terminal voltages of the batteries are shown, (a) Find the equivalent resistance of the circuit and the current out of the battery, (b) Find the current through each resistor, (c) Find the potential drop across each resistor, (d) Find the power dissipated by each resistor, (e) Find the total power supplied by the batteries.Consider the circuit shown below. (a) What is the terminal voltage of the battery? (b) What is the potential drop across resistor R2?Consider the circuit shown below. (a)Determine the equivalent resistance and the current from the battery with switch S1 open, (b) Determine the equivalent resistance and the current from the battery with switch S1 closed.Two resistors, one having a resistance of 145 , are connected in parallel to produce a total resistance of 150 . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Two resistors, one having a resistance of 900k are connected in series to produce a total resistance of 0.500M . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Apply the junction rule at point G shown below.Apply the loop rule to Loop akledcba in the preceding problem.Find the currants flowing in the circuit in the preceding problem. Explicitly show how you follow the steps in the Problem-Solving Strategy: Series and Parallel Resistors.Consider the circuit shown below, (a) Find the current through each resistor, (b) Check the calculations by analyzing the power in the circuit.A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance, (d) What is the resistance of the lamp? (Since average values are given for some quantities, the shape of the pulse profile is not needed.)A 160F capacitor charged to 450 V is dischargedthrough a 31.2k resistor, (a) Find the time constant.(b)Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is 1.67kJ/kg °C,noting that most of the thermal energy is retained in the short time of the discharge, (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?Some camera flashes use flash tubes that requite a high voltage. They obtain a high voltage by charging capacitors in parallel and then internally changing the connections of the capacitors to place diem in series. Consider a circuit that uses four AAA batteries connected in series to charge six 10-mF capacitors through an equivalent resistance of 100 . The connections are thenswitched internally to place the capacitors in series. The capacitors discharge through a lamp with a resistance of 100 . (a) What is the RC time constant and the initialcurrent out of the batteries while they are connected in parallel? (b) How long does it take for the capacitors to charge to 90% of the terminal voltages of the batteries? (c) What is the RC time constant and the initial current of the capacitors connected in series assuming it discharges at 90% of full charge? (d) How long does it rake the current to decrease to 10% of the initial value?Consider the circuit shown below. Each battery has an emf of 1.50 V and an internal resistance of 1.00 . (a) What is the current through the external resistor, which has a resistance of 10.00 ohms? (b) What is the terminal voltage of each battery?Analog meters use a galvanometer, which essentially consists of a coil of wire with a small resistance and a pointer with a scale attached. When current runs through the coil, the pointer turns; die amount the pointer turns is proportional to the amount of current running through the coil. Galvanometers can be used to make an ammeter if a resistor is placed in parallel with the galvanometer. Consider a galvanometer that has a resistance of 25.00and gives a full scale reading when a 50A current runs through it. The galvanometer is to be used to make an ammeter that has a full scale reading of 10.00 A, as shown below. Recall that an ammeter is connected in series with the circuit of interest, so all 10 A must tun through the meter, (a) What is the current through the parallel resistor in the meter? (b) What is the voltage across the parallel resistor? (c) What is the resistance of the parallel resistor?Analog meters use a galvanometer, which essentially consists of a coil of wire with a small resistance and a pointer with a scale attached. When current runs through the coil, the point turns; the amount the pointer turns is proportional to the amount of current running through the coil. Galvanometers can be used to make a voltmeter if a resistor is placed in series with the galvanometer. Consider a galvanometer that has a resistance of 25.00 and gives a full scale reading when a 50A current runs through it. The galvanometer is to be used to make an voltmeter that has a full scale reading of 10.00 V, as shown below. Recall that a voltmeter is connected in parallel with the component of interest, so the meter must have a high resistance or it will change the current running through the component, (a) What is the potential drop across the series resistor in the meter? (b) What is the resistance of the parallel resistor? Av = lo.oo vConsider the circuit shown below. Find I1, V1, I2, and V3 V1=?Consider the circuit below.(a) What is the RC time constant of the circuit? (b) What is the initial current in the circuit once the switch is closed? (c) How much time passes between the instant die switch is closed and the time the current has reached half of the initial current?Consider the circuit below, (a) What is the initial current through resistor R2? when the switch is closed? (b) What is die current through resistor R2 when the capacitor is fully charged, long after die switch is closed? (c) What happens if the switch is opened after it has been closed for some rime? (d) If the switch has been closed for a time period long enough for the capacitor to become fully charged, and then the switch is opened, how long before the current through resistor R1 reaches half of its initial value?Consider the infinitely long chain of resistors shown below. What is the resistance between terminals a and b?Consider the circuit below. The capacitor has a capacitance of 10 mF. The switch is closed and after a long time the capacitor is fully charged, (a) What is the current through each resistor a long time after the switch is closed? (b) What is the voltage across each resistor a long rime after the switch is closed? (c) What is the voltage across the capacitor a long time after the switch is closed? (d) What is the charge on the capacitor a long time after the switch is closed? (e) The switch is then opened. The capacitor discharges through the resistors. How long from the time before the current drops to one fifth of the initial value?A 120-V immersion heater consists of a coil of wire that is placed in a cup to boil the water. The heater can boil one cup of 20.00°C water in 180.00 seconds. You buy one to use in your dorm room, but you are worried that you will overload the circuit and nip the 15.00-A, 120-V circuit breaker, which supplies your dorm room. In your dorm room, you have four 100.00-W incandescent lamps and a 1500.00-W space heater, (a) What is the power rating of the immersion heater? (b) Will it trip the breaker when everything is turned on? (c) If it you replace the incandescent bulbs with 18.00-W LED, will the breaker nip when everything is turned on?Find the resistance that must be placed in series with a 25.0- galvanometer having a 50.0A sensitivity (thesame as die one discussed in the text) to allow it to be used as a voltmeter with a 3000-V full-scale reading. Include a circuit diagram with your solution.Find the resistance that must be placed in parallel with a 60.0- galvanometer having a 1.00-mA sensitivity (the same as die one discussed in the text) to allow it to be used as an ammeter with a 25.0-A full-scale reading. Include a circuit diagram with your solution.Check Your Understanding Repeat the previous problem with the magnetic field in the x-direction rather than in the z-direction. Check your answers with RHR-1.Check Your Understanding A uniform magnetic field of magnitude 1.5 T is directed horizontally from west to east, (a) What is the magnetic force on a proton at the instant when it is moving vertically downward in the field with a speed of 4 x 107 m/s? (b) Compare this force with the weight w of a proton.Check Your Understanding A straight, flexible length of copper wire is immersed in a magnetic field that is directed into the page, (a) If the wire's arrent runs in the +x-direction, which way will the wire bend? (b) Which way will the wire bend if the current nms in the -x-direction?Check Your Understanding In what orientation would a magnetic dipole have to be to produce (a) a maximum torque in a magnetic field? (b) A maximum energy of the dipole?Check Your Understanding A Hall people consists of a copper strip, n=8.51028 electrons per cubic meter, which is 2.0 cm wide and 0.10 cm thick. What is the magnetic held when I = 50 A and the Hall potential is (a) 4.0µV and (b) 60µV?Check Your Understanding A cyclotron is to be designed to accelerate protons to kinetic energies of 20 Mev using a magnetic field of 2.0 T. What is the required radius of the cyclotron?Discuss the similarities and differences between the electrical force on a charge and the magnetic force on a charge.(a) Is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) Is it possible for the electric force on a charge moving in an electric field to be zero? (c) Is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?At a given instant, an electron and a proton are moving with the same velocity in a constant magnetic field. Compare the magnetic forces on these particles. Compare their accelerations.Does increasing the magnitude of a uniform magnetic field through which a charge is traveling necessarily mean increasing the magnetic force on the charge? Does changing the direction of the field necessarily mean a change in the force on the charge?An electron passes through a magnetic field without being deflected. What do you conclude about the magnetic field?If a charged particle moves in a straight line, can you conclude that there is no magnetic field present?How could you determine which pole of an electromagnet is north and which pole is south?Describe the error that results from accidently using your left rather than your right hand when determining the direction of a magnetic force.Considering the magnetic force law, are the velocity and magnetic field always perpendicular? Are the force and velocity always perpendicular? What about the force and magnetic field?Why can a nearby magnet distort a cathode ray tube television picture?A magnetic field exerts a force on the moving electrons in a current carrying wire. What exerts the force on a wire?There are regions where the magnetic field of earth is almost perpendicular to the surface of Earth. What difficulty does this cause in the use of a compass?Hall potentials are much larger for poor conductors than for good conductors. Why?Describe the primary function of the electric field and the magnetic field in a cyclotron.What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases?Repeat previous exercise for a negative charge.What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases, assuming it moves perpendicular to B?Repeat previous exercise for a positive charge.What is the direction of the magnetic field that produces the magnetic force on a positive charge as shown in each of the three cases, assuming B is perpendicular to v?Repeat previous exercise for a negative charge.(a) Aircraft sometimes acquire small static charges, Suppose a supersonic jet has a 0.500C charge and flies due west at a speed of 660.m/s over Earth’s south magnetic pole, where the 8.00105T -T magnetic field points straight down into the ground, What are the direction and the magnitude of the magnetic force on the plane? fb) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect,(a) A cosmic ray proton moving toward Earth at 5.00107 m/s experiences a magnetic force of 1.70l0l6 N. What is the strength of the magnetic field if there is a 45 angle between it and the proton’s velocity? (b) Is the value obtained in part a. consistent with the known strength of Earth's magnetic field on its surface? Discuss.An electron moving at 4.00103 m/s in a 1.25-T magnetic field experiences a magnetic force of 1.401016 N. What angle does the velocity of the electron make with the magnetic field? There are two answers.(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.001012N. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in Earth's field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by comparing it with typical static electricity' and noting that static is often absent,A cosmic-ray electron moves at 7.5 × 106 m/sinches perpendicular to Earth’s magnetic field at an altitude queer the field strength is 1.0 × 105T. What is the radius of the circular path the electron follows?(a) Viewers of Star Trek have heard of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy swore is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then exact them as needed Antimatter annihilates normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at 5.0 × l0 m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?(a) An oxygen-16 ion with a mass of 2.661026 kg travels at 5.0106 m/s perpendicular to a 1.20-T magnetic field. which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an election? (c) Discuss why the ratio found in (b) should be an integer.An electron in a TV CRT moves with a speed of 6.0107 m/s, in a direction perpendicular to Earth's field, which has a strength of 5.0105 T. (a) What strength electric field must be applied perpendicular to the Earth’s field to make the election moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a collection,)(a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if tlie proton had the same speed as the election? (c) What would the radius be if the proton had tlie same kinetic energy' as die electron? (d) The same momentum?(a) What voltage will accelerate electrons to a speed of 6.00107 m/s? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with tire radius of curvature of an electron accelerated through the same potential.An alpha-particle ( m=6.641027kg , q=3.21019C ) travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. (a) What is the speed of the particle? (b) What is the kinetic energy in electron-volts? (c) Through what potential difference must the particle be accelerated in order to give it this kinetic energy?A particle of charge q and mass m is accelerated from rest through a potential difference V, after silica it encounters a uniform magnetic field B. If the particle moves in a plane perpendicular to B, shaft is the radius of its circular orbit?What is the direction of the magnetic force on the current in each of the six cases?What is the direction of a current that experiences the magnetic force shown in each of the three cases, assuming the current runs perpendicular to B ?What is the direction of the magnetic field that produces the magnetic force shown on the currents in each of the three cases, assuming B is perpendicular to I?(a) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to Earth’s 3.0105field? (b) What is the direction of the force if the current is straight up and Earth’s field direction is due north, parallel to the ground?(a) A dc power line for a light-rail system caries 1000 A at an angle of 30.0 to Earth's 5.0105 T field, What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in tire field. What is the average field strength?(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?(a) What is the maximum torque on a 150-tum square loop of wire 13.0 cm oil a side that carries a 50.0-A current in a 1.60-T field? (b) Wliat is the torque when d is 10.9s?Find the current through a loop needed to create a maximum torque of 9.0 N.m. The loop has 50 square turns that are 15.0 cm on a side and is in a uniform 0.800-T magnetic field.Calculate the magnetic field strength needed on a 200-tum square loop 20.0 cm on a side to create a maximum torque of 300 N. m if the loop is carrying 25.0 A.Since the equation for torque on a current-carrying loop is =NIABsin, the units of N .m must equal units of A. m2T. Verify this., (a) At what angle 0 is tlie torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c) 10.0% of maximum?A proton has a magnetic field due to its spin. The field is similar to that created by a circular current loop 0.651015m in radius with a current of 1.05104A . Find the maximum torque on a proton in a 2.50-T field. (This is a significant torque on a small particle.)(a) A 200-turn circular loop of radius SO.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. Earth’s field here is due north, parallel to the ground, with a strength of 3.0105T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?Repeat the previous problem, but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where Earth’s field is north, but at an angle 45.0° below the horizontal and with a strength of 6.0105T.A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be 1.5103V/m (a) What is the drift speed of the conduction electrons? (b) Assuming that n =8.01028 elections per cubic meter and that the cross-sectional area of the strip is 5.0106m2 , calculate the current in the ship, (c) What is the Hall coefficient 1/nq?The cross-sectional dimensions of the copper strip shown are 2.0 cm by 2.0 mm. The strip carries a current of 100 A, and it is placed in a magnetic field of magnitude B = 1.5 T. What are the value and polarity of the Hall potential in the copper strip?The magnitudes of the electric and magnetic fields in a velocity selector are 1.8105V/m and 0.080 T, respectively, (a) What speed must a proton have to pass through tire selector? (b) Also calculate the speeds required for an alpha-particle and a singly ionized SO atom to pass through the selector.A charged particle moves through a velocity selector at constant velocity. In tire selector, E=1.0104NC and B = 0.250 T. When the electric field is turned off, tire charged particle travels in a circular path of radius 3.33 mm. Determine the charge-to-mass ratio of the particle.A Hall probe gives a reading of 1.5V for a current of 2 A when it is placed in a magnetic field of 1 T, What is tire magnetic field in a region where tire reading is 2V for 1.7 A of current?A physicist is designing a cyclotron to accelerate protons to one-tenth the speed of light. The magnetic field will have a strength of 1.5 T. Determine [a) the rotational period of the circulating protons and (b) the maximum radius of the protons' orbit.The strengths of the fields in the velocity selector of a Bainbridge mass spectrometer are B = 0.500 T and E=1.2105 Van, and tire strength of the magnetic field that separates the ions is Bo=0.750 T. A stream of singly charged Li ions is found to bend in a circular arc of radius 2.32 cm. What is the mass of the Li ions?The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What Is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of tire voltage source used to accelerate the piotons? (e) Repeat tire calculations for alpha-particles.A mass spectrometer is being used to separate common oxygen- 16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice s deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.661026kg, , and they are singly charged and travel at 5.00106m/s in a 1.20-T magnetic field. What is the separation between their path when they hit a target after travet5ing a semicircle?(a) Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is used as reactor fuel.) The masses of the ions are 3.901025kgand3.9510-25kg.respectively, and they travel at 3.0105m/sina0.250Tfield What is the separation between their paths 1en they hit a target after traversing a semicircle? (b) Discuss whether this distance between their paths seems to be big from uranium-238. enough to be practical in the separation of uranium-235Calculate the magnetic force on a hypothetical particle of charge 1.010l9C moving with a velocity of 6.0104im/s in a magnetic field of 1.2kT.Repeat the previous problem with a new magnetic field of (0.4i+1.2k)T .An electron is projected into a uniform magnetic field (0.5i+0.8k)T with a velocity of (3.0i+4.0j)106 m/s . What is the magnetic force on the electron?The mass and chaise of a water droplet are 1.0104g and 2.0108C , respectively. If the droplet is given an initial horizontal velocity of 5.0105im/s . what magnetic field will keep it moving in this direction? Why must gravity be considered here?Four different proton velocities are given. For each case, determine the magnetic force on the proton in terms of e, v0and B0.An electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 an apart and kept at a potential difference of 300 V. What is the strength of the uniform magnetic field B that will allow the electron to travel undeflected through the plates? Assume E and B are perpendicular.An alpha-particle (m=6.641027kg,q=3.21019C) moving with a velocity v=(2.0i4.0k)106m/s enters a region where E=(5.0i2.0j)104V/m and B=(1.0i+40.0k)102T . What is the initial force on it?An electron moving with a velocity v=(4.0i+3.0j+2.0k)106m/s enters a region where there is a uniform electric field and a uniform magnetic field. The magnetic field is given by v=(1.0i2.0j+4.0k)102T. If the electron travels through a region without being deflected, what is the electric field?At a particular instant an electron is traveling west to east with a kinetic energy of 10 keV. Earth's magnetic field has a horizontal component of 1.8105 T north and a vertical component of 5.0105 T down. (a) What is the path of the election? (b) What is the radius of curvature of the path?Repeat the calculations of the previous problem for a proton with the same kinetic energy.What magnetic field is required in order to confine a proton moving with a speed of 4.0 × 106 m/s to a circular orbit of radius 10 cm?An electron and a proton move with the same speed in a plane perpendicular to a uniform magnetic field. Compare the radii and periods of their orbits.A proton and an alpha-particle have the same kinetic energy and both move in a plane perpendicular to a uniform magnetic field. Compare the pentodes of their orbits.A singly charged ion takes 2.0 × 10-3 s to complete eaglet revolutions in a uniform magnetic field of magnitude 2.0102 T. What is the mass of the ion?A particle moving downward at a speed of 6.0106 m/s enters a uniform magnetic field that is horizontal and directed from east to west. (a) If the particle is deflected initially to the north in a circular arc, is its charge positive or negative? (b) If B = 0.25 T and the charge-to-mass ratio (q/m) of the particle is 40107 C/kg. what is ±e radius at the path? (c) What is the speed of the particle after c has moved in the field for 1.0105s ? for 2.0s?, A proton, deuteron, and an alpha-particle ae all accelerated from rest through the same potential difference. They then enter the same magnetic field, moving perpendicular to it. Compute the ratios of the radii of their circular paths. Assume that md= 2wmp and ma= 4mp.A singly charged ion is moving in a uniform magnetic field of 7.5102 T completes 10 revolutions in 3.47104 s. Identify the ion.Two particles have the same linear momentum, but particle A has four times the charge of particle B. If both particles move in a plane perpendicular to a uniform magnetic field, what is the ratio RA/RB of the radii of their circular orbits?A uniform magnetic field of magnitude is directed parallel to the z-axis. A proton enters the field with a velocity v=(4j+3k)106m/s and travels in a helical path with a radius of 5.0 cm. (a) What is the value of B? (b) What is the time required for one trip around the helix? (c) Where is the proton 5.0107s after entering the field?An electron moving along the +x -axis at 5.0106m/s enters a magnetic field that makes a 75° angle with the x-axis of magnitude 0,20 T. Calculate the (a) pitch and (b) radius of tire trajectory.(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle of GOP with Earth's 5.5105T field. What is the current when tire wire experiences a farce of 7.010N? (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75-T field, what force is exerted on this segment of wire?(a)What is the angle between a wire carrying an 8.00-A current and the 1.20-T field It Is in if 50.0 cm of the wire experiences a magnetic force of 2.40 N? (b) What is the force on the wire If It Is rotated to make an angle of 90° with the field?A 1.0-rn-long segment of wire lies along the x-axis and carries a current of 2.0 A in the positive x-direction. Around the sire Is the magnetic field of (3.0i4.0k)103T. Find the magnetic force on this segment.A 5.0-m section of a long, straight wire carries a current of 10 A while in a uniform magnetic field of magnitude 8.0103T . Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is (a) 45°; (b) 90°; (C) 0°; or (d) 180°.An electromagnet produces a magnetic field of magnitude 1.5 T throughout a cylindrical region of radius 6.0 cm. A straight wire carrying a current of 25 A passes through the field as shown in the accompanying figure. What is the magnetic force on the wire?The current loop shown in the accompanying figure lies in the plane of the page, as does the magnetic field. Determine the net force and the net torque on the loop if I=10and B=1.5T .A circular coil of radius 5.0 cm is wound with five turns and carries a current of 5.0 A. If the coil is placed in a uniform magnetic field of strength 5.0 T, what is the maximum torque on it?Acircularcoiofwireofradius5.Ocmhas2Otums and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil. (a) What is the magnetic dipole moment of the coil? (b) What is the torque on the coil?A current-carrying coil in a magnetic field experiences a torque that is 75% of the maximum possible torque. What is the angle between the magnetic field and the normal to the plane of the coil?A 40-cm by 6.0-cm rectangular current loop carries a current of 10 A. What Is the magnetic dipole moment of the loop?A circular coil with 200 turns Las a radius of 2.0 cm. (a) What current through tire coil results in a magnetic dipole moment of 3.0 Am2? (b) What is the maximum torque that the coil will experience in a uniform field of strength 5.0102 ? (c) If tire angle between and B is 45°, what is the magnitude of tire torque on the coil? (d) What is the magnetic potential energy of coil for this orientation?The current through a circular wire loop of radius 10 cm is 5.0 A. (a) Calculate themagnetic dipole moment of the loop. (b) What is the torque on the loop if it is in a uniform 0.20-T magnetic field such that p and B are directed at 300 to each other? (C) For this position, what is the potential energy of the dipole?A wire of length 1.0 m is wound into a single-turn planar loop. The loop carries a current of 5.0 A, and it is placed in a uniform magnetic field of strength 0.25 T. (a) What is the maximum torque that the loop will experience if it is square? (b) If it is circular? (c) At what angle relative to B would die normal to the circular coil have to be oriented so that the torque on it would be the same as the maximum torque on the square coil?Consider an electron rotating in a circular orbit of radius r. Show that the magnitudes of the magnetic dipole moment and the angular momentum L of the electron are related by: = L=e2mThe Hall effect is to be used to find the sign of charge carries in a semiconductor sample. The probe is placed between Own poles of a magnet so that magnetic field Is pointed up. A current is passed through a rectangular sample placed horizizontally. As current is passed through the sample in the east direction, the north side of the sample is found to be at a higher potential than the south side. Decide if the number density of charge carriers is positively or negatively charged.The density of charge carriers far copper is 8.471028 electrons per cubic meter. What will be the Hall voltage reading from a probe made up of 3cm2cm1cm ( (LWT) ) copper plate when a current of 1.5 A is passed through it in a magnetic field of 2.5 T perpendicular to the 3cm2cm .