Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 29, Problem 53PQ
To determine
Find the time constant of discharging a node.
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The figure displays two circuits with a charged capacitor that is to be discharged through a resistor when a switch is closed. In figure (a) below, R1 = 21.9 Ω and C1 = 5.26 μF. In figure (b) below, R2 = 10.9 Ω and C2 = 8.08 μF. The ratio of the initial charges on the two capacitors is q02/q01 = 1.64. At time t = 0, both switches are closed. At what time t do the two capacitors have the same charge?
A 1000.0 Ω resistor is placed in series with two 100.0 μF capacitors in series and the combination is connected to a battery. Determine the time constant of the circuit.
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one time constant after the switch is closed? Express your answer in units volts using one decimal place.
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Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 29.1 - What are the SI units of ?Ch. 29.1 - Prob. 29.2CECh. 29.2 - Prob. 29.3CECh. 29.4 - Prob. 29.5CECh. 29.4 - Prob. 29.6CECh. 29.5 - Prob. 29.7CECh. 29 - Study the symbols in Table 29.2. Then, without...Ch. 29 - Prob. 2PQCh. 29 - Prob. 3PQCh. 29 - Suppose you need to measure the potential...
Ch. 29 - Prob. 5PQCh. 29 - Prob. 6PQCh. 29 - A real battery (modeled as an ideal emf device in...Ch. 29 - Prob. 8PQCh. 29 - Two circuits made up of identical ideal emf...Ch. 29 - Prob. 10PQCh. 29 - Prob. 11PQCh. 29 - Prob. 12PQCh. 29 - Eight real batteries, each with an emf of 5.00 V...Ch. 29 - Prob. 14PQCh. 29 - Prob. 15PQCh. 29 - Prob. 16PQCh. 29 - Prob. 17PQCh. 29 - Prob. 18PQCh. 29 - Prob. 19PQCh. 29 - An ideal emf device with emf is connected to two...Ch. 29 - Prob. 21PQCh. 29 - Prob. 22PQCh. 29 - Prob. 23PQCh. 29 - Prob. 24PQCh. 29 - Prob. 25PQCh. 29 - Prob. 26PQCh. 29 - Determine the currents through the resistors R2,...Ch. 29 - The emf devices in the circuits shown in Figure...Ch. 29 - Prob. 29PQCh. 29 - Prob. 30PQCh. 29 - Prob. 31PQCh. 29 - Prob. 32PQCh. 29 - Prob. 33PQCh. 29 - Prob. 34PQCh. 29 - A Figure P29.35 shows a combination of six...Ch. 29 - A Each resistor shown in Figure P29.36 has...Ch. 29 - Each resistor shown in Figure P29.36 has a...Ch. 29 - Prob. 38PQCh. 29 - Prob. 39PQCh. 29 - The emf in Figure P29.40 is 4.54 V. The...Ch. 29 - Figure P29.41 shows three resistors (R1 = 14.0 ,...Ch. 29 - Figure P29.42 shows five resistors and two...Ch. 29 - The emfs in Figure P29.43 are 1 = 6.00 V and 2 =...Ch. 29 - Prob. 44PQCh. 29 - Figure P29.45 shows five resistors connected...Ch. 29 - Figure P29.46 shows a circuit with a 12.0-V...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Two ideal emf devices are connected to a set of...Ch. 29 - Three resistors with resistances R1 = R/2 and R2 =...Ch. 29 - Prob. 51PQCh. 29 - Prob. 52PQCh. 29 - Prob. 53PQCh. 29 - Prob. 55PQCh. 29 - At time t = 0, an RC circuit consists of a 12.0-V...Ch. 29 - A 210.0- resistor and an initially uncharged...Ch. 29 - Prob. 58PQCh. 29 - A real battery with internal resistance 0.500 and...Ch. 29 - Figure P29.60 shows a simple RC circuit with a...Ch. 29 - Prob. 61PQCh. 29 - Prob. 62PQCh. 29 - Prob. 63PQCh. 29 - Ralph has three resistors, R1, R2, and R3,...Ch. 29 - Prob. 65PQCh. 29 - An ideal emf device is connected to a set of...Ch. 29 - Prob. 67PQCh. 29 - An ideal emf device (24.0 V) is connected to a set...Ch. 29 - Prob. 69PQCh. 29 - What is the equivalent resistance between points a...Ch. 29 - A capacitor with initial charge Q0 is connected...Ch. 29 - Prob. 73PQCh. 29 - Prob. 74PQCh. 29 - Prob. 75PQCh. 29 - Prob. 76PQCh. 29 - Figure P29.77 shows a circuit with two batteries...Ch. 29 - In the RC circuit shown in Figure P29.78, an ideal...Ch. 29 - Prob. 79PQCh. 29 - Calculate the equivalent resistance between points...Ch. 29 - In Figure P29.81, N real batteries, each with an...Ch. 29 - Prob. 82PQCh. 29 - Prob. 83PQCh. 29 - Prob. 84PQCh. 29 - Figure P29.84 shows a circuit that consists of two...Ch. 29 - Prob. 86PQCh. 29 - Prob. 87PQCh. 29 - Prob. 88PQCh. 29 - Prob. 89PQCh. 29 - Prob. 90PQCh. 29 - Prob. 91PQCh. 29 - Prob. 92PQCh. 29 - Prob. 93PQCh. 29 - Prob. 94PQCh. 29 - Prob. 95PQ
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- A capacitor with initial charge Q0 is connected across a resistor R at time t = 0. The separation between the plates of the capacitor changes as d = d0/(1 + t) for 0 t 1 s. Find an expression for the voltage drop across the capacitor as a function of time.arrow_forwardThe circuit shown in Figure P28.78 is set up in the laboratory to measure an unknown capacitance C in series with a resistance R = 10.0 M powered by a battery whose emf is 6.19 V. The data given in the table are the measured voltages across the capacitor as a function of lime, where t = 0 represents the instant at which the switch is thrown to position b. (a) Construct a graph of In (/v) versus I and perform a linear least-squares fit to the data, (b) From the slope of your graph, obtain a value for the time constant of the circuit and a value for the capacitance. v(V) t(s) In (/v) 6.19 0 5.56 4.87 4.93 11.1 4.34 19.4 3.72 30.8 3.09 46.6 2.47 67.3 1.83 102.2arrow_forwardThe circuit in Figure P21.59 has been connected for a long time. (a) What is the potential difference across the capacitor? (b) If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?arrow_forward
- (a) Determine the equilibrium charge on the capacitor in the circuit of Figure P27.46 as a function of R. (b) Evaluate the charge when R = 10.0 . (c) Can the charge on the capacitor be zero? If so, for what value of R? (d) What is the maximum possible magnitude of the charge on the capacitor? For what value of R is it achieved? (c) Is it experimentally meaningful to take R = ? Explain your answer. If so, what charge magnitude does it imply? Figure P27.46arrow_forwardThe emf source, ɛ=4.5 V, of the circuit shown in the figure has negligible internal resistance. The resistors have resistances R1=2 Q and R2=4.7 Q. The capacitor has a capacitance C=4.9 µF. Determine the time constant t, in units of microseconds, for charging the capacitor. What is the charge Q on the capacitor in units of microcoulomb?arrow_forwardAn RC circuit consisting of an uncharged capacitor (C = 1.0 µF) in series with a resistor (R = 2800 Ω), a battery (ε = 6.0 V) and an open switch. What is the time needed after the switch is closed for the voltage across the capacitor to reach 4.1 V? Group of answer choices 3.0 ms 4.8 ms 1.2 ms 2.8 msarrow_forward
- You have a circuit with a battery hooked up to 2 capacitors in Parallel. The battery has a voltage of 4.3 V. The capacitors have a value of C1 = 40.0 µF and C2 = 25.0 u F. While finding the actual voltage is very helpful, it's hard to use this as a prediction because not all batteries are the same. So one way to look at this is a percentage. Even if the voltage of the battery is different, the percentage of the voltage should be the same regardless. Find the percentage of the battery voltage that is across capacitor 1. To find percentages: • Find the voltage across the specific capacitor just like previously Divide this voltage by the voltage of the battery • Multiply your answer by 100 to turn it into a percent Your answer should include: 2 Decimal Places Correct SI Units Your Answer:arrow_forwardFour resistors are combined in a circuit along with a battery and an ammeter. The values of the resistors are R1 = 5 Ω, R2 = 5 Ω, R3 = 10 Ω, and R4 = 20 Ω. If the current through the ammeter is 2.6 A and the voltage of the battery is 50 V, what is the configuration of the resistors?arrow_forwardThree capacitors are connected in series in a circuit and the individual capacitance values are 2.4 µF, 5.6 µF, and 3.5 µF. Determine the equivalent capacitance for the circuit.arrow_forward
- In the circuit below the value of the resistance 14 Ω and the value of the capacitance is 2.0 µF. The voltage of the battery is 50 V. The capacitor is initially uncharged. Sometime after the switch is closed, the current in the circuit is measured to be 1.1 A. At this time, what is the charge on the capacitor, in µC? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.arrow_forwardA capacitor is charged with a total charge of q = 8.7E-05 C. The capacitor is wired in series with a resistor, R = 5 Ω. Part (a) Input an expression for the time constant, τ, of this circuit using the variables provided and C for capacitance. τ = Part (b) What is the value of the time constant in s if the capacitor has capacitance of 1.0 μF? τ = Part (c) How long will it take the capacitor to discharge half of its charge in seconds? t =arrow_forwardThe initial voltage across the capacitor at t = 0 in the circuit shown in Figure is 8 V. 4 kn 3 1 kn 2 kn R5 1 kl Vo =8V 2 kl a. Write a node equation at node 1 by summing the currents away from node 1. Notice that the voltage at node 3 is given by v3(t) = v(t). b. Write a node equation at node 2 by summing the currents away from node 2. Notice that the voltage at node 3 is given by v3(!) = v(t). c. Solve the two node equations from (a) and (b) to express v,(t) as a function of v(t), and va(t) as a function of v(t). d. Write a node equation at node 3 by summing the currents away from node 3. Use the results from (c) to simplify the equation as a first- order differential equation of v(t). e. Solve the differential equation to find the voltage v(t), t 2 0, across the capacitor and plot v(t).arrow_forward
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