Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Textbook Question
Chapter 25, Problem 78P
A parallel-plate capacitor has plates of area 10cm2 separated by a 0.10-nun layer of glass insulation with resistivity ρ = 1.2 × 1013 Ω·m and dielectric constant κ = 5.6. Because of the finite resistivity, charge leaks through the insulation, (a) How can such a leaky capacitor be represented in a circuit diagram? (b) Find the time constant for this capacitor to discharge through its insulation, and show that it depends only on the properties of the insulating material and not on its dimensions.
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Students have asked these similar questions
A parallel-plate capacitor of plate area 6.7 cm2 and plate separation 4.7 cm has a dielectric
constant of 2.5. The capacitor is put in series with a 9.5 k2 resistor and a battery of EMF
6 V, and allowed to fully charge.
a) Determine the time constant of the circuit.
b) Show that the SI base unit of the time constant of the circuit is seconds. Ensure you
include any relevant equations and/or definitions in your working.
(c) What is the initial current in the circuit, in mA, when charging begins?
d) What is the final charge on the capacitor once it is fully energised?
(e) The potential difference, V, across the capacitor, at a time t after charging begins is
given ay V = VMAX[1 – e where VMAX is the final potential difference across the
capacitor once charging is complete and T is the time constant of the circuit. Show that
the potential difference across the capacitor is equal to 50% of its maximum, 2.08 ns
after charging begins.
A resistor with value 2-ohm is connected in series with a capacitor that has a capacitance rating of 1.5 F. If the capacitor is initially uncharged, (a) What is the time constant? and (b) What fraction of the final charge is on the plates at time t = 14 s?
A 10-9-F capacitor (1 nanofarad) is charged to 100 V and then disconnected. One can model the charge leakage of the capacitor with a RC circuit with no voltage source and the
resistance of the air between the capacitor plates. On a cold dry day, the resistance of the air gap is 5x 1013 2; on a humid day, the resistance is 6x 10° 2. How long will it take the
capacitor voltage to dissipate to half its original value on each day?
On the dry day, it will take seconds.
(Use scientific notation. Round to three decimal places as needed.)
Chapter 25 Solutions
Essential University Physics (3rd Edition)
Ch. 25.1 - The figure shows three circuits. Which are...Ch. 25.2 - Rank front highest to lowest the voltages across...Ch. 25.2 - The figure shows all four possible combinations of...Ch. 25.2 - The figure shows a circuit with three identical...Ch. 25.3 - Which circuit(s) cannot be analyzed using series...Ch. 25.4 - All resistors in the figure have the same value...Ch. 25.5 - A capacitor is charged to 12 V and then connected...Ch. 25 - Are household electrical outlets connected in...Ch. 25 - All the resistors in Fig. 25.24 have the same...Ch. 25 - Can the voltage across a batterys terminals differ...
Ch. 25 - Can the voltage across a batterys terminals he...Ch. 25 - In some cities, streetlights are wired in such a...Ch. 25 - When the switch in Fig. 25.25 is open, whats the...Ch. 25 - Two identical resistors in series dissipate equal...Ch. 25 - When a large electric load such as a washing...Ch. 25 - How would you connect a pair of equal resistors...Ch. 25 - You have a battery whose voltage and internal...Ch. 25 - A student whos confused about voltage and current...Ch. 25 - A student whos confused about voltage and current...Ch. 25 - Sketch a circuit diagram for a circuit that...Ch. 25 - Sketch a diagram for a circuit consisting of two...Ch. 25 - Resistors R1 and R2 are in series, and the series...Ch. 25 - Whats the emf of a battery that delivers 27 J of...Ch. 25 - A 1.5-V battery stores 4.5 kJ of energy. How long...Ch. 25 - If you accidentally leave your car headlights...Ch. 25 - A 47-k resistor and a 39-k resistor are in...Ch. 25 - What resistance should you place in parallel with...Ch. 25 - A defective starter motor draws 300 A from a cars...Ch. 25 - Find the internal resistance of the battery in...Ch. 25 - When a 9-V battery is temporarily short-circuited,...Ch. 25 - You have a 1.0-, a 2.0-, and a 3.0- resistor. What...Ch. 25 - Find all three currents in the circuit of Fig....Ch. 25 - Prob. 26ECh. 25 - Find all three currents in the circuit of Fig....Ch. 25 - Prob. 28ECh. 25 - An ammeter with 100- resistance is inserted in the...Ch. 25 - A new mechanic foolishly connects an ammeter with...Ch. 25 - Show that the quantity RC has the units of time...Ch. 25 - If capacitance is in F, what will he the units of...Ch. 25 - Show that a capacitor is charged to approximately...Ch. 25 - An uncharged 10-F capacitor and a 470-k resistor...Ch. 25 - Find an expression for the voltage across the...Ch. 25 - In Fig. 25.28, all resistors have the same value,...Ch. 25 - In Fig. 25.28, take all resistors to be 1 k Find...Ch. 25 - Three 1.5-V batteries, with internal resistances...Ch. 25 - A partially discharged car battery can be modeled...Ch. 25 - Your company is overstocked on 50- , 12-W...Ch. 25 - Prob. 41PCh. 25 - How many 100-W, 120-V lightbulbs can be connected...Ch. 25 - You company is designing a battery-based backup...Ch. 25 - Take = 12 V and R1 = 270 in Fig. 25.4. (a) Whats...Ch. 25 - In Fig. 25.29, R1 is a variable resistor and the...Ch. 25 - In the circuit of Fig. 25.30, find (a) the current...Ch. 25 - In Fig. 25.30, how much power is dissipated in the...Ch. 25 - Whats the ammeter reading in Fig. 25.31? FIGURE...Ch. 25 - In Fig. 25.32, find the equivalent resistance...Ch. 25 - Find all three currents in the circuit of Fig....Ch. 25 - The voltage across the 30-k resistor in Fig. 25.33...Ch. 25 - In Fig. 25.34, what are the meter readings when an...Ch. 25 - A resistor draws 1.00 A from an ideal 12.0-V...Ch. 25 - The voltage across a charging capacitor in an RC...Ch. 25 - Youre designing an external defibrillator that...Ch. 25 - A capacitor is charged until it holds 5.0 J of...Ch. 25 - A capacitor is charged until it holds 5.0 J of...Ch. 25 - In Fig. 25.35 the 2.0-F capacitor is charged to...Ch. 25 - For the circuit of Example 25.6, take = 100 V,...Ch. 25 - In Fig. 25.36, the switch is initially open and...Ch. 25 - Prob. 61PCh. 25 - An ammeter with resistance 1.42 is connected...Ch. 25 - In Fig. 25.37, take 1 = 12.0 V, 2 = 6.00 V, 3 =...Ch. 25 - With all values except 2 as given in the preceding...Ch. 25 - The voltage on a charged capacitor is monitored...Ch. 25 - Find the resistance needed in an RC circuit to...Ch. 25 - Suppose the currents into and out of a circuit...Ch. 25 - Show that a battery delivers the most power when...Ch. 25 - Youre writing the instruction manual for a stereo...Ch. 25 - Show that only half the total energy drawn from a...Ch. 25 - Find the equivalent resistance between A and B for...Ch. 25 - Prob. 72PCh. 25 - Obtain an expression for the rate of increase...Ch. 25 - The circuit in Fig. 25.39 extends forever to the...Ch. 25 - Figure 25.40 on the next page shows the voltage...Ch. 25 - Figure 25.41 shows a portion of a circuit used to...Ch. 25 - An electrochemical impulse traveling along the...Ch. 25 - A parallel-plate capacitor has plates of area...Ch. 25 - Write the node and loop equations for the circuit...Ch. 25 - In Problem 60, take C1 = C2 = C, and find the...Ch. 25 - Youre about to purchase a battery. Normally,...Ch. 25 - In the circuit of Fig. 25.42 the switch is...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...Ch. 25 - BIO Stray voltage is a serious problem on dairy...
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