Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 28, Problem 68AP
To determine
The proof that the resistor and the capacitor share equally in the energy from the battery.
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A battery is used to charge a capacitor through a resistor as shown. Show that half the energy supplied by the battery appears as internal energy in the resistor and half is stored in the capacitor.
A 12.0-V battery is attached to a 2.00-mF capacitor and a 100-Ω Once the capacitor is fully charged, what is the energy stored in it? What is the energy dissipated as heat by the resistor as the capacitor is charging?
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Chapter 28 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 28.1 - To maximize the percentage of the power from the...Ch. 28.2 - With the switch in the circuit of Figure 27.4a...Ch. 28.2 - With the switch in the circuit of Figure 27.6a...Ch. 28.2 - Prob. 28.4QQCh. 28.4 - Consider the circuit in Figure 27.17 and assume...Ch. 28 - Prob. 1OQCh. 28 - Prob. 2OQCh. 28 - Prob. 3OQCh. 28 - Prob. 4OQCh. 28 - Prob. 5OQ
Ch. 28 - Prob. 6OQCh. 28 - Prob. 7OQCh. 28 - Prob. 8OQCh. 28 - Prob. 9OQCh. 28 - Prob. 10OQCh. 28 - Prob. 11OQCh. 28 - Prob. 12OQCh. 28 - Prob. 13OQCh. 28 - Prob. 14OQCh. 28 - Prob. 15OQCh. 28 - Prob. 1CQCh. 28 - Prob. 2CQCh. 28 - Why is it possible for a bird to sit on a...Ch. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Is the direction of current in a battery always...Ch. 28 - Prob. 10CQCh. 28 - Prob. 1PCh. 28 - Two 1.50-V batterieswith their positive terminals...Ch. 28 - An automobile battery has an emf of 12.6 V and an...Ch. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Why is the following situation impossible? A...Ch. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - The following equations describe an electric...Ch. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - An uncharged capacitor and a resistor are...Ch. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - A 10.0-F capacitor is charged by a 10.0-V battery...Ch. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - A charged capacitor is connected to a resistor and...Ch. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49APCh. 28 - Prob. 50APCh. 28 - Prob. 51APCh. 28 - Prob. 52APCh. 28 - Prob. 53APCh. 28 - Prob. 54APCh. 28 - Prob. 55APCh. 28 - Prob. 56APCh. 28 - Prob. 57APCh. 28 - Why is the following situation impossible? A...Ch. 28 - Prob. 59APCh. 28 - Prob. 60APCh. 28 - When two unknown resistors are connected in series...Ch. 28 - Prob. 62APCh. 28 - Prob. 63APCh. 28 - A power supply has an open-circuit voltage of 40.0...Ch. 28 - Prob. 65APCh. 28 - Prob. 66APCh. 28 - Prob. 67APCh. 28 - Prob. 68APCh. 28 - Prob. 69APCh. 28 - Prob. 70APCh. 28 - Prob. 71APCh. 28 - Prob. 72APCh. 28 - A regular tetrahedron is a pyramid with a...Ch. 28 - An ideal voltmeter connected across a certain...Ch. 28 - Prob. 75APCh. 28 - Prob. 76APCh. 28 - Prob. 77APCh. 28 - Prob. 78APCh. 28 - Prob. 79APCh. 28 - Prob. 80APCh. 28 - Prob. 81APCh. 28 - Prob. 82CPCh. 28 - Prob. 83CP
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- A charge Q is placed on a capacitor of capacitance C. The capacitor is connected into the circuit shown in Figure P26.37, with an open switch, a resistor, and an initially uncharged capacitor of capacitance 3C. The switch is then closed, and the circuit comes to equilibrium. In terms of Q and C, find (a) the final potential difference between the plates of each capacitor, (b) the charge on each capacitor, and (c) the final energy stored in each capacitor. (d) Find the internal energy appearing in the resistor. Figure P26.37arrow_forwardThe- pair of capacitors in Figure P28.63 are fully charged by a 12.0-V battery. The battery is disconnected, and the switch is then closed. Alter 1.00 ms has elapsed, (a) how much charge remains 011 the 3.00-F capacitor? (b) How much charge remains on the 2.00-F capacitor? (c) What is the current in the resistor at this time?arrow_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
- The 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_forwardThree 100- resistors are connected as shown in Figure P21.41 The maximum power that can safely be delivered to any one resistor is 25.0 W. (a) What is the maximum potential difference that can be applied to the terminals a and b? (b) For the voltage determined in part (a), what is the power delivered to each resistor? (c) What is the total power delivered to the combination of resistors?arrow_forwardConsider the circuit shown in Figure P26.24, where C1, = 6.00 F, C2 = 3.00 F. and V = 20.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing Calculate (a) the initial charge acquired by C, and (b) the final charge on each capacitor.arrow_forward
- Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in Figure 21.38, starting from t = 0. Draw the other for discharging a capacitor through a resistor, as in the circuit in Figure 21.39, starting at t = 0, with an initial charge Q0. Show at least two intervals of t.arrow_forwardFigure P29.46 shows a circuit with a 12.0-V battery connected to four resistors. How much power is delivered to each resistor?arrow_forwardAn oceanographer is studying how the ion concentration in seawater depends on depth. She makes a measurement by lowering into the water a pair of concentric metallic cylinders (Fig. P21.66) at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ra, outer radius rb, and length L much larger than rb. The scientist applies a potential difference V between the inner and outer surfaces, producing an outward radial current I. Let represent the resistivity of the water. (a) Find the resistance of the water between the cylinders in terms of L, , ra, an rb. (b) Express the resistivity of the water in terms of the measured quantities L, ra, rb, V, and I. Figure P21.66arrow_forward
- Consider the circuit shown in Figure P20.52, where C1 = 6.00 F, C2 = 3.00 F, and V = 20.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing S2. Calculate (a) the initial charge acquired by C1 and (b) the final charge on each capacitor. Figure P20.52arrow_forwardA Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.arrow_forwardA 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_forward
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