Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 28, Problem 28.68AP
A battery is used to charge a capacitor through a resistor as shown in Figure P27.44. Show that half the energy supplied by the battery appears as internal energy in the resistor and half is stored in the capacitor.
Figure P27.44
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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.
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Chapter 28 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 28 - To maximize the percentage of the power from the...Ch. 28 - With the switch in the circuit of Figure 27.4a...Ch. 28 - With the switch in the circuit of Figure 27.6a...Ch. 28 - Prob. 28.4QQCh. 28 - Consider the circuit in Figure 27.17 and assume...Ch. 28 - Is a circuit breaker wired (a) in series with the...Ch. 28 - A battery has some internal resistance. (i) Clan...Ch. 28 - The terminals of a battery are connected across...Ch. 28 - When operating on a 120-V circuit, an electric...Ch. 28 - If the terminals of a battery with zero internal...
Ch. 28 - Prob. 28.6OQCh. 28 - What is the time constant of the circuit shown in...Ch. 28 - When resistors with different resistances are...Ch. 28 - When resistors with different resistances are...Ch. 28 - The terminals of a battery are connected across...Ch. 28 - Are the two headlights of a car wired (a) in...Ch. 28 - In the circuit shown in Figure OQ28.12, each...Ch. 28 - Prob. 28.13OQCh. 28 - A circuit consists of three identical lamps...Ch. 28 - A series circuit consists of three identical lamps...Ch. 28 - Suppose a parachutist lands on a high-voltage wire...Ch. 28 - A student claims that the second of two lightbulbs...Ch. 28 - Why is ii possible for a bird to sit on a...Ch. 28 - Given three lightbulbs and a battery, sketch as...Ch. 28 - Prob. 28.5CQCh. 28 - Referring to Figure CQ28.6, describe what happens...Ch. 28 - Prob. 28.7CQCh. 28 - (a) What advantage does 120-V operation offer over...Ch. 28 - Prob. 28.9CQCh. 28 - Prob. 28.10CQCh. 28 - A battery has an emf of 15.0 V. The terminal...Ch. 28 - Two 1.50-V batterieswith their positive terminals...Ch. 28 - An automobile battery has an emf of 12.6 V and 171...Ch. 28 - As in Example 27.2, consider a power supply with...Ch. 28 - Three 100- resistors are connected as shown in...Ch. 28 - Prob. 28.6PCh. 28 - What is the equivalent resistance of the...Ch. 28 - Consider the two circuits shown in Figure P27.5 in...Ch. 28 - Consider the circuit shown in Figure P28.9. Find...Ch. 28 - (a) You need a 45- resistor, but the stockroom has...Ch. 28 - A battery with = 6.00 V and no internal...Ch. 28 - A battery with emf and no internal resistance...Ch. 28 - (a) Kind the equivalent resistance between points...Ch. 28 - (a) When the switch S in the circuit of Figure...Ch. 28 - Prob. 28.15PCh. 28 - Four resistors are connected to a battery as shown...Ch. 28 - Consider die combination of resistors shown in...Ch. 28 - For the purpose of measuring the electric...Ch. 28 - Calculate the power delivered to each resistor in...Ch. 28 - Why is the following situation impossible? A...Ch. 28 - Consider the circuit shown in Figure P28.21 on...Ch. 28 - In Figure P28.22, show how to add just enough...Ch. 28 - The circuit shown in Figure P27.17 is connected...Ch. 28 - For the circuit shown in Figure P28.24, calculate...Ch. 28 - What are the expected readings of (a) the ideal...Ch. 28 - The following equations describe an electric...Ch. 28 - Taking R = 1.00 k and = 250 V in Figure P27.19,...Ch. 28 - You have a faculty position at a community college...Ch. 28 - The ammeter shown in Figure P28.29 reads 2.00 A....Ch. 28 - In the circuit of Figure P28.30, determine (a) the...Ch. 28 - Using Kirchhoffs rules, (a) find (he current in...Ch. 28 - In the circuit of Figure P27.20, the current I1 =...Ch. 28 - In Figure P28.33, find (a) the current in each...Ch. 28 - For the circuit shown in Figure P27.22, we wish to...Ch. 28 - Find the potential difference across each resistor...Ch. 28 - (a) Can the circuit shown in Figure P27.21 be...Ch. 28 - An uncharged capacitor and a resistor are...Ch. 28 - Consider a series RC circuit as in Figure P28.38...Ch. 28 - A 2.00-nF capacitor with an initial charge of 5.10...Ch. 28 - A 10.0-F capacitor is charged by a 10.0-V battery...Ch. 28 - In the circuit of Figure P27.25, the switch S has...Ch. 28 - In the circuit of Figure P27.25, the switch S has...Ch. 28 - The circuit in Figure P28.43 has been connected...Ch. 28 - Show that the integral 0e2t/RCdtin Example 27.11...Ch. 28 - A charged capacitor is connected to a resistor and...Ch. 28 - Prob. 28.46PCh. 28 - Prob. 28.47PCh. 28 - Turn on your desk lamp. Pick up the cord, with...Ch. 28 - Assume you have a battery of emf and three...Ch. 28 - Find the equivalent resistance between points a...Ch. 28 - Four 1.50-V AA batteries in series are used to...Ch. 28 - Four resistors are connected in parallel across a...Ch. 28 - The circuit in Figure P27.35 has been connected...Ch. 28 - The circuit in Figure P27.34a consists of three...Ch. 28 - For the circuit shown in Figure P28.55. the ideal...Ch. 28 - The resistance between terminals a and b in Figure...Ch. 28 - (a) Calculate the potential difference between...Ch. 28 - Why is the following situation impossible? A...Ch. 28 - A rechargeable battery has an emf of 13.2 V and an...Ch. 28 - Find (a) the equivalent resistance of the circuit...Ch. 28 - When two unknown resistors are connected in series...Ch. 28 - When two unknown resistors are connected in series...Ch. 28 - The- pair of capacitors in Figure P28.63 are fully...Ch. 28 - A power supply has an open-circuit voltage of 40.0...Ch. 28 - The circuit in Figure P27.41 contains two...Ch. 28 - Two resistors R1 and R2 are in parallel with each...Ch. 28 - Prob. 28.67APCh. 28 - A battery is used to charge a capacitor through a...Ch. 28 - A young man owns a canister vacuum cleaner marked...Ch. 28 - (a) Determine the equilibrium charge on the...Ch. 28 - Switch S shown in Figure P28.71 has been closed...Ch. 28 - Three identical 60.0-W, 120-V lightbulbs are...Ch. 28 - A regular tetrahedron is a pyramid with a...Ch. 28 - An ideal voltmeter connected across a certain...Ch. 28 - In Figure P27.47, suppose the switch has been...Ch. 28 - Figure P27.48 shows a circuit model for the...Ch. 28 - The student engineer of a campus radio station...Ch. 28 - The circuit shown in Figure P28.78 is set up in...Ch. 28 - An electric teakettle has a multiposition switch...Ch. 28 - A voltage V is applied to a series configuration...Ch. 28 - In places such as hospital operating rooms or...Ch. 28 - The switch in Figure P27.51a closes when Vc23Vand...Ch. 28 - The resistor R in Figure P28.83 receives 20.0 W of...
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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 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_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_forward
- Consider 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_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_forwardConsider 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_forward
- An 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_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_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_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_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 circuit in Figure P27.85 shows four capacitors connected to a battery. The switch S is initially open, and all capacitors have reached their final charge. The capacitances are C1 = 6.00 F, C2 = 12.00 F, C3 = 8.00 F, and C4 = 4.00 F. a. Find the potential difference across each capacitor and the charge stored in each. b. The switch is now closed. What is the new final potential difference across each capacitor and the new charge stored in each? Figure P27.85arrow_forward
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