Physics for Scientists and Engineers: Foundations and Connections
Author: Katz, Debora M.
Publisher: Cengage Learning
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An arrangement of capacitors is shown in Figure P27.23. a. If C = 9.70 105 F, what is the equivalent capacitance between points a and b? b. A battery with a potential difference of 12.00 V is connected to a capacitor with the equivalent capacitance. What is the energy stored by this capacitor? Figure P27.23 Problems 23 and 24.
An electric potential exists in a region of space such that V = 8x4 2y2 + 9z3 and V is in units of volts, when x, y, and z are in meters. a. Find an expression for the electric field as a function of position. b. What is the electric field at (2.0 m, 4.5 m, 2.0 m)?
What If? The two capacitors of Problem 13 (C1 = 5.00 F and C2 = 12.0 F) are now connected in series and to a 9.00-Y battery. Find (a) the equivalent capacitance of the combination. (b) the potential difference across each capacitor, and (c) the charge on each capacitor.
A 2.0F capacitor and a 4.0F capacitor are connected in series across a 1.0-kV potential. The charged capacitors are then disconnected from the source and connected to each other with terminals of like sign together. Find the charge on each capacitor and the voltage across each capacitor.
(i) A battery is attached to several different capacitors connected in parallel. Which of the following statements is true? (a) All capacitors have the same charge, and the equivalent capacitance is greater than the capacitance of any of the capacitors in the group, (b) The capacitor with the largest capacitance carries the smallest charge, (c) The potential difference across each capacitor is the same, and the equivalent capacitance is greater than any of the capacitors in the group. (d) The capacitor with the smallest capacitance carries the largest charge. (e) The potential differences across the capacitors are the same only if the capacitances are the same, (ii) The capacitors are reconnected in series, and the combination is again connected to the battery. From the same choices, choose the one that is true.
Suppose that the capacitance of a variable capacitor can be manually changed from 100 pF to 800 pF by turning a dial, connected to one set of plates by a shaft from 0° to 180°. With the dial set at 180° (corresponding to C — 800 pF), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to 0°. If friction is negligible, how much work is required to turn the dial from 180° to 0°?
In Figure P27.7, capacitor 1 (C1 = 20.0 F) initially has a potential difference of 50.0 V and capacitor 2 (C2 = 5.00 F) has none. The switches are then closed simultaneously. a. Find the final charge on each capacitor after a long time has passed. b. Calculate the percentage of the initial stored energy that was lost when the switches were closed. FIGURE P27.7
Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure P20.51. Figure P20.51
Given the arrangement of capacitors in Figure P27.23, find an expression for the equivalent capacitance between points a and b. Figure P27.23 Problems 23 and 24.
(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.46 if C1 = 5.00 F, C2 = 10.00 F, and C3 = 2.00 F. (b) If the potential between points a and b is 60.0 V, what charge is stored on C5? Figure P16.46
A pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?
A 10.0-F capacitor is charged to 15.0 V. It is next connected in series with an uncharged 5.00-F capacitor. The series combination is finally connected across a 50.0-V battery as diagrammed in Figure P20.83. Find the new potential differences across the 5.00-F and 10.0-F capacitors after the switch is thrown closed. Figure P20.83
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