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°?

Check Your Understanding When a cylindrical capacitor is given a charge of 0.500 nC, a potential difference of 20.0 V is measured between the cylinders, (a) What is the capacitance of this system? (b) If the cylinders are 1.0 m long, what is the ratio of their radii?

(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.

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.

Check Your Understanding The potential difference across a 5.0-pF capacitor is 0.40 V. (a) What is the energy stored in this capacitor? (b) The potential difference is now increased to 1.20 V. By what factor is the stored energy increased?

Check Your Understanding The capacitance of a parallel-plate capacitor is 2.0 pF. If the area of each plate is 2.4 cm2, what is the plate separation?

How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?