According to UE=12C(V)2 (Eq. 27.3), a greater capacitance means more energy is stored by the capacitor, but according to UE = Q2/2C (Eq. 27.2), a greater capacitance means less energy is stored. How can both of these equations be correct?

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?

Check Your Understanding Determine the net capacitance C of each network of capacitors shown below. Assume the C1= 1.0 pF, C2=2.0pF, C3=4.0pF, and C4=5.0 pF. Find the charge on each capacitor, assuming there is a potential difference of 12.0 V across each network.

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°?

When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

Check Your Understanding Repeat the calculations of Example 8.10 for the case in which the battery remains connected while the dielectric is placed in the 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.

A parallel-plate capacitor with capacitance 5.0F is charged with a 12.0-V battery, after which the battery is disconnected. Determine the minimum work required to increase the separation between the plates by a factor of 3.

Check Your Understanding Continuing with Example 8.12, show that when the battery is connected across the plates the energy stored in dielectric-filled capacitor is U=kU0 (larger than the energy U0 of an empty capacitor kept at the same voltage). Compare this result with the result U=U0/K found previously for an isolated, charged capacitor.