A parallel plate capacitor with plate separation d is connected to a battery. Th

Question

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

After being disconnected from the battery, decreasing d increases U.

With the capacitor connected to the battery, inserting a dielectric with will decrease C.

After being disconnected from the battery, decreasing d decreases C.

With the capacitor connected to the battery, decreasing d decreases Q.

After being disconnected from the battery, inserting a dielectric with will increase V.

With the capacitor connected to the battery, inserting a dielectric with will increase U.

Explanation / Answer

a) FALSE: After being disconnected from the battery, decreasing d increases U.
Charge Q is constant, energy stored is U = (0.5)Q2/C
Since C = A/d, increasing d causes C to decrease. Since C decreases, U then increases.

b) FALSE: With the capacitor connected to the battery, inserting a dielectric with k will decrease C.

Since C = kA/d, inserting a dielectric k will cause C to increase.

c) FALSE: After being disconnected from the battery, decreasing d decreases C.

ince C = A/d, decreasing d causes C to increase.

d) FALSE: With the capacitor connected to the battery, decreasing d decreases Q.

Since C = A/d, decreasing d causes C to increase. But, Q = CV, Cincreases , then Q increases.

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