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.

After being disconnected from the battery, increasing d increases V.

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

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

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

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

Explanation / Answer

1)

False

Explanation :

U = 0.5*Q^2/C = 0.5*Q^2/(eA/d)

decresing d increases C thus decreasing U

2)

True

Explanation:

Q = CV

As C = eA/d

increasing d decreases C , thus amounting to the increase in V so that Q remains constant

3)

True

Explanation:

U = 0.5*C*V^2

C = eA/d

Thus introducing a dielectric k increases the C by k thus U increases by k

4)

True

Explanation:

Q = CV

introducing a dielectric k increases C thus decreasing V for Q to remain constant.

5)

False

Explanation:

C = eA/d

indroducing a dielectric k increases C by k

6)

False

C = eA/d

decreasing d increases C

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