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.

With the capacitor connected to the battery, increasing d decreases Q.
After being disconnected from the battery, inserting a dielectric with will increase V.
After being disconnected from the battery, inserting a dielectric with will increase C.
With the capacitor connected to the battery, inserting a dielectric with will decrease U.
With the capacitor connected to the battery, increasing d increases U.
After being disconnected from the battery, decreasing d increases C.

answers that have been wrong: FTTFTT, FFTFTT, TFTFTT, TFTFTF

Explanation / Answer

a)With the capacitor connected to the battery, increasing d decreases Q.

answer is True,since Q=CV(where Q is charge and V is voltage)

, capacitance is proportional to the charge andtThe voltage is constant since the battery is attached and capacitance decreases with distance, so the charge must drop

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

answer is False because,in this case C will increase and V decrease

C=keoA/d

c)After being disconnected from the battery, inserting a dielectric with will increase C.

answer is true as explained in b part

d)With the capacitor connected to the battery, inserting a dielectric with will decrease U.

False ,since U=1/2Cv^2

c increases so U also increases

e)With the capacitor connected to the battery, increasing d increases U

True

since C=eoA/d

and U=1/2Cv^2

so U is inversly propotional to d,increasing d decreases U

f)After being disconnected from the battery, decreasing d increases C.

True

C=eoA/d

decreasing d increases C

so answer is C i.e TFTFTT

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