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.

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

Explanation / Answer

Given,

Charge = Q ; Voltage = V

i)True

since, C = k epsilon0 A/d

ii)True

C = epsilon0 A/d

d increases, c decreases and vice versa

iii)False

Q = CV => V = Q/C

with the insertion of dielectric C has increased so V will decrease.

iv)

U = 1/2 C V^2

directly proportional to C. With decrease in d, C increases and hence the U.

v)False

Since, U = 1/2 C V^2

V will decrrease

vi)True

Q = CV

C decreases with increase in d hence Q also decreases.

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