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 full y charged to QCoulombs and a voltage of V. (Cis the capacitance and U is the stored energy.) Answer the following questions regarding the capacitör charged by a battery. For each statement below, select True or False. After being disconnected from the battery, inserting a dielectric with K will increase U. OA: True OB: False With the capacitor connected to the battery, increasing d increases U. A: True oB: False With the capacitor connected to the battery, decreasing d decreases Q. A: True OB: False With the capacitor connected to the battery, inserting a dielectric with k will increase C. OA: True OB: False With the capacitor connected to the battery, decreasing d increases C OA: TrueB: False After being disconnected from the battery, inserting a dielectric with K will decrease V A: True B: False

Explanation / Answer

According to the given problem,

a) True:

Since the voltage is constant, increasing the capacitance with the dielectric will increase U by U = 1/2CV2.

b)Flase:

Capacitance is proportional to the charge. The voltage is constant since the battery is attached and capacitance decreases with distance, so the charge must drop. Thus the energy, U = 1/2QV2 decreases.

c)True:

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

d) True:

Since the voltage is constant and capacitance increases.

e)True:

Using basic capacitance formula, where C incrase as d decrease.

f) True:

The charges are isolated, so Q is fixed. The electric field decreases in the presence of a capacitor.

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