A parallel plate capacitor with plate separation d is connec

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, inserting a dielectric with will decrease C.

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

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

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

With the capacitor connected to the battery, increasing d increases C.

With the capacitor connected to the battery, increasing d increases U.

Solution

False, the charges are isolated, so Q is fixed. The electric field decreases in the presence of a capacitor. Thus,, the capacitance will increase.

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.

False, since the voltage is constant, increasing the capacitance with the dielectric will increase U by U = 0.5*CV²

False, C = Q /V = Q/ Ed which shows that capacitance decreases with an increase in distance.

False, as C = Q /V = Q/ Ed, 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 2QV decreases.