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

Answer 1

Before answering, Let's look at some capacitance equations.

C = k_o A / d

where k is dielectric constant, A is area and d is distance between plates, C is capacitance

U = 0.5CV² ( where U is stored energy)

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After being disconnected from the battery, inserting a dielectric with κ will increase U

False

Reason - Insertion of k will increase Capacitance, thus energy stored will increase, however battery is disconnected, so U should decrease

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

True

Reason - decreasing the d will increase the capacitance, thus U will increase

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With the capacitor connected to the battery, inserting a dielectric with κ will increase C.

True

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

False

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

False. V should increase

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

True