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.

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

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

3. With the capacitor connected to the battery, decreasing d decreases Q.

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

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

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

Answer 1

1)false.

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

charge Q is constant .energy stored U=0.5*Q^2/C

where C= εA/d

2)true

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

C = kεA/d, inserting a dielectric k will cause C to increase. Since charge Q is constant, and Q = CV, increasing C causes V to decrease.

3)false

With the capacitor connected to the battery, decreasing d decreases Q

C increases U will increases and Q will increases.

4) false

Charge Q is constant, energy store is U = (0.5)Q²/C
Since C = kεA/d, inserting dielectric k will cause C to increase. Since C increases, U then decreases.

5)false

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

Since C = kεA/d, inserting a dielectric k will cause C to increase.

6)false

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

Since C = εA/d, decreasing d causes C to increase.