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. and please explain answers Thanks!

1) With the capacitor connected to the battery, decreasing d increases U

2) After being disconnected from the battery, inserting a dielectric with ? will decrease V

3) After being disconnected from the battery, decreasing d increases C

4) With the capacitor connected to the battery, inserting a dielectric with a dielectric constant "k" will decrease C

5) After being disconnected from the battery, increasing d decreases V

6) With the capacitor connected to the battery, inserting a dielectric with a dielectric constant "k" will decrease U

Answer 1

Capacitance of a || plate capacitor with no dielectric between the plates is

Capacitance of a || plate capacitor with dielectric of dielectric constant inserted between the between the plates is

Energy stored in a capacitor is

1)

Decreasing d increases C and thus increases U as

when the capacitor is connected to the battery of constant emf = V.

So, the given statememt is false.

2.

After being disconnected

Inserting the dielectric with dielectric constant increases C by a factor of . Conservation of charge says that charge will not change and remain same as before. Thus

Thus V decreases by a factor of . Note that .

So, the given statememt is true.

3.

Decreasing increases C in any case ( explained in 1 as an example).

So, the given statememt is true.

4.

Inserting a dielectric with a dielectric constant will increase C by a factor of .

So, the given statememt is false.

5.

Increasing decreases C, thus, increases V.

So, the given statememt is false.

6.

Inserting a dielectric with a dielectric constant increases U by a factor as it increases C by a factor of and as given above