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 C.

With the capacitor connected to the battery, inserting a dielectric with κ will decrease U.

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

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

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

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

Answer 1

Capacitance of a capacitor without dielectric, C = ε₀ A/d

Capacitance of a capacitor with dielectric, C = ε₀ KA/d

Where, A-area of the plates, d – plate separation, K- dielectric constant of the medium.

Energy stored in a capacitor, U = ½ CV²

Where V is the potential difference applied to the capacitor.

Capacitance C, pd V and charge Q can be related as C = Q/V

1.capacitance C can be increased by inserting a dielectric .

The statement is True

2. with the capacitor connected to the battery, new capacitance is K times original capacitance and the p.d V between the plates remains the same , the energy stored becomes k times initial energy.

The statement is False

3. a decrease in separation d increases the capacitance C

The statement is False

4. decrease in separation d increases the capacitance C which in turn increases the energy U as V remains the same with the capacitor connected to the battery

The statement is True

5. potential V = Q/C, insertion of dielectric increases C and decreases V when battery is disconnected from the capacitor.

The statement is False

6. with capacitor connected to battery, V remains the same and charge Q = CV. Increasing d decreases C and hence decreases charge Q

The statement is True