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 volts. Let C be the capacitance and U the stored energy. Select True or False for each statement.

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

2. With the capacitor connected to the battery, decreasing d increases C.
3. With the capacitor connected to the battery, decreasing d decreases Q.
4. With the capacitor connected to the battery, inserting a dielectric with κ > 1 will decrease Q.
5. With the capacitor connected to the battery, decreasing d increases U.
6. With the capacitor connected to the battery, inserting a dielectric with κ > 1 will decrease U.

Please explain thoroughly! Will Rate!

Answer 1

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

Reason:-

Capacitance (C) of a parallel plate capacitor is given by:

Where, ε₀ is a constant, A is the area of the plates and d is the separation of plates.

So, capacitance (C) is inversely proportional to the plate separation (d), no matter it is connected to the battery or not.

Hence, as d decreases, capacitance (c) increases, no matter it is connected to the battery or not.

2. With the capacitor connected to the battery, decreasing d increases C. - TRUE

Reason:-

Same reason mentioned in part 1.

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

Reason:-

Charge in capacitor is given by, Q = CV

From part 1, we know that, as d decreases, capacitance C increases, and therefore, charge (Q) also increases.

4. With the capacitor connected to the battery, inserting a dielectric with κ > 1 will decrease Q.- FALSE

Reason:-

When a dielectric is inserted between the plates of capacitor, the capacitance will become:

Charge in capacitor is given by, Q = CV

Hence, inserting a dielectric with k>1, capacitance C increases, and therefore, charge (Q) also increases.

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

Reason:-

Energy (U) is given by:

From part 1, we know that, as d decreases, capacitance C increases, and therefore, energy (U) also increases.

6. With the capacitor connected to the battery, inserting a dielectric with κ > 1 will decrease U. -FALSE

Reason:-

Energy (U) is given by:

Inserting a dielectric with k>1, capacitance C increases, and therefore, energy (U) also increases.

(feel free to clear any doubts via comments. Please let me know If you need more information)