Question

Which of the following do not affect capacitance?

(a) Area of the plates.

(b) Separation of the plates.

(c) Material between the plates.

(d) Charge on the plates.

(e) Energy stored in the capacitor.

Short answer

(d) Charge on the plates.

(e) Energy stored in the capacitor.

Step-by-step solution

Understanding the capacitance of the capacitor

Capacitance establishes an inverse relation with the potential difference and a direct relation with the charge of the plates. In the parallel plates, the capacitance shows an inverse relation with the separation distance of the plates.

Determination of the factors that do not affect the capacitance

The capacitance can be expressed as:

\(C = \frac{Q}{V}\)

Here, Qis the charge andVis the potential difference. The above equation of capacitance gives the constant ratio value.

The variation in the charge will cause the potential difference to vary. There is no change in the capacitance.

For the parallel plate’s capacitor, thecapacitance can be expressed as:

\(C = { \in _0}\frac{A}{d}\)

Here, A is the area of the plates, d is the separation distance, and\({ \in _0}\)is the permittivity of free space.

The potential energy stored by the capacitor can be expressed as:

\(\begin{aligned}E &= \frac{1}{2}C{V^2}\\C &= \frac{{2E}}{{{V^2}}}\end{aligned}\)

The variation in the potential energy will cause the charge of the parallel plates and the difference in the potential between the plates to vary. This will not change the capacitance of the plates.

Thus, the capacitance is affected by the plates' area, the separation between the plates, and the dielectric material between the two plates.