Question

A capacitor of 5 µF is charged to 1C by using a constant voltage supply. If one of the plates of charged capacitor is earthed after disconnecting it from external voltage supply, find the new

(a) Capacitance

(b) Voltage across the capacitor

(c) Charge on the capacitor.

Answer 1

(a) Capacitance of the capacitor

C = \(\frac{\varepsilon_0A}{d}\)

Since capacitance of capacitor does not depend on the charge of the capacitor, hence it will remain the same Fig. 

(b) Voltage across the' capacitor plates when charged capacitor is earthed V' = \(\frac{V}{2}\) i.e. voltage across the plates will be halved Fig. 

(c) Since q = CV 

∴ q' = \(C'(\frac{V}{2}) = \frac{1}{2}(CV) = \frac{q}{2}\)

Hence, charge will reduce to half the original value.