Question

Four capacitors are of the same capacitance. 

(a) If three of them are connected in parallel and the remaining one is connected in series with this combination, the resultant capacitance is 3.75 µF. Find the capacitance of each capacitor.

(b) When three of them are connected in series and the remaining one is connected in parallel with this combination, find the resultant capacitance of the combination.

Answer 1

(a) Let C be the capacitance of each capacitor.

Between points A and B, three capacitors, each of capacitance C, are connected in parallel from figure. 

Their effective capacitance (C_p) is given by

C_p = C + C + C = 3C

When a capacitor of capacitance C_p is connected in series with C , their resultant capacitance (C_s) is given by

(b) The arrangement is shown in below figure.

The effective capacitance (C_s) of the series combination of three capacitors, each of capacitance C, is given by

When another capacitor of capacitance C is connected in parallel with the combination, the result ant capacitance is