A potential difference of 20V is applied across a parallel combination of three identical capacitors. If the total charge in the combination be 30C, determine the capacitance of each capacitor. What will be the charge in the series combination of these three capacitors with the same potential difference?

Explanation

Let the capacitance of each capacitor be C.
Potential difference across each capacitor when they are connected in parallel combination, `V = 20V`.
Charge on the three capacitors, `Q_1= Q_2= Q_3 = CV`
`Q_1+Q_2+Q_3= 3CV`
or, `30 3xxCxx20 = 60C`
or, `C = (1)/(2) = 0.5 F`
Capacitance of each capacitor = 0.5 F
In the second case when the capacitors are connected in series, let us suppose that equivalent capacitance is C'.
`(1)/(C')= (1)/(C )+(1)/(C )+(1)/(C )= (3)/(C )`
or, `C' = (C )/(3) = (0.5)/(3) = (1)/(6)F`
In this case, the total charge of the combination,
`Q'= C'V= (1)/(6)xx20 = (10)/(3)= 3.33C`.