Question

A capacitor of capacitance C is charged to a potential difference `V_(0)`. The charged battery is disconnected and the capacitor is connected to a capacitor of unknown capacitance `C_(x)`. The potential difference across the combination is V. The value of `C_(x)` should be
A. `(C(V_(0) - V))/(V)`
B. `(C(V - V_(0)))/(V)`
C. `(CV)/(V_(0))`
D. `(CV_(0))/(V)`

Answer 1

Correct Answer - A
The initial charge on first capacitor is `Q = CV_(0)`
After connection, voltages of both capacitors become same, i.e. V
`:. Q = q_(1) + q_(2) or CV_(0) = CV + C_(x)V`
`V = (CV_(0))/(C + C_(x)) :. C_(x) = (C(V_(0) - V))/(V)`