The capacitance of a variable radio capacitor can be cahanged from `50pF` to `200pF` by turning the dial from `0^(@)` to `180^(@)`. With the dial set at `180^(@)`, the capacitor is connected to a `400V` battery. After cahrging, the capacitor is disconnected from the battery and dial is tuned at `0^(@)`?
(a) what is the `p.d.` across the capacitor when dial reads `0^(@)`?
(b) how much work is required to turn the dial, if friction is naglected?

Explanation

When dial reads `180^(@),C=200pF`
when dial reads `0^(@),C'=50pF`
(a) since cahrge remains same
`Q=CV=C'Vimplies200xx400=50 V'`
`V'=1600V`
`Q=CV=200xx10^(-12)xx400=8xx10^(-8)` coul
(b) `W_(1rarr2)=U'-U=(Q^(2))/(2C')-(Q^(2))/(2C)`
`=(Q^(2))/(2)((1)/(C')-(1)/(c))`
`=((8xx10^(-8))^(2))/(2)[(1)/(50)-(1)/(200)]xx(1)/(10^(-12))`
`48xx10^(-6)J=48muJ`