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A capacitor having initial charge q0 = C...

A capacitor having initial charge `q_0 = CE//2` is connected to a cell of emf E through a resistor R as shown. Find the total heat generated in the circuit after the switch S is closed.

A

`(1//12) CE^2`

B

`(1//8)CE^2`

C

`(1//4)CE^2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
b. Final charge on capacitor `q_(f) = CE`
Charge flown `= CE-CE//2 = CE//2`
Work done by battery: `W_(b) = E(CE//2) = 1/2 CE^2`
Change in energy of capacitor is
`DeltaU = 1/(2C)[q_(f)^(2) - q_(0)^(2)]`
` = 1/(2C) [(CE)^2 - (CE//2)^2] = (3CE^2)/8`
Heat `= W_(b) - Delta U = 1/8 CE^2` .
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