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A capacitor of capacitance 10 m F is cha...

A capacitor of capacitance `10 m F` is charged up a potential difference of `2V` and then the cell is removed. Now it is connected to a cell of `emf 4V` and is charged fully. In both cases the polarities of the two cells are in the same directions. Total heat produced in the second charging process is :

A

`10 mJ`

B

`20 muJ`

C

`40 muJ`

D

`80 muJ`

Text Solution

Verified by Experts

The correct Answer is:
B
b. Energy stored in capacitor when it is charged up to 2 V is
`1/2 xx 10 xx 2^2 = 20 muJ = u_1` (suppose)
Energy stored in capacitor when it is charged up to 4 V is
`1/2 xx 10 xx 4^2 = 80 muJ = u_2` (suppose)
Increase in charge = 40 -20 = `20muC`.
Energy drawn from cell `= 20 xx 4 = 80 muC` = u (suppose)
heat produced ` = u_1 + u-u_2`
`= 20 + 80 - 80 = 20 muJ` .
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