The amount of work done in increasing the voltage across the plates of capacitor from 5 V to 10 V is W. The work done in increasing it from 10 V to 15 V will be

Options

A. W
B. `0.6W`
C. `1.25W`
D. `1.67W`

Answer

D

Explanation

According to question, work done in increasing the voltage from 5 V to 10 V is given by
=`1/2C(V_2^2-V_1^2)`
=`1/2xxCxx(10^2-5^2)`
`W=1/2xxCxx75=(75C)/2`
Again work done in increasing the plate voltage from 10 V to 15 V is given by
`W=1/2xxCxx(15^2-10^2)`
Rightarrow `W_1=1/2xxCxx125=(125C)/2`
From Eqs. (1) and (ii), we get
`W/W_1=(75C)/(2xx125C)xx2`
Rightarrow `W_1/W=125/75=5/3`
Rightarrow `W_1=1.67 W`