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Q.
The amount of work done in increasing the voltage across the plates of capacitor from $5V$ to $10V$ is ‘$W$’. The work done in increasing it from $10V$ to $15V$ will be
MHT CETMHT CET 2016Electrostatic Potential and Capacitance
Solution:
Let the capacitance of the capacitor be C.
Energy stored in the capacitor $E =\frac{1}{2} CV ^{2}$
Work done in changing the potential from $5 V$ to $10 V , $
$W =\frac{1}{2} C \left( V _{2}^{2}- V _{1}^{2}\right)$
$\therefore W =\frac{1}{2} C \left(10^{2}-5^{2}\right)=\frac{1}{2} C (75)$
Work done in changing the potential from $10 V$ to $15 V ,$
$ W '=\frac{1}{2} C \left(15^{2}-10^{2}\right)$
$\therefore W'=\frac{1}{2} C(125)$
$\Rightarrow \frac{ W '}{ W }=\frac{125}{75}=1.67$
We get $W '=1.67 \,W$