First slide

Capacitance

Question

The work done in increasing the P.D. across the plates of a capacitor from 4 V to 6 V is W. The further work done in increasing the P.D. from 6 V to 8 V is

Moderate

A

$\frac{4 W}{3}$
B

$\frac{3 W}{4}$
C

$\frac{7 W}{5}$
D

$\frac{5 W}{7}$

Solution

$\begin{array}{rcl} \frac{w_{1}}{w_{2}} & = & \frac{\frac{1}{2} C {({V_{2}}^{2} - {V_{1}}^{2})}_{1}}{\frac{1}{2} C {({V_{2}}^{2} - {V_{1}}^{2})}_{2}} = \frac{6^{2} - 4^{2}}{8^{2} - 6^{2}} \\ \frac{w}{w_{2}} & = & \frac{36 - 16}{64 - 36} = \frac{20}{28} = \frac{5}{7}; \\ w_{2} & = & 7 w / 5 \end{array}$

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