Question 499: Electrostatics & Capacitance

Question

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

Accepted Answer

To calculate the work done in increasing the voltage across the plates of a capacitor from 5 V to 10 V and then from 10 V to 15 V, we use the formula for the work done on a capacitor:
$ W = \frac{1}{2} C V^2 $
For a constant capacitance $ C $, the work done, $ W $, is proportional to the square of the voltage, $ V $, so $ W \propto V^2 $.
Thus, the ratio of work done in two different voltage intervals is given by:
$ \frac{W_1}{W_2} = \frac{V_2^2 - V_1^2}{V_3^2 - V_2^2} $
Where:
$ V_1 = 5 \, 	ext{V} $
$ V_2 = 10 \, 	ext{V} $
$ V_3 = 15 \, 	ext{V} $
Using these values, we find:
$ \frac{W}{W_2} = \frac{10^2 - 5^2}{15^2 - 10^2} = \frac{100 - 25}{225 - 100} = \frac{75}{125} = \frac{3}{5} $
Solving for $ W_2 $, we have:
$ W_2 = \frac{5}{3} W = 1.67 W $
Hence, the work done in increasing the voltage from 10 V to 15 V is approximately $ 1.67 \, W $.

Answer

0.6 W

Answer

W

Answer

1.25 W

Answer

1.67 W

Electrostatics & Capacitance

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

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