Question 540: Electrostats & Capacitance

Question

If the charge on the capacitor is increased by 3 coulombs, the energy stored in it increases by $$44 \%$$. The original charge on the capacitor is

Accepted Answer

Energy stored in a charged capacitor is
$$\mathrm{U}=\frac{\mathrm{Q}^2}{2 \mathrm{C}} \quad \Rightarrow \mathrm{U} \propto \mathrm{Q}^2$$
As per given condition, when, $$\mathrm{Q}_2=\left(\mathrm{Q}_1+3ight)$$,
$$\begin{array}{ll}
	herefore & \mathrm{U}_2=44 \% 	ext { of } \mathrm{U}_1=\frac{144}{100} \mathrm{U}_1 \
	herefore & \frac{\mathrm{Q}_2^2}{2 \mathrm{C}}=\frac{144}{100} 	imes \frac{\mathrm{Q}_1^2}{2 \mathrm{C}} \
	herefore & \mathrm{Q}_1=\frac{10}{12} \mathrm{Q}_2 \
	herefore & \mathrm{Q}_1=\frac{5}{6}\left(\mathrm{Q}_1+3ight) \
	herefore & 6 \mathrm{Q}_1=5 \mathrm{Q}_1+15 \
	herefore & \mathrm{Q}_1=15 \mathrm{C}
\end{array}$$

Answer

10 C

Answer

15 C

Answer

20 C

Answer

25 C

Electrostats & Capacitance

If the charge on the capacitor is increased by 3 coulombs, the energy stored in it increases by $44 \%$. The original charge on the capacitor is

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