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(D) The energy stored in a capacitor is given by the formula $U = \frac{1}{2}CV^2$.Since the capacitor is connected to a constant voltage source of $V

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$4 	imes 10^{-2} \ J$

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(D) The energy stored in a capacitor is given by the formula $U = \frac{1}{2}CV^2$.Since the capacitor is connected to a constant voltage source of $V = 100 \ V$,the change in energy $\Delta U$ is given by:$\Delta U = U_2 - U_1 = \frac{1}{2}C_2V^2 - \frac{1}{2}C_1V^2 = \frac{1}{2}V^2(C_2 - C_1)$.Given $C_1 = 2 \ \mu F = 2 	imes 10^{-6} \ F$,$C_2 = 10 \ \mu F = 10 	imes 10^{-6} \ F$,and $V = 100 \ V$.Substituting the values:$\Delta U = \frac{1}{2} 	imes (100)^2 	imes (10 - 2) 	imes 10^{-6} \ J$$\Delta U = \frac{1}{2} 	imes 10000 	imes 8 	imes 10^{-6} \ J$$\Delta U = 5000 	imes 8 	imes 10^{-6} \ J = 40000 	imes 10^{-6} \ J = 4 	imes 10^{-2} \ J$.

$A$ variable condenser is permanently connected to a $100 \ V$ battery. If the capacity is changed from $2 \ \mu F$ to $10 \ \mu F$,then the change in energy is equal to:

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