Two capacitors of capacitances 1 mu F and 3 m | vedclass

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(D) Initial charges on the capacitors are $Q_1 = C_1V = 1\ \mu F 	imes 5\ V = 5\ \mu C$ and $Q_2 = C_2V = 3\ \mu F 	imes 5\ V = 15\ \mu C$.Since the

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$B$ and $C$ both.

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(D) Initial charges on the capacitors are $Q_1 = C_1V = 1\ \mu F 	imes 5\ V = 5\ \mu C$ and $Q_2 = C_2V = 3\ \mu F 	imes 5\ V = 15\ \mu C$.Since they are connected with oppositely charged plates together,the net charge is $Q_{net} = |Q_2 - Q_1| = |15\ \mu C - 5\ \mu C| = 10\ \mu C$.The equivalent capacitance in parallel is $C_{eq} = C_1 + C_2 = 1\ \mu F + 3\ \mu F = 4\ \mu F$.The final common voltage is $V_f = \frac{Q_{net}}{C_{eq}} = \frac{10\ \mu C}{4\ \mu F} = 2.5\ V$.Initial energy stored is $U_i = \frac{1}{2}C_1V^2 + \frac{1}{2}C_2V^2 = \frac{1}{2}(1 + 3)\ \mu F 	imes (5\ V)^2 = 2\ \mu F 	imes 25\ V^2 = 50\ \mu J$.Final energy stored is $U_f = \frac{1}{2}C_{eq}V_f^2 = \frac{1}{2}(4\ \mu F) 	imes (2.5\ V)^2 = 2\ \mu F 	imes 6.25\ V^2 = 12.5\ \mu J$.Heat produced is $H = U_i - U_f = 50\ \mu J - 12.5\ \mu J = 37.5\ \mu J$.Thus,both $B$ and $C$ are correct.

Two capacitors of capacitances $1\ \mu F$ and $3\ \mu F$ are charged to the same voltages $5\ V$. They are connected in parallel with oppositely charged plates connected together. Then:

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