A capacitor of capacitance C has charge Q. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

Question

A capacitor of capacitance C has charge Q. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is (A) (Q2/2 C) (B) (Q2/4 C) (C) (Q2/8 C) (D) dependent on the value of the resistance

Tardigrade Admin · Accepted Answer

As the capacitors are identical, each of them finally have charge

Q /2

.
Initial energy of the system is

E_{i} = \frac{Q ^{2}}{2 C}

Final energy of the system is

E_{f} = 2 [\frac{( Q /2 ) ^{2}}{2 C}] = \frac{Q ^{2}}{4 C}

Heat produced

=

loss in energy

= E_{i} - E_{f} = \frac{Q ^{2}}{4 C}

Q. A capacitor of capacitance $C$ has charge $Q$ . It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

$\frac{Q ^{2}}{2 C}$

$\frac{Q ^{2}}{4 C}$

$\frac{Q ^{2}}{8 C}$

dependent on the value of the resistance

As the capacitors are identical, each of them finally have charge $Q /2$ .
Initial energy of the system is $E_{i} = \frac{Q ^{2}}{2 C}$
Final energy of the system is $E_{f} = 2 [\frac{( Q /2 ) ^{2}}{2 C}] = \frac{Q ^{2}}{4 C}$
Heat produced $=$ loss in energy $= E_{i} - E_{f} = \frac{Q ^{2}}{4 C}$

Q. A capacitor of capacitance C has charge Q. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

2CQ2​

4CQ2​

8CQ2​