JEE Advanced 2022 Paper 1 · Physics · Capacitors · hard

A 2 muF capacitor charged to 120 V and a 3 muF capacitor charged to 60 V are joined through a resistor, positive plate of the first to the negative…

Numerical answer

2\ \mu\mathrm{F}

capacitor charged to

120\ \mathrm{V}

and a

3\ \mu\mathrm{F}

capacitor charged to

60\ \mathrm{V}

are joined through a resistor, positive plate of the first to the negative plate of the second and negative plate to positive plate. The total heat (in mJ) dissipated in the resistor until the currents cease is ______ . Give the answer correct to two decimal places.

Show answer and solution

Answer: 19.44

Charges are

Q_1=240\ \mu\mathrm{C}

and

Q_2=180\ \mu\mathrm{C}

. Because plates of opposite sign are connected, the net charge shared is

60\ \mu\mathrm{C}

on the parallel combination of

5\ \mu\mathrm{F}

. Final voltage

=12\ \mathrm{V}

. Initial energy

=\tfrac12(2\times10^{-6})(120)^2+\tfrac12(3\times10^{-6})(60)^2=19.8\ \mathrm{mJ}

. Final energy

=\tfrac12(5\times10^{-6})(12)^2=0.36\ \mathrm{mJ}

. Heat

=19.8-0.36=19.44\ \mathrm{mJ}

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