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Standard XII

Physics

Parallel and Series Combination of Capacitors

Three capacit...

Question

Three capacitors (of capacitances C, 2C and 3C) and three resistors (of resistance R, 2R and 3R) are connected with a battery and switch S as shown in the figure. When switch S is open, charges on the capacitors are shown. Switch S is closed at t =0 sec. The time constant of the circuit will be

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\frac{6 R C}{11}

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\frac{36 R C}{121}

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Solution

The correct option is C $\frac{36 R C}{121}$
Equivalent capacitance of the circuit:-

$\frac{1}{C_{o}} = \frac{1}{C} + \frac{1}{2 C} + \frac{1}{3 C}$

$⟹ \frac{1}{C_{o}} = \frac{6 + 3 + 2}{6 C}$

$⟹ C_{o} = \frac{6 C}{11}$

Equivalent resistance of the circuit:-

$\frac{1}{R_{o}} = \frac{1}{R} + \frac{1}{2 R} + \frac{1}{3 R}$

$⟹ \frac{1}{R_{o}} = \frac{6 + 3 + 2}{6 R}$

$⟹ R_{o} = \frac{6 R}{11}$

Time constant $= τ = R_{o} C_{o} = \frac{36 R C}{121}$

Answer-(C)

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Three capacitors (of capacitances C, 2C and 3C) and three resistors (of resistance R, 2R and 3R) are connected with a battery and switch S as shown in the figure. When switch S is open, charges on the capacitors are shown. Switch S is closed at t =0 sec. The time constant of the circuit will be

The correct option is C 36RC121Equivalent capacitance of the circuit:-1Co=1C+12C+13C⟹1Co=6+3+26C⟹Co=6C11Equivalent resistance of the circuit:-1Ro=1R+12R+13R⟹1Ro=6+3+26R⟹Ro=6R11Time constant=τ=RoCo=36RC121Answer-(C)