Find the time constant of the $R C$ circuit:

3 R C

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\frac{3 R C}{2}

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\frac{R C}{3}

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R C

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Solution

The correct option is B $\frac{3 R C}{2}$
For calculating the effective resistance of the circuit we can remove the capacitor and the corresponding circuit is as shown in figure.
$R_{e q} = R + \frac{R R}{R + R} = (3 / 2) R$
For R-C circuit, time constant $τ = C R_{e q} = \frac{3 C R}{2}$

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The electric current in a charging R-C circuit is given by $i = i_{o} e^{\frac{- t}{R C}}$ where io, R and C are constant parameter of the circuit and t is time. Find the rate of change of current at (x)t=0, (y)t=RC, (z)t=10 RC

$(i) \frac{- i_{o}}{R C} (i i) 0 (i i i) \frac{- i_{o}}{R C_{e}} (i v) \frac{- i_{o}}{R C_{e}^{10}} (v) \frac{- i_{o} e^{10}}{R C}$