Find the time constant for the given circuit.

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(A) To find the time constant $	au = R_{eq} C$,we first determine the equivalent resistance $R_{eq}$ across the capacitor terminals by replacing the

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$\frac{3}{2} RC$

Vedclass · Answer

(A) To find the time constant $	au = R_{eq} C$,we first determine the equivalent resistance $R_{eq}$ across the capacitor terminals by replacing the voltage source with a short circuit.When the voltage source is shorted,the two resistors $R$ (the one in series with the source and the one in parallel with the capacitor branch) are connected in parallel.The equivalent resistance of these two parallel resistors is $R_p = \frac{R 	imes R}{R + R} = \frac{R}{2}$.This parallel combination is then in series with the resistor $R$ that is in series with the capacitor.Thus,the total equivalent resistance is $R_{eq} = R + \frac{R}{2} = \frac{3R}{2}$.The time constant is $	au = R_{eq} C = \left( \frac{3R}{2} ight) C = \frac{3}{2} RC$.

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