The time constant of the given circuit is:

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(A) To find the time constant of the $RC$ circuit,we first determine the equivalent resistance $(R_{eq})$ across the terminals of the capacitor.$1$. S

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$\frac{3RC}{2}$

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(A) To find the time constant of the $RC$ circuit,we first determine the equivalent resistance $(R_{eq})$ across the terminals of the capacitor.$1$. Short-circuit the voltage source (replace the battery with a wire).$2$. The circuit now consists of two resistors in parallel (the one in the middle and the one on the left),which are then in series with the resistor on the right.$3$. The two resistors of resistance $R$ in parallel have an equivalent resistance of $R_p = \frac{R 	imes R}{R + R} = \frac{R}{2}$.$4$. This $R_p$ is in series with the third resistor $R$,so $R_{eq} = R_p + R = \frac{R}{2} + R = \frac{3R}{2}$.$5$. The time constant $	au$ is given by $	au = R_{eq} C = \frac{3RC}{2}$.

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