Given,{R_1} = 1,Omega, R_2 = 2,Omega{C_1} = 2 | vedclass

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(D) The time constant of an $RC$ circuit is given by $	au = R_{eq} C_{eq}$.For circuit $I$:$R_{eq} = \frac{R_1 R_2}{R_1 + R_2} = \frac{1 	imes 2}{1

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$8/9, 18, 4$

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(D) The time constant of an $RC$ circuit is given by $	au = R_{eq} C_{eq}$.For circuit $I$:$R_{eq} = \frac{R_1 R_2}{R_1 + R_2} = \frac{1 	imes 2}{1 + 2} = \frac{2}{3}\,\Omega$$C_{eq} = \frac{C_1 C_2}{C_1 + C_2} = \frac{2 	imes 4}{2 + 4} = \frac{8}{6} = \frac{4}{3}\,\mu F$$	au_I = R_{eq} C_{eq} = \frac{2}{3} 	imes \frac{4}{3} = \frac{8}{9}\,\mu s$For circuit $II$:$R_{eq} = R_1 + R_2 = 1 + 2 = 3\,\Omega$$C_{eq} = C_1 + C_2 = 2 + 4 = 6\,\mu F$$	au_{II} = R_{eq} C_{eq} = 3 	imes 6 = 18\,\mu s$For circuit $III$:$R_{eq} = \frac{R_1 R_2}{R_1 + R_2} = \frac{1 	imes 2}{1 + 2} = \frac{2}{3}\,\Omega$$C_{eq} = C_1 + C_2 = 2 + 4 = 6\,\mu F$$	au_{III} = R_{eq} C_{eq} = \frac{2}{3} 	imes 6 = 4\,\mu s$Thus, the time constants are $8/9, 18, 4$.

Given,
${R_1} = 1\,\Omega, R_2 = 2\,\Omega$
${C_1} = 2\,\mu F, C_2 = 4\,\mu F$
The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

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Given,${R_1} = 1\,\Omega, R_2 = 2\,\Omega$${C_1} = 2\,\mu F, C_2 = 4\,\mu F$The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively: