Given R_1 = 1,Omega,C_1 = 2,mu F and R_2 = 2, | vedclass

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(D) The time constant for an $RC$ circuit is given by $	au = R_{eq} C_{eq}$.For circuit $I$: $R_1$ and $R_2$ are in parallel,so $R_{eq} = \frac{R_1 R

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$8/9, 18, 4$

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

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

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