Given,
${R_1} = 1\,\Omega $ $C_1 \,= 2\,\mu F$
${R_2} = 2\,\Omega $ $C_2 \,= 4\,\mu F$
The time constants ( in $\mu\, s$) for the circuits $I, II, III$ are respectively
Diffcult
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$\tau_{1}=\mathrm{RC}=\left(\frac{1 \times 2}{1+2}\right) \times\left(\frac{2 \times 4}{2+4}\right)=\frac{2}{3} \times \frac{8}{6}=8 / 9\, \mu \mathrm{s}$
$\tau_{2}=\mathrm{RC}=(1+2)(2+4)=3 \times 6=18\, \mu \mathrm{s}$
$\tau_{3}=\left(\frac{1 \times 2}{1+2}\right)(2+4)=\frac{2}{3} \times 6=4\, \mu \mathrm{s}$
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