Q. Given, $R_{1} = 1\Omega\ \ \ C_{1} = 2\mu F$ $R_{2} = 2\Omega\ \ \ C_{2} = 4\mu F$

The time constant (in $\mu\ s$) for the circuits, I, II, III, are respectively

A) $18,\ 18/9,\ 4$
B) $18,4,8/9$
C) $4,8/9,18$
D) $8/9,18,4$
Explanation

(d) $\tau_{1} = RC\left( \frac{1 \times 2}{1 + 2} \right) \times \left( \frac{2 \times 4}{2 + 4} \right) = \frac{2}{3} \times \frac{8}{6} = 8/9\ \mu\ s$
$\tau_{2} = RC = (1 + 2)(2 + 4) = 3 \times 6 = 18\ \mu\ s$
$\tau_{3} = \left( \frac{1 \times 2}{1 + 2} \right)(2 + 4) = \frac{2}{3} \times 6 = 4\ \mu\ s$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.