Electrostatics 6 Question 2
2. Find the time constant for the given $R C$ circuits in correct order (in $\mu s$ ).
$(2006,3 M)$
$R _1=1 \Omega, R _2=2 \Omega, C _1=4 \mu F, C _2=2 \mu F$.
(a) $18,4,8 / 9$
(b) $18,8 / 9,4$
(c) $4,18,8 / 9$
(d) $4,8 / 9,18$
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Solution:
$$ \begin{aligned} \tau & =C R \\ \tau _1 & =\left(C _1+C _2\right)\left(R _1+R _2\right)=18 \mu s \\ \tau _2 & =\frac{C _1 C _2}{C _1+C _2} \quad \frac{R _1 R _2}{R _1+R _2}=\frac{8}{6} \times \frac{2}{3}=\frac{8}{9} \mu s \\ \tau _3 & =\left(C _1+C _2\right) \frac{R _1 R _2}{R _1+R _2}=(6) \frac{2}{3}=4 \mu s \end{aligned} $$
