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