Question 86: Electrostats & Capacitance

Question

In the following circuits, it is given that $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F}$ and $\mathrm{C}_2=4 \mu \mathrm{~F}$.The time constants (in $\mu \mathrm{s}$ ) for the circuits I, II, III are, rcspectively.

Accepted Answer

For (i) : The net capacitance
$$ \begin{aligned} \mathrm{C} & =\frac{C_1 C_2}{C_1+C_2} \ & =\frac{2 	imes 4}{2+4}=\frac{8}{6}=\frac{4}{3} \mu \mathrm{~F} \end{aligned} $$
And net resistance, $R=\frac{R_1 R_2}{R_1+R_2}$
$$ =\frac{1 	imes 2}{1+2}=\frac{2}{3} \Omega $$
Thus, time constant, $\mathrm{T}=\mathrm{C} . \mathrm{R}=\frac{4}{3} 	imes \frac{2}{3}=\frac{8}{9} \mu \mathrm{~s}$
For (ii) :
$$ \begin{aligned} \mathrm{C} & =\mathrm{C}_1+\mathrm{C}_2 \ & =2+4=6 \mu \mathrm{~F} 	ext { and } \ \mathrm{R} & =\mathrm{R}_1+\mathrm{R}_2 \ & =1+2=3 \Omega \end{aligned} $$
Time constant T = C.R
$$ =6 	imes 3=18 \mu \mathrm{~s} $$
$$ \begin{aligned} &	ext { For (iii) : }\ &\begin{aligned} \mathrm{C} & =\mathrm{C}_1+\mathrm{C}_2 \ & =2+4=6 \mu \mathrm{~F} 	ext { and } \ \mathrm{R} & =\frac{\mathrm{R}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2} \ & =\frac{1 	imes 2}{1+2}=\frac{2}{3} \Omega \ \mathrm{~T} & =\mathrm{C} . \mathrm{R}=6 	imes \frac{2}{3} \ & =4 \mu \mathrm{~s} \end{aligned} \end{aligned} $$

Answer

$18,8 / 9,4$

Answer

$18,4,8 / 9$

Answer

$4,8 / 9,18$

Answer

$8 / 9,18,4$

Electrostats & Capacitance

In the following circuits, it is given that \mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F} and \mathrm{C}_2=4 \mu \mathrm{~F}.The time constants (in \mu \mathrm{s} ) for the circuits I, II, III are, rcspectively.

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