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  4. Find the time constant for the given RC circuits in correct order (in μ s). R1=1 Ω, R2=2 Ω, C1=4 μ F,C2=2 μ F .

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Q. Find the time constant for the given RC circuits in correct order (in $\mu s). $
$R_1=1 \Omega, R_2=2 \Omega, C_1=4 \mu F,C_2=2 \mu F . $Physics Question Image

IIT JEEIIT JEE 2006Electrostatic Potential and Capacitance

Solution:

$\tau =CR $
$\tau_1 =(C_1+C_2)(R_1+R_2)=18 \mu s $
$\tau_2 =\bigg (\frac {C_1C_2}{C_1+C_2} \bigg )\bigg (\frac {R_1R_2}{R_1+R_2} \bigg )= \frac {8}{6} \times \frac {2}{3}= \frac {8}{9} \mu s $
$\tau_3 =(C_1+C_2) \bigg (\frac {R_1R_2}{R_1+R_2}\bigg )=(6) \bigg (\frac {2}{3}\bigg )=4 \mu s $