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In the circuit diagram shown, initially ...

In the circuit diagram shown, initially there is no energy in the inductor and the capacitor, The switch is closed at `t = 0`. Find the current `I` as a function of time if `R=sqrt(L//C)`

Text Solution

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`tau_L=L/R`
and `tau_C=CR, tau_C/tau_L=(CR^2)/L=C/L.L/C=1`
`:. tau_L=tau_C`
`:.` From the given condition `tau_L=tau_C=tau(say)`
Now, in L-R circuit
`I_1=V/R(1-e^(-t//tau))`
In `CR` circuit, `I_2=V/Re^(-t//tau)`
`:. I=I_1+I_2=V/R=`constant.
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