Question

For given circuit if switch $S_1,S_2$ and $S_3$ are closed simultaneously at t = 0. Choose correct options.

• A. Current through $4\Omega$ is $\frac{5}{2}A$ at t =0.
• B. Current through $2\Omega$ is OA at t =0.
• C. Time constant of circuit is $4\mu s$.
• D. Current through $2\Omega$ at t = 0 is not zero.

Answer 1

Answer: (A), (C), (D)

The correct options are
A Current through $4\Omega$ is $\frac{5}{2}A$ at t =0.
C Time constant of circuit is $4\mu s$.
D Current through $2\Omega$ at t = 0 is not zero.


By $K-L-L\Rightarrow$
$12=4i+2(i-i^{\prime })$ -(1)
$10=4i+\frac{q}{c}-\left(2\right)$
where $i^{\prime }=\frac{dq}{dt}-\left(3\right)$

By solving (1), (2) & (3) :
$q=\frac{6C}{3}(1-e^{\frac{-3t}{4c}})\&i^{\prime }=\frac{3}{2}{e}^{\frac{-3t}{4c}}$
At $t=0,i^{\prime }=\frac{3}{2}$
& By (1) $=i=\frac{5}{2}$ at t = 0