Q 12-07-103JEE MainJEE Main 2022 (26 Jul, Shift 1)Medium
The effective current $I$ in the given circuit at very high frequencies will be ______ A.
Numerical value type. Enter your answer.
Answer: 44
At very high frequency, inductors behave as open circuits ($X_L\to\infty$) and capacitors as short circuits ($X_C\to0$).
The top branches containing $20\ \text{mH}$ and $50\ \text{mH}$ carry no current. The vertical capacitors join each top junction to the bottom junction below it. So the current flows: $1\ \Omega$ (bottom left), then $4\ \Omega$ (top middle) in parallel with $4\ \Omega$ (bottom middle) $= 2\ \Omega$, then $2\ \Omega$ (bottom right).
$$R = 1 + 2 + 2 = 5\ \Omega,\qquad I = \frac{220}{5} = 44\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics