Q 12-07-114JEE MainJEE Main 2021 (31 Aug, Shift 2)Medium
At very high frequencies, the effective impedance of the given circuit will be ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 2
At very high frequency, $X_C = \dfrac{1}{\omega C} \to 0$ (capacitors act as wires) and $X_L = \omega L \to \infty$ (inductor acts as an open circuit).
The lower $1\ \Omega$ leads only to the open inductor, so it carries no current.
Current flows through the upper $1\ \Omega$, then through the middle capacitor (now a wire) which joins the two branches, and then through the two $2\ \Omega$ resistors in parallel ($1\ \Omega$).
$Z = 1 + 1 = 2\ \Omega$.
Solution by Sreeraj P, M.Sc Physics