JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Alternating Current

At very high frequency each capacitor behaves as a short ($X_C=1/\omega C\to 0$) and the inductor as an open circuit ($X_L=\omega L\to \infty$). The lower-left branch containing the $20$ H coil is broken and carries no current. The upper-left branch reduces to its $1\Omega$ resistor, its capacitor shorted. The central capacitor shorts the two middle nodes together, placing the two $2\Omega$ resistors of the right-hand branches in parallel, This $1\Omega$ is in series with the left $1\Omega$, so the effective impedance is $2\Omega$.