PhysicsAlternating Current

Find the effective impedance in the circuit if the source is a) DC so…

Find the effective impedance in the circuit if the source is a) DC source and b) High frequency AC source.

$Figure for the question$

Answer & explanation

Correct answer: option 2

The correct answer is Option (2) → For DC, $ Z = R_1 $ and for AC, $ Z = R_2 + R_3 $

An inductor has reactance $ \omega L $ and a capacitor has reactance $ \frac{1}{\omega C} $. At d.c. ($ \omega = 0 $) an inductor is a plain wire and a capacitor is an open gap. At a very high frequency the inductor is practically an open gap and the capacitor is a plain wire.

(a) DC source

The inductors $ L_1 $, $ L_2 $ act as wires and the capacitors $ C_1 $, $ C_2 $ block the current. The upper branch carries the current through $ R_1 $ alone; the branch with $ C_2 $ is open.

$ Z = R_1 $

(b) High frequency AC source

The inductors $ L_1 $, $ L_2 $ block the current, so the upper branch carries none, while the capacitors $ C_1 $, $ C_2 $ act as wires. The current goes through the lower branch, $ C_2 $, $ R_2 $ and $ R_3 $, with $ C_2 $ shorted.

$ Z = R_2 + R_3 $