Question

An alternating current of frequency ′f′ is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit is

1. \(\sqrt {{R^2} + 4{\pi ^2}{f^2}{L^2}} \)
2. R + 2πfL
3. \(\sqrt {{R^2} + {L^2}} \)
4. \(\sqrt {{R^2} + 2\pi fL} \)

Answer 1

Correct Answer - Option 1 : \(\sqrt {{R^2} + 4{\pi ^2}{f^2}{L^2}} \)

Choke coil is simply a coil having a large inductance but a small resistance. This make a simple LR circuit with impedence

\(Z\; = \;\sqrt {{R^2} + {\omega ^2}{L^2}} \; = \;\sqrt {{R^2} + 4{\pi ^2}{f^2}{L^2}} \)

By using the choke coil, the voltage across the resistor is reduced by a factor of \(\frac{R}{{\sqrt {{R^2} + {\omega ^2}{L^2}} }}\)