Question

The impedance of a circuit, when a resistance R and an inductor of inductance L are connected in series in an AC circuit of frequency f, is

• A. $\sqrt{ R + 2 \pi^2 \, f^2 \, L^2 }$
• B. $\sqrt{ R + 4 \pi^2 \, f^2 \, L^2 }$
• C. $\sqrt{ R^2 + 4 \pi^2 \, f^2 \, L^2 }$
• D. $\sqrt{ R^2 + 2 \pi^2 \, f^2 \, L^2 }$

Answer 1

Answer: (C)

$\sqrt{ R^2 + 4 \pi^2 \, f^2 \, L^2 }$

Answer 2

In L-R circuit,
Impedance Z = $\sqrt{ R^2 + X_L^2 }$
Here, $X_L = \omega L = 2 \pi f L$
$\therefore Z = \sqrt{ R^2 + 4 \pi^2 f^2 \, L^2 }$