Q. 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) $\sqrt{R^{2} + 2\pi^{2}\ f^{2}\ L^{2}}$
Explanation
(c) In L – R circuit, impedance
$Z = \sqrt{R^{2} + X_{L}^{2}}$
Here, $X_{L} = \omega L = 2\pi\ fL$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z = \sqrt{R^{2} + 4\pi^{2}\ f^{2}L^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.