Question

Impedance of circuit when a resistance R and inductor of inductance L are connected in series in an A.C. circuit of frequency $ f $ is:

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

Answer 1

Answer: (B)

Here: Resistance $ =R, $ inductance $ =L $ and frequency of the circuit $ =f $ As the effective resistance or impedance $ Z=\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}} $ (where $ \omega = $ angular frequency of A.C circuits equal to $ 2\pi f $ ) Hence impedance $ Z=\sqrt{{{R}^{2}}+{{(2\pi f)}^{2}}{{L}^{2}}}=\sqrt{{{R}^{2}}+4{{\pi }^{2}}{{f}^{2}}{{L}^{2}}} $