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) \[\sqrt{R+2{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}\]
Correct Answer: B
Solution :
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 \[Z=\sqrt{{{R}^{2}}+{{(2\pi f)}^{2}}{{L}^{2}}}=\sqrt{{{R}^{2}}+4{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}\]
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