Discussion
An AC circuit with R= 2π2 Ω and L=0.02 π H powered with an a.c. source of frequency 50 Hz has an impedance of
Answer: B
The impedance is \(2\sqrt{2}\,\pi^{2}\ \Omega\).
First find the inductive reactance, then combine it with R.
\[ \begin{aligned} X_L &= 2\pi f L = 2\pi \times 50 \times 0.02\pi \\ &= 2\pi^{2}\ \Omega \\ Z &= \sqrt{R^{2} + X_L^{2}} = \sqrt{2}\times 2\pi^{2} \end{aligned} \]
R and \(X_L\) are equal, so the impedance is \(\sqrt{2}\) times either. \(2\pi^{2}\ \Omega\) is R or \(X_L\) alone, and the other options drop a factor of \(\pi\).
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