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If a resistance of \(100\ \Omega\), inductance of \(0.5\) henry, and capacitance of \(6\times10^{-6}\) F are connected in series to a 50 Hz AC supply, then the impedance is

1. 1.876
2. 18.76
3. 189.72
4. 101.3

Correct answer: 189.72

Solution

For a series LCR circuit, impedance is \(Z=\sqrt{R^2+(X_L-X_C)^2}\). With \(\omega=2\pi f\), the reactances are very different, so the net reactance is large and the impedance comes out to about 189.72 \(\Omega\).

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