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Alternating Current

Question

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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

$\sqrt{R + 2 π^{2} f^{2} L^{2}}$

$\sqrt{R + 4 π^{2} f^{2} L^{2}}$

$\sqrt{R^{2} + 4 π^{2} f^{2} L^{2}}$

$\sqrt{R^{2} + 2 π^{2} f^{2} L^{2}}$

Solution

C.

$\sqrt{R^{2} + 4 π^{2} f^{2} L^{2}}$

In L-R circuit,

Z = $\sqrt{R^{2} + {(X_{L})}^{2}}$

Here, $X_{L} = ω L = 2 π f L$

⇒ $Z = \sqrt{R^{2} + 4 π^{2} f^{2} L^{2}}$

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