An alternating source of emf $v = 10 \cos 100 π t$ volt is connected across a R - L series circuit. If the phase difference between the resulting current and supply voltage is $60^{o}$ and $R = 1 Ω$ , the rms value of current in the circuit is

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$\frac{5}{2 \sqrt{2}} A$

$5 A$

$5 \sqrt{2} A$

$5 / \sqrt{2} A$

answer is D.

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Detailed Solution

$\frac{ω L}{R} = \tan 60^{o} \Rightarrow ω L = \sqrt{3} R$

$∴ Z = \sqrt{R^{2} + {(ω_{L})}^{2}} = \sqrt{R^{2} + {(\sqrt{3} R)}^{2}} = 2 R = 2 Ω$

$∴ I_{r m s} = \frac{V_{r m s}}{Z} = \frac{10 / \sqrt{2}}{2} A = \frac{5}{\sqrt{2}} A$

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