A coil having an inductance of 1π henry is connected in series with a resistance of 300 Ω. If 20 V 200 Hz AC source is applied across the combination, the phase angle between the voltage and the current is

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A coil having an inductance of $\frac{1}{π}$ henry is connected in series with a resistance of 300 $Ω$ . If 20 V 200 Hz AC source is applied across the combination, the phase angle between the voltage and the current is

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tan^-1 $\frac{5}{4}$

tan^-1 $\frac{4}{3}$

tan^-1 $\frac{4}{5}$

tan^-1 $\frac{3}{4}$

answer is D.

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Detailed Solution

$X_{L} = 2 πfL = 2 π \times 200 \times \frac{1}{π} = 400 Ω$

$∴ \tan ϕ = \frac{X_{L}}{R} = \frac{400}{300} = \frac{4}{3} \Rightarrow ϕ = \tan^{- 1} (\frac{4}{3})$

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