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Q.

A sinusoidal voltage $V (t) = 210 \sin 3000 t$ volt is applied to a series LCR circuit in which $L = 10$ $mH, C = 25 μF$ and $R = 100 Ω$ . The phase difference $(Φ)$ between the applied voltage and resultant current will be :

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a

$\tan^{- 1} (0.30)$

b

$\tan^{- 1} (9.46)$

c

$\tan^{- 1} (0.17)$

d

$\tan^{- 1} (13.33)$

answer is A.

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Detailed Solution

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$\begin{aligned} X_{L} = 10^{- 2} \times 3000 = 30 Ω \\ X_{C} = \frac{1}{3000 \times 25 \times 10^{- 6}} = \frac{40}{3} Ω \\ X = X_{L} - X_{C} \\ = 30 - \frac{40}{3} = \frac{50}{3} \\ \tan δ = \frac{X}{R} = \frac{50}{3 \times 100} = \frac{1}{6} \\ δ = \tan^{- 1} (\frac{1}{6}) = \tan^{- 1} (0.17) \end{aligned}$

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