In an L-R circuit, the voltage is given by $V$ as $283 s i n 314 t$ . The current is found tc be $4 s i n (314 t - \frac{π}{4})$ Calculate the resistance of the circuit.

25 Ω

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50 Ω

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75 Ω

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90 Ω

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Solution

The correct option is C $50 Ω$
In L-R series circuit current lags the voltage by an angle,
$ϕ = t a n^{- 1} (\frac{X_{L}}{R})$
$ϕ = \frac{π}{4}, X_{L} = R, ω L = R$
Given, $V = 283 s i n 314 t$
Comparing with standard equation
$V = V_{0} s i n ω t$
$ω = 314$
$314 L = R$
Further $V_{0} = i_{0} | Z |$
$283 = 4 \sqrt{R^{2} + X_{L}^{2}}$
$R^{2} + (ω L)^{2} = {(\frac{283}{4})}^{2} = 5005.86$
$2 R^{2} = 5005.56$
$R = 50 Ω$

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V = 283 sin (314 t)

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