When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be . The power dissipated in the circuit is ______ W.

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Solution

Q.
When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be $20 \sqrt{3} Ω$ . The power dissipated in the circuit is ______ W. [2024]

Ans.
(250)

$For DC voltage, R = \frac{V}{i} = \frac{100}{5} = 20 Ω$

$For AC voltage, X_{L} = 20 \sqrt{3} Ω, R = 20 Ω$

$Z = \sqrt{X_{L}^{2} + R^{2}} = \sqrt{3 \times 400 + 400} = 40 Ω$

$Power dissipated, P = i_{r m s} V_{r m s} \cos ϕ$

$P = \frac{V_{r m s}^{2}}{Z} \cdot \cos ϕ = \frac{{(\frac{200}{\sqrt{2}})}^{2}}{40} \times \frac{1}{2} = \frac{2 \times 10000}{40} \times \frac{1}{2} \Rightarrow P = 250 W$

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