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Q.

The virtual current of 4 A and 50 Hz flows in an AC circuit containing coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, then its resistance will be

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a

$\frac{1}{π} Ω$

b

$\frac{1}{3 π} Ω$

c

$\frac{1}{5 π} Ω$

d

$15 Ω$

answer is C.

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Detailed Solution

$Power = ε_{r} I_{r} \cos ϕ and \cos ϕ = \frac{R}{Z}$

$Power = 240 = 100 \times 4 cosϕ cosϕ = 0.6$

$Z = V \div I = 25$

$\cos ϕ = 0.6 = \frac{R}{25} R = 15 Ω$

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