Alternating Current

JEE Main level, single correct, medium

161 of 190

Question 161 of 190

For the series LCRL C R circuit connected with 220 V,50 Hz220 \mathrm{~V}, 50 \mathrm{~Hz} a.c source as shown in the figure, the power factor is α10\frac{\alpha}{10}. The value of α\alpha is ____\_\_\_\_.

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Answer: (C) 6

Net reactance: X=XC−XL=150−70=80ΩX = X_C - X_L = 150 - 70 = 80Ω.
Impedance: Z=R2+X2=602+802=10000=100ΩZ = \sqrt{R^2 + X^2} = \sqrt{60^2 + 80^2} = \sqrt{10000} = 100Ω.
Power factor: cos⁡ϕ=R/Z=60/100=0.6\cos\phi = R/Z = 60/100 = 0.6.
Since power factor is α/10\alpha/10, we have 0.6=α/100.6 = \alpha/10, so α=6\alpha = 6

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