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Question

# A circuit, containing an inductance and a resistance connected in series, has an AC source of 200 V,50 Hz connected across it. An AC rms current of 10 A flows through the circuit and the power loss is measured to be 1 kW. Then

A
The inductance of the circuit is 310π H.
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B
The frequency of the AC when the phase difference between the current and emf becomes π4, with the above components is 503Hz
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C
The frequency of AC, at which the reactive power is half of the actual power lost is 253Hz
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D
The frequency of the AC when the phase difference between the current and emf becomes π4, with the above components is 253Hz.
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Solution

## The correct options are A The inductance of the circuit is √310π H. B The frequency of the AC when the phase difference between the current and emf becomes π4, with the above components is 50√3Hz C The frequency of AC, at which the reactive power is half of the actual power lost is 25√3Hz (A) The power loss in the circuit is Ploss=Vrms×Irmscosϕ=200×10×cosϕ=1000 W cosϕ=12 ∴ϕ=π3 (since, the circuit element is an inductor) The inductance in the circuit is calculated as follows: XL=20010×sinπ3=10√3 ∴L=10√32π×50=√310π H (B) I=VZ 10=200√X2L+R2 400=X2L+R2, ∵XL=√3R 4R2=400 ⇒R=10 Ω ωLR=tanπ4=1 2πf×√310π×110=1 f=50√3Hz. (C)PreactivePloss=12=tanϕ=ωLR ∴f=25√3Hz, which is half of the previous value.

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