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A 200 V, 50 Hz supply is connected to a resistance (R) of 20 Ω in series with an iron cored choke coil (r in series with L). The readings of the voltmeters connected across the resistance and the coil are 120 V and 150 V respectively. Find the resistance “r” of the coil (in ohms). Also find the power lost in the coil (in watts)
Asked by ojastej235 | 13 Nov, 2021, 12:22: PM
Expert Answer
Voltmeter connected across Resistor reads RMS voltage across resistor.
Hence RMS current in the circuit = RMS voltage / resistance = 120 V / 20 Ω = 6 A
Voltmeter connected across inductor reads RMS voltage across inductor.
Hence Inductive reactance XL = RMS voltage / RMS current = 150 V / 6 A = 25 Ω
Power delivered to circuit = V × I × cosΦ
where V = 200 volt is the RMS voltage of power supply , I = 6 A is RMS current delivered to circuit and cosΦ is the power factor.
Φ = tan-1 ( XL / R ) = tan-1 ( 25/20 ) = 51.34
Power delivered to circuit = 200 × 6 × cos(51.34) ≈ 750 W
Power dissipated in resistor = 120 V × 6 A = 720 W
Hence power lost in Inductor = ( 750 - 720 ) W = 30 W
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