Question #200845

A series R L circuit is connected to a 110V, 50 Hz ac source. If the voltage across the resistor is 85 V,

find the power dissipated in the circuit, if the value of inductor is 0.05 H

Expert's answer

Let us introduce the notation

"U=110 V,f=50 Hz, U_R=85 V, L=0.05H"

1).Determine the resistance of the inductor

"X_L=2 \\cdot \\pi \\cdot f \\cdot L=2 \\cdot 3.14 \\cdot 50 \\cdot 0.05=15.71 \\Omega"

2).Determine the voltage across the inductor

"U_L=\\sqrt{U^2-U_R^{2}}=\\sqrt{110^2-85^{2}}=\\sqrt{12100-7225}=69.82V"

3).Determine the current in the circuit

"I=\\frac{U_L}{X_L}=\\frac{69.82}{15.71}=4.45A"

4).Determine the total power of the circuit

"S=U \\cdot I=110 \\cdot4.45=489.5VA"

5).Determine the reactive power of the circuit

"Q=I^2 \\cdot X_L=4.45^2 \\cdot 15.71=311.1var"

5).Determine the active power dissipated in the circuit

"P=\\sqrt{S^2-Q^{2}}=\\sqrt{489.5^2-311.1^{2}}=377.93W"

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