Asked by clyde
7. A coil has a resistance of 50 ohms and a reactance of 70 ohms. A capacitor is connected
in parallel to produce resonance. The source voltage is 120 V. What is the power drawn
by the circuit?
in parallel to produce resonance. The source voltage is 120 V. What is the power drawn
by the circuit?
Answers
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Answered by
GPT-5 mini
At parallel resonance the capacitive susceptance cancels the inductive susceptance. For the coil Z = R + jX (R = 50 Ω, X = 70 Ω)
Admittance of the coil: Y_L = 1/(R + jX) = R/(R^2+X^2) − j X/(R^2+X^2).
Set capacitor susceptance B_C = X/(R^2+X^2) so
X_C = (R^2 + X^2)/X = (50^2 + 70^2)/70 = 7400/70 ≈ 105.71 Ω.
Total conductance at resonance G = R/(R^2+X^2) = 50/7400 = 0.00675676 S.
Power drawn P = V^2 G = 120^2 × 0.00675676 ≈ 97.3 W.
(So the circuit draws about 97.3 W; the capacitor reactance required is ≈105.7 Ω.)
Admittance of the coil: Y_L = 1/(R + jX) = R/(R^2+X^2) − j X/(R^2+X^2).
Set capacitor susceptance B_C = X/(R^2+X^2) so
X_C = (R^2 + X^2)/X = (50^2 + 70^2)/70 = 7400/70 ≈ 105.71 Ω.
Total conductance at resonance G = R/(R^2+X^2) = 50/7400 = 0.00675676 S.
Power drawn P = V^2 G = 120^2 × 0.00675676 ≈ 97.3 W.
(So the circuit draws about 97.3 W; the capacitor reactance required is ≈105.7 Ω.)
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