a series RLC with a resistance of 400 ohm has capacitive and inductive reactance

Question

a series RLC with a resistance of 400 ohm has capacitive and inductive reactances of 300 ohms and 500 ohms respectively. If the circuit operates at 60 Hz, what are the values of the capacitance and inductance? What is the power factor of the circuit? If an additional capacitor were connected to the capacitor in the circuit, what would the value of that new capacitor be to achieve a power factor of one?

Explanation / Answer

1/wC = 300 ; w = 2*pi*f = 2*pi*60 = 376.99 C = 1/(376.99*300) = 8.8419 uF wL = 500 L = 500/376.99 = 1.3263 H power factor = acos(400/ sqrt(400^2 + (500-300)^2) ) p.f. = acos(400/447.213) = .8944 for p.f = 1; wL = 1/wC ==> 1/wC = 500 C = 1/376.99*500 = 5.305 additional capacitance should be in series and its value be C 8.8419*C = (8.8419 + C)*5.305 ==> C = 13.26 uF

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