A 10 mH inductor, a 0 .1 a_0.1 a 0 .1 μF capacitor and a 100 Ω resistor are connected in series across a 220 V, 70 Hz AC source. The power factor of the circuit is 0.5. If the magnitude of the difference between the inductive and capacitive reactances is √3 α Ω, find α.
Physics · AC Circuits · Series AC Circuits: Impedance, Phase Difference, Resonance and Power Factor
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Question

A 10 mH inductor, a 0 .1 a_0.1 a 0 ​ .1 μF capacitor and a 100 Ω resistor are connected in series across a 220 V, 70 Hz AC source. The power factor of the circuit is 0.5. If the magnitude of the difference between the inductive and capacitive reactances is √3 α Ω, find α.

G1 Physics · Accepted Answer

For a series LCR circuit, cosφ = R ÷ Z. Given, cosφ = 0.5, so φ = 60°. Also, tanφ = |X(L)-X(C)| ÷ R. Therefore, |X(L)-X(C)| = R tan60° = 100√3 Ω. Given, |X(L)-X(C)| = √3 α Ω. Hence, α = 100.

A 10 mH inductor, a 0 .1 a_0.1 a 0 ​ .1 μF capacitor and a 100 Ω resistor are connected in series across a 220 V, 70 Hz AC source. The power factor of the circuit is 0.5. If the magnitude of the difference between the inductive and capacitive reactances is √3 α Ω, find α.

A 10 mH inductor, a 0 .1 a_0.1 a 0 .1 μF capacitor and a 100 Ω resistor are connected in series across a 220 V, 70 Hz AC source. The power factor of the circuit is 0.5. If the magnitude of the difference between the inductive and capacitive reactances is √3 α Ω, find α.