Find the value of an inductance which should be connected in series with a capacitor of 5μF, a resistance of 10Ω and an ac source of 50 Hz so that the power factor of the circuit is unity.
Physics · AC Circuits
JEE Advanced

Question

Find the value of an inductance which should be connected in series with a capacitor of 5μF, a resistance of 10Ω and an ac source of 50 Hz so that the power factor of the circuit is unity.

G1 Physics · Accepted Answer

Use Z=√[R²+(Xₗ−X꜀)²], Xₗ=ωL, X꜀=1/(ωC), and P̄=VᵣₘₛIᵣₘₛcosφ with cosφ=R/Z. Substitution gives 20/π² ≈ 2 H.