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ConceptPower in Ac Circuit: the Power Factor

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#### Question

(i) An a.c. source of voltage V = V_{0} sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expression for impedance of a circuit and the phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit, X_{L} = R and power factor of the circuit is P_{1}. When capacitor with capacitance C such that X_{L} = X_{C} is put in series, the power factor becomes P_{2}. Calculate P_{1}/P_{2}

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