An inductor of reactance 100 Ω, a capacitor of reactance 50 Ω and a resistor of 50 Ω are connected in series. What is the power factor of the circuit?

In a series RLC circuit, the net impedance is given by:

Z = R + j (XL - XC)

XL = Inductive Reactance given by:

XL = ωL

XC = Capacitive Reactance given by:

\(X_C=\frac{1}{\omega C}\)

The resonance curve of the series RLC circuit is given as:

Observation:

• Below the resonance frequency, XL is low and XC is high → circuit behaves like a capacitive circuit (leading power factor)
• At the resonance frequency, XL equals to XC → circuit behaves like a purely resistive circuit (Unity power factor)
• At the above resonance frequency, XL is high and XC is low → circuit behaves like an inductive circuit (lagging power factor)

Calculation:

Given that, 

R = 50 Ω

X_L = 100 Ω 

X_C = 50 Ω 

Z = 50 + j (100-50) Ω 

|Z| = √(50² + 50²) = 70.71 Ω 

Power Factor = cos ϕ = R/Z = 50/70.71 = .7071 = 1/√2