For a series LCR circuit, at the condition of resonance, the value of the power factor will be:
- Zero
- 1
- 0.2
- 0.5
The Correct Option is B
Approach Solution - 1
In a series LCR circuit, resonance occurs when the inductive reactance equals the capacitive reactance, effectively canceling each other out. At this point, the circuit's impedance is purely resistive. The power factor, which is defined as the cosine of the phase angle between the voltage and current, is given by:
Power Factor \((PF) = cos(ϕ)\)
At resonance, the phase difference ϕ is zero because the current and voltage are in phase. This leads to:
\(PF = cos(0) = 1\)
Therefore, at the condition of resonance in a series LCR circuit, the value of the power factor is 1.
Approach Solution -2
Series LCR Circuit at Resonance:
- At resonance: Inductive reactance (XL) = Capacitive reactance (XC)
- Net impedance becomes purely resistive: Z = R (minimum impedance)
- Phase difference (φ) between current and voltage becomes zero
Power Factor Calculation:
Power factor = cosφ = R/|Z|
At resonance:
|Z| = √[R² + (XL - XC)²] = R (since XL = XC)
∴ Power factor = cosφ = R/R = 1
Final Answer: The power factor will be 1 (unity) at resonance.
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