Question

The potential differences across the resistor, capacitor and inductor are \(80\) V, \(40\) V and \(100\) V respectively in series LCR circuit. The power factor of this circuit is

• A. \(0.4\)
• B. \(0.5\)
• C. \(0.8\)
• D. \(1.0\)

Hint:

Find the net reactive voltage from the difference of VL and VC, then take VR over the source voltage.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a series LCR circuit \(V_L\) and \(V_C\) are in opposite phase and both are perpendicular to \(V_R\).

Step 2: Net reactive voltage
\(V_L-V_C=100-40=60\) V

Step 3: Supply voltage
\(V=\sqrt{V_R^{2}+(V_L-V_C)^{2}}=\sqrt{80^{2}+60^{2}}=100\) V

Step 4: Power factor
\(\cos\phi=\dfrac{V_R}{V}=\dfrac{80}{100}=0.8\), option (C).

Final Answer:
The power factor of the circuit is 0.8. \[ \boxed{\text{(C) }0.8} \]