Question

The potential differences across the resistance, capacitance and inductance are $80\, V$, $40\, V$ and $100\, V$ respectively in an $L-C-R$ circuit . The power factor of this circuit is

• A. 0.4
• B. 0.5
• C. 0.8
• D. 1

Answer 1

The Correct Option is C

Cosine of Phase Angle Calculation 

The cosine of the phase angle \( \phi \) is given by the formula:

\(\cos\phi = \frac{V_R}{V_{net}} = \frac{V_R}{\sqrt{(V_L - V_C)^2 + V_R^2}}\)

Substituting the given values:

\(= \frac{80}{\sqrt{(100 - 40)^2 + 80^2}} = \frac{80}{100} = 0.8\)

Conclusion:

The value of \( \cos\phi \) is \( 0.8 \).

Answer 2

Answer: 0.8

Explanation:

The power factor in an LCR circuit is given by:

\(\cos \phi = \frac{V_R}{V}\)

Where:

• \(V_R = 80\, V\) (voltage across the resistor)
• \(V_C = 40\, V\) (voltage across the capacitor)
• \(V_L = 100\, V\) (voltage across the inductor)
• \(V\) is the net voltage across the whole circuit

Net voltage across the circuit is found using the formula:

\(V = \sqrt{V_R^2 + (V_L - V_C)^2}\)

Substitute the values:

\(V = \sqrt{80^2 + (100 - 40)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100\, V\)

Now calculate power factor:

\(\cos \phi = \frac{V_R}{V} = \frac{80}{100} = 0.8\)