Q194 / 200 · MHT CET - Medical 2026 (23 April Shift 2) · Physics
The potential differences across the resistor, capacitor and inductor are $80$ V, $40$ and $100$ V respectively in series LCR circuit. The power factor of this circuit is
- A$0.4$
- B$0.5$
- Correct answerC$0.8$
- D$1.0$
Solution
Given $V_R = 80$ V, $V_C = 40$ V, and $V_L = 100$ V.
The total voltage $V$ across the series LCR circuit is given by:
$V = \sqrt{V_R^2 + (V_L - V_C)^2}$
Substituting the given values:
$V = \sqrt{80^2 + (100 - 40)^2}$
$V = \sqrt{80^2 + 60^2}$
$V = \sqrt{6400 + 3600} = \sqrt{10000} = 100$ V
The power factor of the circuit is:
$\cos \phi = \dfrac{V_R}{V}$
$\cos \phi = \dfrac{80}{100} = 0.8$
Answer: $0.8$
The total voltage $V$ across the series LCR circuit is given by:
$V = \sqrt{V_R^2 + (V_L - V_C)^2}$
Substituting the given values:
$V = \sqrt{80^2 + (100 - 40)^2}$
$V = \sqrt{80^2 + 60^2}$
$V = \sqrt{6400 + 3600} = \sqrt{10000} = 100$ V
The power factor of the circuit is:
$\cos \phi = \dfrac{V_R}{V}$
$\cos \phi = \dfrac{80}{100} = 0.8$
Answer: $0.8$
Hence, the correct answer is option: 'C'.