Q70 / 75 · JEE Main 2026 (06 April Shift 1) · Physics
A LCR series circuit driven with $E_{rms} = 90$ V at frequency $f_d = 30$ Hz has resistance $R = 80\,\Omega$, an inductance with inductive reactance $X_L = 20.0\,\Omega$ and capacitance with capacitive reactance $X_C = 80.0\,\Omega$. The power factor of the circuit is _______.
- Correct answerA$0.8$
- B$0.64$
- C$0.9$
- D$0.5$
Solution
The impedance of the LCR series circuit is given by $Z = \sqrt{R^2 + (X_C - X_L)^2}$.
Substituting the given values:
$Z = \sqrt{80^2 + (80 - 20)^2}$
$Z = \sqrt{80^2 + 60^2}$
$Z = \sqrt{6400 + 3600} = \sqrt{10000} = 100\,\Omega$
The power factor of the circuit is given by $\cos \phi = \dfrac{R}{Z}$.
$\cos \phi = \dfrac{80}{100} = 0.8$
Answer: $0.8$
Substituting the given values:
$Z = \sqrt{80^2 + (80 - 20)^2}$
$Z = \sqrt{80^2 + 60^2}$
$Z = \sqrt{6400 + 3600} = \sqrt{10000} = 100\,\Omega$
The power factor of the circuit is given by $\cos \phi = \dfrac{R}{Z}$.
$\cos \phi = \dfrac{80}{100} = 0.8$
Answer: $0.8$
Hence, the correct answer is option: 'A'.