Q143 / 150 · MHT CET 2026 (11 April Shift 2) · Physics
In an a.c. circuit containing L, C and R in series, the ratio of apparent power to the true power is
(Z= impedance of the circuit and R= resistance )
(Z= impedance of the circuit and R= resistance )
- A$RZ$
- B$\cos \phi$
- C$\cot \phi$
- Correct answerD$\dfrac{Z}{R}$
Solution
Apparent power is given by $P_{app} = V_{rms} I_{rms}$
True power is given by $P_{true} = V_{rms} I_{rms} \cos \phi$
The ratio of apparent power to true power is $\dfrac{P_{app}}{P_{true}} = \dfrac{V_{rms} I_{rms}}{V_{rms} I_{rms} \cos \phi} = \dfrac{1}{\cos \phi}$
In a series LCR circuit, the power factor is $\cos \phi = \dfrac{R}{Z}$
Substituting this value, the ratio becomes $\dfrac{Z}{R}$
Answer: $\dfrac{Z}{R}$
True power is given by $P_{true} = V_{rms} I_{rms} \cos \phi$
The ratio of apparent power to true power is $\dfrac{P_{app}}{P_{true}} = \dfrac{V_{rms} I_{rms}}{V_{rms} I_{rms} \cos \phi} = \dfrac{1}{\cos \phi}$
In a series LCR circuit, the power factor is $\cos \phi = \dfrac{R}{Z}$
Substituting this value, the ratio becomes $\dfrac{Z}{R}$
Answer: $\dfrac{Z}{R}$
Hence, the correct answer is option: 'D'.