Q142 / 150 · MHT CET 2026 (18 April Shift 1) · Physics
In an a.c. circuit, a resistance R is connected in series with an inductance 'L'. If phase angle between voltage and current is $45^\circ$, the value of inductive reactance will be
($\sin 45^\circ = \dfrac{1}{\sqrt{2}} = \cos 45^\circ$)
($\sin 45^\circ = \dfrac{1}{\sqrt{2}} = \cos 45^\circ$)
- A$2R$
- Correct answerB$R$
- C$\sqrt{2}R$
- D$\dfrac{1}{\sqrt{2}}R$
Solution
In a series RL circuit, the phase angle $\phi$ between the voltage and the current is given by the relation:
$\tan \phi = \dfrac{X_L}{R}$
Given that the phase angle $\phi = 45^\circ$:
$\tan 45^\circ = \dfrac{X_L}{R}$
Since $\tan 45^\circ = 1$:
$1 = \dfrac{X_L}{R}$
$X_L = R$
The inductive reactance is equal to the resistance $R$.
Answer: $R$
$\tan \phi = \dfrac{X_L}{R}$
Given that the phase angle $\phi = 45^\circ$:
$\tan 45^\circ = \dfrac{X_L}{R}$
Since $\tan 45^\circ = 1$:
$1 = \dfrac{X_L}{R}$
$X_L = R$
The inductive reactance is equal to the resistance $R$.
Answer: $R$
Hence, the correct answer is option: 'B'.