Question

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 ($\tan 45^\circ = 1$) ______.

• A. $R$
• B. $R/2$
• C. $R/4$
• D. $R/\sqrt{2}$

Hint:

When resistance and reactance are perfectly equal in an AC circuit ($R = X_L$ or $R = X_C$), the phase angle is always exactly $45^\circ$ ($\pi/4$ radians), and the power factor is $\cos(45^\circ) = 1/\sqrt{2} = 0.707$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In an L-R series circuit, the phase angle $\phi$ between the voltage and the current is determined by the ratio of reactance to resistance.

Step 2: Formula Application:
The formula for the phase angle is $\tan \phi = \frac{X_L}{R}$.

Step 3: Explanation:
Given $\phi = 45^\circ$ and $\tan 45^\circ = 1$. $1 = \frac{X_L}{R} \implies X_L = R$.

Step 4: Final Answer:
The inductive reactance is equal to $R$.