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 Question:
We have a series AC circuit with a resistor and an inductor. We are given the phase angle difference between the total voltage and the current, and must find the relationship between inductive reactance ($X_L$) and resistance ($R$).

Step 2: Key Formula or Approach:
The phase angle $\theta$ in a series LR circuit is determined by the ratio of the inductive reactance to the resistance, visualized using an impedance triangle.
$$\tan \theta = \frac{X_L}{R}$$

Step 3: Detailed Explanation:
The given phase angle is $\theta = 45^\circ$.
Substitute this into the tangent formula:
$$\tan(45^\circ) = \frac{X_L}{R}$$
The problem helpfully reminds us that $\tan(45^\circ) = 1$:
$$1 = \frac{X_L}{R}$$
Multiply both sides by $R$:
$$X_L = R$$

Step 4: Final Answer:
The inductive reactance is exactly equal to $R$, matching option (a).