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
(\(sin45^{\circ} = \frac{1}{\sqrt{2}} = cos45^{\circ}\))

• A. \(2R\)
• B. \(R\)
• C. \(\sqrt{2}R\)
• D. \(\frac{1}{\sqrt{2}}R\)

Hint:

For an LR series circuit, tan of the phase angle equals X_L over R.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a series LR circuit the phase angle between voltage and current satisfies \(\tan\phi = \frac{X_L}{R}\).

Step 2: Key Formula or Approach:
Here \(\phi = 45^{\circ}\), and \(\tan 45^{\circ} = \frac{\sin 45^{\circ}}{\cos 45^{\circ}} = 1\).

Step 3: Detailed Explanation:
\[ \frac{X_L}{R} = 1 \Rightarrow X_L = R \]
Option C, \(\sqrt2 R\), is the impedance \(Z = \sqrt{R^2 + X_L^2}\) and not the reactance.
In the phasor diagram, the voltage across \(R\) and the voltage across \(L\) are equal in size when \(X_L = R\), so the resultant voltage leads the current by \(45^{\circ}\).

Final Answer:
The inductive reactance is \(R\), option (B). \[ \boxed{R} \]