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: Use sine and cosine:
$\sin\phi = \frac{X_L}{Z}$ and $\cos\phi = \frac RZ$. At $45^{\circ}$ they are equal.

Step 2: Result:
Equal values give $X_L = R$.

Final Answer:
$X_L = R$, option (B). \[ \boxed{R} \]