Question

The inductive reactance of a coil is \(R\ \Omega\). If the inductance of a coil is doubled and frequency of a.c. supply is also doubled then the new inductive reactance will be

• A. \(2R\)
• B. \(8R\)
• C. \(\frac{R}{2}\)
• D. \(4R\)

Hint:

Inductive reactance \(X_L = \omega L = 2\pi f L\). It is directly proportional to both frequency and inductance.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Inductive reactance \(X_L = 2\pi f L\). Initially \(X_L = R\).

Step 2: Key Formula or Approach:
\(X_L \propto fL\).

Step 3: Detailed Explanation:
Initial: \(X_{L1} = 2\pi f L = R\).
New: \(L' = 2L\), \(f' = 2f\). Then \(X_{L2} = 2\pi (2f)(2L) = 2\pi f L \times 4 = 4R\).

Step 4: Final Answer:
Option (D) is correct.