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: Understand the question.
A coil has inductive reactance $R$. The inductance is doubled and the supply frequency is also doubled. We find the new reactance.
Step 2: Recall the reactance formula.
Inductive reactance is \[ X_L = 2\pi f L, \] where $f$ is frequency and $L$ is inductance.
Step 3: Note the original value.
Originally $X_L = 2\pi f L = R$.
Step 4: Apply the changes.
New frequency is $2f$ and new inductance is $2L$, so \[ X_L' = 2\pi(2f)(2L). \]
Step 5: Simplify.
\[ X_L' = 4\times(2\pi f L) = 4R. \]
Step 6: State the answer.
The new inductive reactance is $4R$. \[ \boxed{X_L' = 4R} \]