What is the inductance (L) of an inductor whose reactance is 1Ω at 50/ π hertz (H)?

1. Analyze the question

We are given:

• Inductive Reactance ($X_L$) = $1 \, \Omega$
• Frequency ($f$) = $\frac{50}{\pi} \, \text{Hz}$
• We need to find the Inductance ($L$).

2. Explain the concept

In an AC circuit, the inductive reactance ($X_L$) is the opposition offered by an inductor to the flow of alternating current. The formula relating these variables is:

Where:

• $X_L$ is the inductive reactance in Ohms ($\Omega$)
• $f$ is the frequency in Hertz (Hz)
• $L$ is the inductance in Henry (H)

3. Show the solution

Step 1: Substitute the given values into the formula:

Step 2: Simplify the right side of the equation. Notice that the $\pi$ in the numerator and the $\pi$ in the denominator cancel each other out:

Step 3: Solve for $L$ by dividing both sides by 100:

4. Identify the answer

Comparing our result to the given options, $0.01 \, \text{H}$ corresponds to option B.

5. Tip

When dealing with AC circuit formulas involving frequency, always look for opportunities to cancel out $\pi$. In many JAMB physics questions, the frequency is intentionally given as a fraction of $\pi$ (like $50/\pi$ or $100/\pi$) specifically to make the calculation easier by canceling the $\pi$ in the $2\pi fL$ or $1/2\pi fC$ formulas.