Question

The magnetic potential energy stored in a certain inductor is \(49 \text{mJ}\) when the current in the inductor is \(70 \text{mA}\). The inductance of the inductor is

• A. \(0.20 \text{H}\)
• B. \(2.0 \text{H}\)
• C. \(20 \text{H}\)
• D. \(200 \text{H}\)

Hint:

Use U = (1/2) L I squared.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The energy stored in an inductor is \(U = \frac12 LI^2\).

Step 2: Key Formula or Approach:
Rearrange: \(L = \frac{2U}{I^2}\). Use SI units: \(U = 49\ \text{mJ} = 0.049\) J and \(I = 70\ \text{mA} = 0.07\) A.

Step 3: Detailed Explanation:
\[ L = \frac{2 \times 0.049}{(0.07)^2} = \frac{0.098}{0.0049} = 20\ \text{H} \]
The options \(0.2\), \(2.0\) and \(200\) H differ by powers of \(10\) and come from slips in converting milli units.

Final Answer:
The inductance is \(20\) H, option (C). \[ \boxed{20\ \text{H}} \]