Question

If $0.1$ J of energy is stored for the flow of current of $0.2$ A in an inductor, then its inductance value is

• A. $5$ H
• B. $0.5$ H
• C. $5$ mH
• D. $50$ H
• E. $50$ mH

Hint:

Energy in inductor = $\frac{1}{2}LI^2$ → always remember square of current.

Answer 1

The Correct Option is A

Concept: Energy stored in an inductor
When current flows through an inductor, energy is stored in its magnetic field. This energy is given by: \[ U = \frac{1}{2} L I^2 \] where:
• $U$ = energy stored
• $L$ = inductance
• $I$ = current ---

Step 1: Identify given values \[ U = 0.1 \text{ J}, \quad I = 0.2 \text{ A} \] ---

Step 2: Substitute into formula \[ 0.1 = \frac{1}{2} L (0.2)^2 \] ---

Step 3: Simplify current term \[ (0.2)^2 = 0.04 \] So: \[ 0.1 = \frac{1}{2} L \times 0.04 \] ---

Step 4: Solve step-by-step \[ 0.1 = 0.02L \] \[ L = \frac{0.1}{0.02} \] \[ L = 5 \] ---

Step 5: Units Since SI units are used: \[ L = 5 \text{ H} \] --- Physical Interpretation:
• Larger inductance → more energy stored for same current
• Energy grows with square of current ($I^2$)
• Even small current can store energy if inductance is large --- Final Answer: \[ \boxed{5 \text{ H}} \]