Question

When three inductors of same inductance '\(L\)' are connected in series and '\(I\)' is the current passing through the circuit. The energy stored in the circuit is

• A. \(\frac{1}{2}\text{LI}^2\)
• B. \(\frac{3}{2}\text{LI}^2\)
• C. \(\frac{5}{2}\text{LI}^2\)
• D. \(\frac{7}{2}\text{LI}^2\)

Hint:

Series inductors add directly like resistors.

Answer 1

The Correct Option is B

Concept:
Energy stored: \[ U = \frac{1}{2}L_{\text{eq}} I^2 \] Step 1: Equivalent inductance. For series connection: \[ L_{\text{eq}} = L + L + L = 3L \]
Step 2: Substitute in formula. \[ U = \frac{1}{2} \cdot 3L \cdot I^2 \] \[ U = \frac{3}{2}LI^2 \]
Step 3: Conclusion. Energy stored = \(\frac{3}{2}LI^2\)