Inductor energy dependence on current: When the current through an inductor is reduced to half its original value, how does the stored magnetic energy change?

Introduction / Context:
Energy storage in inductors underpins power conversion, snubbers, and resonant circuits. The relationship between current and stored energy is quadratic, not linear, and mixing these up leads to major design errors. This question checks that you remember the exact current-squared dependence.

Given Data / Assumptions:

• Ideal inductor with inductance L (constant).
• Initial current I; then current is reduced to I/2.
• No losses considered during the change for the purpose of comparing stored energy values.

Concept / Approach:
The magnetic energy stored in an inductor is W = 0.5 * L * I^2. If current changes by a factor k, the energy scales by k^2. Halving current (k = 0.5) therefore reduces energy by (0.5)^2 = 0.25, i.e., one quarter of the original.

Step-by-Step Solution:

Verification / Alternative check:
Pick L = 1 H, I = 2 A for a quick check: W1 = 0.514 = 2 J. With I/2 = 1 A, W2 = 0.511 = 0.5 J = 2/4, confirming the quartering effect.

Why Other Options Are Wrong:

• Quadruples or doubles: These imply increasing, not reducing, energy.
• Does not change: Contradicts the I^2 dependence; energy must change when current changes.

Common Pitfalls:

• Assuming linear energy-current relation instead of quadratic.
• Confusing inductive energy with capacitor energy (which also uses a squared term, but in voltage).

Final Answer:
is quartered