Reluctance from MMF and flux: A wire with 40 turns carries 900 mA. If the resulting magnetic flux is 400 µWb, find the magnetic circuit reluctance.

Introduction / Context:
In magnetic circuits, reluctance relates the applied magnetomotive force (MMF) to the resulting flux, analogous to resistance relating voltage to current. When MMF and flux are known, reluctance directly characterizes the magnetic path's opposition to flux.

Given Data / Assumptions:

• Number of turns, N = 40.
• Current, I = 900 mA = 0.9 A.
• Flux, phi = 400 µWb = 400 * 10^-6 Wb = 4 * 10^-4 Wb.
• Uniform linkage and steady-state conditions.

Concept / Approach:

Reluctance is ℜ = MMF / phi, where MMF = N * I in ampere–turns. Compute MMF, then divide by flux to obtain ℜ in At/Wb.

Step-by-Step Solution:

Verification / Alternative check:

Unit check: At/Wb is correct for reluctance. The value is large, consistent with modest flux produced by a sizeable MMF, indicating a relatively reluctant magnetic path.

Why Other Options Are Wrong:

14,400, 9,000, and 1,440 At/Wb result from misplacing decimal points or incorrect flux conversion. 144 At/Wb is orders of magnitude too small.

Common Pitfalls:

Forgetting that 400 µWb is 4e-4 Wb; using 400e-6 incorrectly in a calculator can lead to factor-of-10 errors. Always standardize units first.

Final Answer:

90,000 At/Wb