Using the electrical–magnetic circuit analogy, permeability (a material property that facilitates magnetic flux) is most closely analogous to which electrical quantity (the inverse counterpart to resistance)?

Introduction / Context:
Magnetic circuits can be analyzed using an analogy to electric circuits. In this analogy, magnetomotive force (MMF) corresponds to voltage, flux Φ to current, reluctance to resistance, and permeance to conductance. Understanding where permeability fits helps engineers reason about core materials and flux paths.

Given Data / Assumptions:

• We use the standard analogy: Φ ↔ I, MMF ↔ V, reluctance ℜ ↔ R, permeance ↔ G.
• Permeability μ is a material property appearing in permeance: P = μ * A / l.
• We are choosing the electrical quantity that plays the inverse role of resistance.

Concept / Approach:
Reluctance ℜ = l / (μ * A) opposes magnetic flux, directly analogous to resistance R = l / (σ * A) in conductors. Its inverse is permeance P = μ * A / l, which is analogous to electrical conductance G = σ * A / l. Since permeability μ multiplies into permeance, μ aligns with the “conductive” side of the analogy. Thus, the closest electrical counterpart—in the sense of being inverse to resistance—is conductance.

Step-by-Step Solution:
Write magnetic reluctance: ℜ = l / (μ * A).Write electrical resistance: R = l / (σ * A).Take inverses: P = 1/ℜ = μ * A / l and G = 1/R = σ * A / l.Therefore, permeability (μ) corresponds to conductance-type behavior (via permeance).

Verification / Alternative check:
Higher μ reduces reluctance just as higher conductivity increases conductance (reducing resistance). Both promote “flow” (flux for magnetics; current for electrics).

Why Other Options Are Wrong:
Resistance is analogous to reluctance, the opposite role of permeability.

Voltage and current correspond to MMF and flux, respectively, not to μ.

Capacitance does not map directly into this particular magnetic property analogy.

Common Pitfalls:
Confusing permeability with permeance. Permeability is a material property (like conductivity), while permeance is a geometric/material combination (like conductance).

Final Answer:
Conductance