(i) When the length of the material increases, what happens to reluctance? (ii) When the area of cross-section

Question

(i) When the length of the material increases, what happens to reluctance? (ii) When the area of cross-section of the material increases, what happens to reluctance?

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Option A: (i) Increase (ii) Decrease

Explanation & Concepts:
Reluctance ($\mathcal{R}$) in a magnetic circuit is the opposition offered to the setting up of magnetic flux. It is directly proportional to the length of the magnetic path ($l$) and inversely proportional to the cross-sectional area ($A$). Therefore, increasing the length increases reluctance, while increasing the cross-sectional area decreases reluctance.

Working Principle: Magnetic reluctance is the magnetic equivalent of electrical resistance. Just as resistance increases with conductor length and decreases with cross-sectional area ($R = ho l / A$), magnetic reluctance follows the exact same geometric relationships due to the distribution of flux lines in the core material.

Key Formulas: $\mathcal{R} = \frac{l}{\mu A} = \frac{l}{\mu_0 \mu_r A}$ — Reluctance formula showing direct relationship with length ($l$) and inverse relationship with area ($A$); $\mathcal{R} = \frac{	ext{MMF}}{\Phi}$ — Magnetic reluctance expressed as Magnetomotive Force per unit flux

Key Points: Reluctance is directly proportional to the magnetic path length ($l$).; Reluctance is inversely proportional to the cross-sectional area ($A$).; The unit of reluctance is $A\cdot t/Wb$ (Ampere-turns per Weber) or $H^{-1}$ (per Henry).

Advantages: Minimizing path length reduces total reluctance, leading to higher magnetic flux density.; Increasing cross-sectional area lowers reluctance, preventing magnetic saturation in cores.

Disadvantages: High reluctance requires higher MMF (more turns or current) to produce the required magnetic flux.; Air gaps in magnetic circuits drastically increase total reluctance due to low permeability.

Applications: Designing transformer cores with optimized magnetic path lengths and large cross-sections to reduce reluctance.; Designing air gaps in electrical machines and inductors to control magnetic circuit reluctance and store energy.

Additional Info: Permeability ($\mu$) represents how easily a material allows magnetic lines of force to pass through it, serving as the inverse analog to resistivity.. Option B incorrectly states that reluctance increases with area.. Option C incorrectly states that reluctance decreases with length.. Option D is incorrect as reluctance is non-constant with respect to physical dimension changes.

Answer: A is correct — Reluctance increases with an increase in length ($\mathcal{R} \propto l$) and decreases with an increase in cross-sectional area ($\mathcal{R} \propto 1/A$).

Exam Tip: Reluctance in magnetic circuits is analogous to resistance in electrical circuits ($R = ho l / A$). Remembering this direct analogy helps solve magnetic field questions rapidly without memorizing duplicate formulas.

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Option B: (i) Increase (ii) Increase

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Option C: (i) Decrease (ii) Increase

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Option D: (i) Constant (ii) Constant

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