In electromagnetism of parallel magnetic circuits, the reluctance offered for two parallel paths will be _____

Question

In electromagnetism of parallel magnetic circuits, the reluctance offered for two parallel paths will be _________.

Examoogle · Accepted Answer

The correct answer is Option B: half for each path. In magnetic circuits, when two identical reluctance paths are connected in parallel, the total equivalent reluctance of the circuit is halved. This follows the same mathematical principle as resistors connected in parallel in an electric circuit.

Step-by-Step Solution & Concepts:
In magnetic circuits, when two identical reluctance paths are connected in parallel, the total equivalent reluctance of the circuit is halved. This follows the same mathematical principle as resistors connected in parallel in an electric circuit.

Working Principle: Reluctance is defined as the opposition to magnetic flux, given by $\mathcal{R} = \frac{l}{\mu A}$. When two parallel paths of equal reluctance $\mathcal{R}$ are provided, the equivalent reluctance $\mathcal{R}_{eq}$ is calculated as $\frac{1}{\mathcal{R}_{eq}} = \frac{1}{\mathcal{R}} + \frac{1}{\mathcal{R}}$, resulting in $\mathcal{R}_{eq} = \frac{\mathcal{R}}{2}$.

Key Formulas: $\mathcal{R} = \frac{l}{\mu A}$ — Formula for reluctance where $l$ is length, $\mu$ is permeability, and $A$ is cross-sectional area; $\frac{1}{\mathcal{R}_{eq}} = \sum \frac{1}{\mathcal{R}_i}$ — Equivalent reluctance for parallel magnetic circuits

Key Points: Reluctance is analogous to electrical resistance in an electric circuit.; Magnetic flux $\Phi$ is analogous to electric current $I$.; Magnetomotive force (MMF) is analogous to electromotive force (EMF) or voltage.; For parallel paths, the total reluctance decreases, thereby increasing the total flux for a constant MMF.

Advantages: Reduces total circuit reluctance; Increases total magnetic flux carrying capacity

Disadvantages: Requires more magnetic material; Increased risk of leakage flux

Applications: Transformers with multi-limb cores; Electrical machines (stator and rotor magnetic paths)

Additional Info: The analogy is derived from the Hopkinson's law of magnetic circuits, which mirrors Ohm's law.. Option A, C, and D are incorrect as they do not follow the inverse sum law for parallel components.

Answer: B is correct — The total reluctance of two parallel magnetic paths of equal reluctance is half of the individual reluctance value.

Exam Tip: Always remember the analogy: MMF $\approx$ Voltage, Flux $\approx$ Current, and Reluctance $\approx$ Resistance. This makes parallel/series circuit problems intuitive.

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Option A: square for each path

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Option C: cube for each path

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Option D: quarter for each path

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