Inductance is ________ to number of turns in the coil.

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Examoogle · Accepted Answer

Directly proportional

Explanation: The inductance $L$ of a coil is directly proportional to the square of the number of turns $N$ in the coil. This relationship is derived from the magnetic flux linkage principles in electromagnetic theory.

Working Principle: According to Faraday's law, the magnetic flux $\Phi$ produced by a coil is proportional to the current $I$ and the number of turns $N$. Since Inductance is defined as $L = \frac{N\Phi}{I}$ and $\Phi$ itself is proportional to $N$ (because each turn contributes to the total magnetomotive force), substituting $\Phi \propto N$ yields $L \propto N^2$. Therefore, increasing the number of turns increases the magnetic flux linkage per unit of current, resulting in higher inductance.

Key Formulas: $L = \frac{N\Phi}{I}$ — Definition of inductance in terms of flux linkage; $L = \frac{\mu N^{2}A}{l}$ — Inductance of a solenoid where $\mu$ is permeability, $A$ is area, and $l$ is length

Key Points: Inductance is proportional to the square of the number of turns ($L \propto N^2$).; Inductance also depends linearly on the cross-sectional area and the magnetic permeability of the core material.; Increasing the length of the coil decreases the inductance, assuming $N$ remains constant.

Advantages: Higher inductance allows for more effective energy storage in magnetic fields.; Increased $N$ allows for higher impedance at lower frequencies in filters.

Disadvantages: Increasing the number of turns increases the resistance of the coil due to wire length.; Higher $N$ values increase the physical size and weight of the inductor.

Applications: Transformers; Inductors in SMPS circuits; Radio frequency tuning circuits

Additional Info: The inductance formula $L = \frac{\mu N^2 A}{l}$ assumes a long, tightly wound coil (solenoid approximation).. Option B is incorrect because inductance increases as the number of turns increases, not decreases.

Answer: A is correct — Inductance is directly proportional to the square of the number of turns ($N^2$) in the coil.

Exam Tip: In competitive exams, remember that $L \propto N^2$ for a fixed core, whereas $L \propto \mu$ (permeability). If a question asks about doubling turns, the inductance increases by 4 times.

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