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 fundamental definition of flux linkage and the magnetic circuit parameters.

Working Principle: Inductance is defined as flux linkage per unit current ($L = N\phi / I$). Since magnetic flux $\phi$ is proportional to the magnetomotive force ($F = NI$), and the flux $\phi$ is itself proportional to $N$, the total flux linkage ($N\phi$) becomes proportional to $N^2$. Thus, $L = \frac{N^2\mu A}{l}$, where $\mu$ is permeability, $A$ is area, and $l$ is length.

Key Formulas: $L = \frac{N^2 \mu A}{l}$ — Formula for inductance of a solenoid; $L \propto N^2$ — Relationship between inductance and number of turns

Key Points: Inductance increases as the square of the number of turns.; Higher turns result in more magnetic flux per ampere of current.; Core material permeability significantly affects the inductance value.; Physical dimensions like length and cross-sectional area also influence the value.

Advantages: Higher inductance allows for better filtering in power circuits.; Greater energy storage capability in magnetic fields.

Disadvantages: Increased number of turns leads to higher internal DC resistance (copper loss).; Physical size and weight of the inductor increase.

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

Additional Info: The proportionality $L \propto N^2$ holds strictly for magnetic circuits with constant permeability.. Option B (Inversely proportional) is incorrect as increasing turns increases the coil's ability to store energy magnetically.

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

Exam Tip: Always remember that $L$ scales with $N^2$, whereas the EMF induced in a transformer coil is just proportional to $N$.

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