In case of an inductance, current is proportional to

Question

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Option B: Magnetic field

Explanation & Concepts:
In an inductor, the current $i(t)$ is fundamentally related to the magnetic flux linkage $\Phi$ through the relationship $N\Phi = Li$. Since the magnetic field $B$ is directly proportional to the magnetic flux $\Phi$ (where $\Phi = \int B \cdot dA$), the current is directly proportional to the strength of the magnetic field.

Working Principle: According to Ampere's Law and the definition of self-inductance, the magnetic flux $\Phi$ produced by a coil is linearly proportional to the current $i$ flowing through it, assuming a linear magnetic material. The relationship is expressed as $\Phi = \frac{Li}{N}$. Because $B$ is proportional to $\Phi$, it follows that $i \propto B$. In contrast, the voltage across an inductor is proportional to the *rate of change* of current ($v = L \frac{di}{dt}$), not the current itself.

Key Formulas: $\Phi = \frac{Li}{N}$ — Flux linkage relation to current; $v = L \frac{di}{dt}$ — Voltage relation to rate of change of current

Key Points: Current is proportional to flux (and thus magnetic field) in a linear inductor.; Voltage is proportional to the time derivative of the current, not the current magnitude.; The constant of proportionality is related to the geometry and core material properties (permeability $\mu$).; This linear relationship holds only when the magnetic core is not saturated.

Advantages: Energy storage in magnetic field; Smooths current ripples in power electronics

Disadvantages: Cannot change current instantaneously (infinite voltage requirement); Susceptible to magnetic saturation

Applications: Transformers; Electromagnetic relays; Induction motors

Additional Info: In highly non-linear magnetic materials (like iron cores), $L$ becomes a function of $i$, making the proportionality non-linear.. Option A is incorrect because voltage depends on the time derivative of current ($di/dt$), not the current value itself.

Answer: B is correct — In a linear inductor, the magnetic field strength is directly proportional to the current flowing through the coil windings.

Exam Tip: Always distinguish between integral relationships (current and flux) and differential relationships (voltage and current) when analyzing inductors.

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Option A: Voltage across the inductance

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Option C: Both (a) and (b)

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Option D: Neither (a) nor (b)

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