The relation between current and voltage in the case of inductor isa.v=Ldt/dib.v=di/dtc.v=Ldi/dtd.v=dt/di

The relationship between current $i$ and voltage $v$ in an inductor is governed by Faraday's law of electromagnetic induction. The correct expression that relates the voltage across an inductor to the rate of change of current through it is given by:

$v = L \frac{di}{dt}$

where:

• $v$ is the voltage across the inductor,
• $L$ is the inductance of the inductor, and
• $\frac{di}{dt}$ is the rate of change of current through the inductor with respect to time.

This expression indicates that the voltage across the inductor is directly proportional to how quickly the current through it is changing.

Now, let's analyze the options you provided:

1. $v = L \frac{dt}{di}$ - This is incorrect because it suggests voltage depends inversely on the rate of change of current, which contradicts the nature of inductive behavior.
2. $v = \frac{di}{dt}$ - This is incorrect as it omits the inductance $L$.
3. $v = L \frac{di}{dt}$ - This is the correct relationship.
4. $v = \frac{dt}{di}$ - This is incorrect because it suggests a direct relationship rather than a rate of change.

Final Answer

The correct relation for an inductor is:

$v = L \frac{di}{dt}$

This emphasizes that the induced voltage in an inductor is proportional to the rate of change of current flowing through it.