# Voltage across inductor – formula, polarity of voltage drop

We know three basic passive circuit components – Resistor, Capacitor and Inductor. One can find the voltage drop across a resistor simply by using Ohm’s law of current electricity. In another article, we have discussed the ways to find the voltage drop across a capacitor as well. In this article, we are going to explain the formula and polarity of voltage drop across an inductor. This is very much important, because we need to study the electrical circuits that contain these circuit components. Inductor coils are widely used in Transformer.

• Why is there a voltage drop across inductor in AC circuit?
• Voltage across Inductor formula
• Polarity of voltage drop across an inductor
• How to find the voltage across an inductor?

## Voltage drop across Inductor in AC circuit

First question should be why is there a voltage drop across an inductor in AC circuit? The answer is, if a varying current passes through an inductor a varying voltage induces across the inductor. Because, the inductor is nothing but a coil and the varying current produces a varying magnetic field in that coil which causes the change in magnetic flux linked with the coil. Now, according to the Faraday’s law of electromagnetic induction, an alternating voltage induces due to varying magnetic flux through a coil.

In an electrical circuit, the source of varying current is an external alternating voltage. Thus, the application of an AC voltage across an inductor produces alternating voltage drop across the inductor. Obviously, a direct current (DC) cannot produce varying magnetic flux. So, the DC voltage cannot drop a voltage across an ideal inductor which have zero resistance.

## Voltage across Inductor formula

The formula of voltage drop across an inductor of inductance L is, $\color{Blue} V= L \frac{dI}{dt}$………(1)

Where, I is the time-varying current.

This formula comes from the Faraday’s law of electromagnetic induction. Using this equation of voltage across an Inductor, one can find the induced voltage across an inductive coil.

## Polarity of voltage drop across an inductor

The polarity of induced voltage across the inductor is determined by the Lenz’s law of electromagnetic induction. According to this law, the direction of induced voltage will be such that it opposes the charge in alternating current passing through it. Since, the alternating current always changes its polarity, then the induced voltage will also change its polarity with the same frequency as that of the alternating current passing through it.

## How to find the voltage across an inductor?

To find the voltage across an inductor, you need to know two things –

1. The inductance L of the inductor.
2. The expression for time-varying current through the inductor.

After knowing these two parameters you can easily calculate the induced alternating voltage across the inductor by using equation-(1).

Again, you can find it by using the voltage across inductor calculator which is available in internet.

This is all from this article on the voltage drop across the inductor. If you have any doubt on this topic can ask me in the comment section.

Thank you!

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