JEE Physics Notes: Electromagnetic Induction (EMI) & Alternating Current (AC)

Introduction to Electromagnetic Induction (EMI)

Electromagnetic Induction (EMI) is the process of generating an electromotive force (EMF) across a conductor when it is exposed to a changing magnetic field. It is the fundamental principle behind electrical generators and transformers.

Faraday’s Laws of Electromagnetic Induction

First Law

An EMF is induced in a conductor whenever there is a change in magnetic flux linked with the conductor.

Second Law

The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.

EMF = - dΦ/dt

where Φ is the magnetic flux.

Lenz’s Law

Lenz’s Law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it.

Self-Induction

Self-induction is the property of a coil by which it opposes the change in current flowing through it. The induced EMF is given by:

EMF = -L (dI/dt)

where L is the self-inductance of the coil.

Mutual Induction

Mutual induction is the process by which a change in current in one coil induces an EMF in another coil placed nearby.

Alternating Current (AC)

Alternating Current (AC) is an electric current that periodically reverses its direction. It is represented as:

I = I₀ sin(ωt)

where I₀ is the peak current and ω is the angular frequency.

Characteristics of AC

• Frequency (f) – Number of cycles per second (Hertz).
• Amplitude – Maximum value of current or voltage.
• Root Mean Square (RMS) Value – The effective value of AC.

AC Circuits

Resistor in an AC Circuit

For a purely resistive AC circuit, the current and voltage are in phase.

V = V₀ sin(ωt)
I = I₀ sin(ωt)

Inductor in an AC Circuit

For a purely inductive circuit, the current lags the voltage by 90°.

V = V₀ sin(ωt)
I = I₀ sin(ωt - π/2)

The inductive reactance is given by:

XL = ωL

Capacitor in an AC Circuit

For a purely capacitive circuit, the current leads the voltage by 90°.

V = V₀ sin(ωt)
I = I₀ sin(ωt + π/2)

The capacitive reactance is given by:

XC = 1/(ωC)

LC Oscillations

LC circuits consist of an inductor (L) and a capacitor (C) that produce electrical oscillations. The frequency of oscillations is given by:

ω = 1/√(LC)

Transformer

A transformer is a device used to increase or decrease AC voltage. The transformer equation is:</