Comprehensive NEET Physics Notes for Electromagnetic Induction and Alternating Current

Electromagnetic Induction and Alternating Current

Electromagnetic Induction

1. Introduction

Electromagnetic induction involves generating electric currents through changing magnetic fields. Experiments by Michael Faraday and Joseph Henry in the 1830s demonstrated this phenomenon. This principle is foundational for many modern technologies, including generators and transformers.

Did You Know?

Michael Faraday, often called the "Father of Electricity," discovered electromagnetic induction independently around the same time as Joseph Henry in the USA.

2. Faraday's Experiments

Faraday conducted several experiments to understand electromagnetic induction:

Magnet and Coil (Experiment 6.1)
- Moving a bar magnet towards a coil induces a current in the coil, as detected by a galvanometer.
- The direction of current reverses when the magnet is moved away from the coil.
Two Coils (Experiment 6.2)
- A current-carrying coil moved towards a stationary coil induces current in the stationary coil.
- Relative motion between the two coils is necessary for induction.
Changing Current (Experiment 6.3)
- A coil connected to a battery and a switch can induce current in a nearby stationary coil when the switch is opened or closed.

Real-life Application:

Electromagnetic induction is used in metal detectors, electric generators, and induction cooktops.

3. Magnetic Flux

Magnetic flux (Φ_B) through a surface area (A) in a uniform magnetic field (B) is given by: $Φ_{B} = B \cdot A = B A cos θ$

where:

B is the magnetic field.
A is the area.
θ is the angle between B and A.

4. Faraday’s Law of Induction

Faraday's Law states that the induced emf (ε) in a coil is equal to the rate of change of magnetic flux through the coil: $ϵ = - \frac{d Φ _{B}}{d t}$

For a coil with N turns: $ϵ = - N \frac{d Φ _{B}}{d t}$

Common Misconception:

Increasing the magnetic field alone induces current; it’s the change in magnetic flux that matters.

5. Lenz's Law

Lenz's Law states that the direction of the induced current opposes the change in magnetic flux that caused it. This can be written as: $ϵ = - N \frac{d Φ _{B}}{d t}$

Example:

Pushing a magnet into a coil induces a current that creates a magnetic field opposing the magnet's motion.

6. Motional Electromotive Force

When a conductor moves in a magnetic field, an emf is induced across its length. For a conductor of length l moving at velocity v in a magnetic field B: $ϵ = Bl v$

Mnemonic:

"BLV" – Magnetic field (B), Length (L), Velocity (V).

7. Self-Inductance and Mutual Inductance

7.1 Self-Inductance

Self-inductance (L) is the property of a coil to oppose changes in current flowing through it. It is given by: $L = \frac{N Φ _{B}}{I}$

7.2 Mutual Inductance

Mutual inductance (M) between two coils is given by: $ϵ_{1} = - M \frac{d I _{2}}{d t}$

where:

$ϵ_{1}$ is the emf induced in coil 1 due to the change in current in coil 2.

Did You Know?

Joseph Henry, who discovered mutual inductance, also invented the electromagnetic relay used in telegraphy.

8. Energy Stored in an Inductor

The energy (U) stored in an inductor with inductance L and current I is: $U = \frac{1}{2} L I^{2}$

NEET Tip:

Understand the analogy between electrical inductance and mechanical inertia for better conceptual clarity.

Alternating Current

1. Introduction to Alternating Current (AC)

Alternating current changes direction periodically. It is characterized by its frequency (f), measured in hertz (Hz), and amplitude (A).

2. AC Generators

AC generators convert mechanical energy into electrical energy using electromagnetic induction. The output emf (ε) is given by: $ϵ = ϵ_{0} sin (ω t)$

where:

$ϵ_{0}$ is the peak emf.
$ω$ is the angular frequency.

3. RMS Value of AC

The root mean square (RMS) value of AC is used for measuring the effective voltage or current. For an AC voltage: $V_{r m s} = \frac{V _{0}}{2}$

where:

$V_{0}$ is the peak voltage.

4. AC Circuit Components

4.1 Resistor in AC Circuit

For a resistor (R) in an AC circuit, the voltage and current are in phase. The power dissipated is: $P = V_{r m s} I_{r m s} = I_{r m s}^{2} R$

4.2 Inductor in AC Circuit

For an inductor (L) in an AC circuit, the voltage leads the current by 90°. The inductive reactance (X_L) is: $X_{L} = ω L$

4.3 Capacitor in AC Circuit

For a capacitor (C) in an AC circuit, the current leads the voltage by 90°. The capacitive reactance (X_C) is: $X_{C} = \frac{1}{ω C}$

5. LCR Circuit

An LCR circuit contains an inductor (L), a capacitor (C), and a resistor (R). The impedance (Z) of the circuit is given by: $Z = R^{2} + (X_{L} - X_{C})^{2}$

The resonant frequency (f_r) is where the impedance is minimum, and it is given by: $f_{r} = \frac{1}{2 π L C}$

Real-life Application:

LCR circuits are used in radio tuning to select desired frequencies.

6. Power in AC Circuits

The average power (P) in an AC circuit is given by: $P = V_{r m s} I_{r m s} cos ϕ$

where:

$ϕ$ is the phase difference between voltage and current.

Practice Questions

Calculate the emf induced in a coil with 50 turns if the magnetic flux changes by 0.1 Wb in 2 seconds.
Explain Lenz's Law with an example.
Determine the energy stored in an inductor with an inductance of 5 H carrying a current of 2 A.
A 100-turn coil is rotated in a magnetic field at 60 Hz, producing a peak emf of 20 V. Calculate the maximum magnetic flux.
In an LCR circuit, the inductive reactance is 30 Ω, the capacitive reactance is 20 Ω, and the resistance is 10 Ω. Calculate the impedance.

Answers to Practice Questions

Using Faraday's Law: $ϵ = - N \frac{d Φ _{B}}{d t} = - 50 \frac{0.1}{2} = - 2.5, V$
Lenz's Law states that the direction of induced current opposes the change in magnetic flux. For example, if a magnet is moved towards a coil, the induced current creates a magnetic field opposing the magnet's motion.
Energy stored: $U = \frac{1}{2} L I^{2} = \frac{1}{2} \times 5 \times 2^{2} = 10, s$