Electromagnetic Induction and Generators

A potential difference (voltage) is induced across a conductor when:

• The conductor moves through a magnetic field, OR
• The magnetic field changes around a stationary conductor

In both cases, the magnetic field lines are being "cut" by the conductor.

If the conductor is part of a complete circuit, the induced voltage drives an induced current.

Faraday's Law

The size of the induced voltage is increased by:

• Moving the conductor or magnet faster
• Using a stronger magnet
• Using more turns of wire in a coil
• Increasing the area of the coil

Lenz's Law

The direction of the induced current is always such that it opposes the change that produced it. This is a consequence of conservation of energy.

Example: If you push a magnet into a coil, the induced current creates a magnetic field that repels the magnet — you have to do work to push it in.

A generator converts kinetic energy into electrical energy using electromagnetic induction.

AC Generator (Alternator)

• A coil rotates in a magnetic field
• As the coil rotates, it cuts through field lines, inducing a voltage
• Slip rings and brushes connect the rotating coil to the external circuit
• The voltage (and current) reverses every half turn → alternating current (AC)

The output is a sine wave — voltage oscillates between positive and negative.

DC Generator (Dynamo)

• Similar to AC generator but uses a split-ring commutator instead of slip rings
• The commutator reverses the connections every half turn
• Output is always in one direction → direct current (DC) (though it pulses)

Increasing Generator Output

• Spin the coil faster (higher frequency and higher peak voltage)
• Use a stronger magnet
• Use more turns on the coil
• Increase the area of the coil

A transformer changes the voltage of an AC supply. It works by electromagnetic induction.

Structure

• Primary coil — connected to the input AC supply
• Secondary coil — connected to the output
• Iron core — links the two coils magnetically

How It Works

1. AC in the primary coil creates a changing magnetic field
2. The iron core carries this changing field to the secondary coil
3. The changing field induces a voltage in the secondary coil

Transformer Equation

$\boxed{\frac{V_s}{V_p} = \frac{N_s}{N_p}}$

Where:

• $V_s$ = secondary voltage, $V_p$ = primary voltage
• $N_s$ = number of turns on secondary, $N_p$ = number of turns on primary

Types of Transformer

Step-up transformer: $N_s > N_p$ → $V_s > V_p$ (increases voltage)

Step-down transformer: $N_s < N_p$ → $V_s < V_p$ (decreases voltage)

Power in Transformers

For an ideal (100% efficient) transformer: $V_p \times I_p = V_s \times I_s$

Power in = Power out. If voltage goes up, current must come down (and vice versa).

Why Transformers Are Important

The National Grid uses transformers to transmit electricity efficiently:

1. Step-up transformer at the power station: increases voltage to ~400,000 V
2. High voltage → low current → less energy wasted as heat in cables ($P = I^2R$)
3. Step-down transformer near homes: reduces voltage to 230 V for safe use

• Electromagnetic induction: voltage induced by changing magnetic field
• Generator: rotating coil in magnetic field → AC (with slip rings) or DC (with commutator)
• Transformer: $V_s/V_p = N_s/N_p$; only works with AC
• Step-up: increases voltage; Step-down: decreases voltage
• National Grid: step-up → high V, low I → less heat loss → step-down for homes