Electromagnetic Induction and Generators Overview

Magnetic Flux (Φ)

The total magnetic field passing through an area; Φ = B·A·cosθ.

Magnetic Field (B)

A region where a magnetic force is experienced; measured in tesla (T).

Area (A)

The surface area through which the magnetic field passes.

Angle (θ)

The angle between the field direction and the perpendicular to the coil area.

EMF (Electromotive Force, ε)

The voltage induced in a circuit due to changing flux.

Induced Current

Current that arises due to an induced EMF in a closed circuit.

Faraday's Law

States that ε = −N(ΔΦ/Δt).

Lenz's Law

The direction of induced current opposes the change in flux causing it.

Number of Turns (N)

The number of loops in a coil; more turns increase EMF.

Flux Linkage

Product of magnetic flux and number of turns (NΦ).

Rate of Change of Flux (ΔΦ/Δt)

Determines the size of induced EMF.

Right-hand Grip Rule

A tool to determine magnetic field direction due to current.

Perpendicular Flux

When θ = 0°, maximum flux occurs (cosθ = 1).

Zero Flux

When θ = 90°, no flux through the area (cosθ = 0).

Solenoid

A coil of wire generating a magnetic field when current flows.

Galvanometer

A device that detects current direction and magnitude.

Data Logger/CRO

Measures and records induced voltage over time.

Flux-Time Graph

Shows how magnetic flux varies over time.

EMF-Time Graph

The gradient (slope) of a flux-time graph.

Opposing Magnetic Field

Created by an induced current per Lenz's Law.

Magnetic Flux Formula

Φ = B·A·cosθ

Faraday's Law Formula

ε = −N(ΔΦ/Δt)

Current from EMF & Resistance

I = ε/R (in simple loops)

AC Generator

A device that converts mechanical energy to alternating electrical energy using slip rings.

DC Generator

A generator that uses a split-ring commutator to produce direct current.

Slip Rings

Conductive rings that maintain constant contact with external circuit while allowing full rotation.

Split Ring Commutator

Reverses connection to the circuit every half-turn, producing DC output.

Armature

The rotating coil in a generator.

Peak Voltage (Vp)

Maximum voltage from zero on a CRO trace.

Peak-to-Peak Voltage (Vp-p)

Voltage from maximum positive to maximum negative on a CRO.

RMS Voltage (Vrms)

Root mean square value of AC voltage; equivalent to DC for power calculations.

Period (T)

Time for one complete cycle of a waveform.

Frequency (f)

Number of waveform cycles per second; f = 1/T.

Waveform

A graph showing how voltage varies with time.

Sinusoidal Output

Smooth, repetitive wave produced by uniform coil rotation in a field.

Unidirectional Pulses

Output of a DC generator (no polarity reversal).

CRO (Cathode Ray Oscilloscope)

Displays voltage over time.

Mechanical Input

The rotational energy supplied to spin the generator.

Electromagnetic Induction

Process generating current in a coil moving through a magnetic field.

Zero EMF Points

Where flux is maximum and rate of change is zero.

Phase

Relative alignment of waveform peaks and zero crossings.

Rotation Speed

Affects frequency and peak voltage.

Saturation

When increasing input no longer increases output significantly.

Frequency Formula

f = 1/T

Peak-to-Peak Voltage Formula

Vp-p = 2·Vp

RMS Voltage Formula

Vrms = Vp / √2

Sinusoidal EMF Formula

ε(t) = εmax·sin(ωt)

Angular Frequency Formula

ω = 2πf

Power (AC) Formula

P = Vrms·Irms

EMF from generator coil Formula

ε = NABω·sin(ωt)

Voltage output

Dependent on the rate of change of magnetic flux, not just field strength.

Coil perpendicular to field lines

Flux is maximum, but no EMF.

Coil at 45° in rotation

Gives partial flux and partial EMF.

Mechanical energy input

Converted into electrical energy through changing flux.

Increasing turns per coil

Multiplies the output voltage.

Commutator failure

If commutator fails or brushes misalign, waveform becomes erratic or drops out.

Comparing AC and DC generator outputs

Helps diagnose commutator type in experiments.

Transformer

A device that changes AC voltage using electromagnetic induction.

Primary Coil

The coil connected to the input voltage.

Secondary Coil

The coil connected to the output voltage.

Iron Core

Magnetic material linking primary and secondary coils to enhance flux.

Turns Ratio

The ratio of coils: Vp/Vs = Np/Ns.

Step-Up Transformer

Increases voltage, decreases current.

Step-Down Transformer

Decreases voltage, increases current.

Ideal Transformer

Assumes no energy loss: input power = output power.

Power Loss (Ploss)

Power lost in wires: Ploss = I²R.

Transmission Line

The high-voltage cable system connecting power stations to users.

Efficiency

Ratio of useful power output to total input.

Load

The device or system receiving power.

Voltage Drop

Reduction in voltage along a wire due to resistance.

I²R Loss

Energy loss in a wire due to current and resistance.

Current (I)

Flow of electric charge; higher current = more power loss.

AC Voltage

Needed for transformers to function (changing flux).

Eddy Currents

Currents in the core that reduce efficiency (minimized by laminating).

Voltage Rating

The specified output or input voltage level of a transformer.

Impedance

Opposition to current in AC circuits.

Back EMF

Induced voltage opposing the applied voltage.

Transformer ratio

Vp/Vs = Np/Ns = Is/Ip.

Power balance (ideal)

Vp·Ip = Vs·Is.

Current for given power

I = P/V.

Efficiency formula

η = (Pout/Pin) × 100%.

Voltage drop in wire

Vdrop = I·R.

AC power in resistive loads

P = Vrms·Irms.

Photovoltaic (PV) Cell

Converts light energy into DC electricity.

Irradiance

Power received per unit area, typically in W/m².

Solar Panel

An array of PV cells wired together.

Inverter

Device converting DC from panels into AC for household use.

Direct Current (DC)

Current that flows in one direction.

Alternating Current (AC)

Current that changes direction periodically.

Series Connection

Increases voltage, same current.

Parallel Connection

Increases current, same voltage.

Load

The appliance or circuit powered by solar output.

Power Output (P)

The rate of energy output: P = VI.

Internal Resistance

Resistance inside the panel that reduces output.

Voltage Drop

Reduction in voltage due to resistance in wires.

Ohmic Losses

Power lost due to current through resistance (I²R).

Sun Angle

The angle of incoming sunlight; affects power via cos(θ).

Optimal Tilt

Panel angle that maximizes sunlight capture.

Standard Test Conditions (STC)

Lab conditions for PV rating: 1000 W/m², 25°C.

Maximum Power Point (MPP)

The voltage and current combination yielding highest power.