Electricity Generation: Notes

Induced Currents & Electromagnetic Induction

Oersted discovered current creates magnetic field (1820).
Henry & Faraday (1831) discovered electromagnetic induction: magnets can create current.

Faraday's Experiment & Induced Current

Faraday's experiment involved two coils around an iron ring.
Current is induced only when the magnetic field through the coil is changing.
Induced current: current in a circuit due to a changing magnetic field.

Examples of Electromagnetic Induction

Moving a magnet near a coil induces current.
Moving the coil in a magnetic field induces current.
Opening/closing a switch near a coil induces momentary current.
Relative motion between coil and magnet induces emf.

EMF & Induced Current Relationship

Changing magnetic field induces emf (electromotive force) in the coil.
Induced emf leads to induced current.

Motional EMF

A conductor of length l moving with velocity v through a perpendicular magnetic field B experiences magnetic force.
Magnetic force: F = qvB
This leads to charge separation and an electric field inside the conductor.
Equilibrium when electric force balances magnetic force: qE = qvB.
Electric field strength: E = vB
The motion induces a potential difference (emf) between the ends of the conductor.

Induced Current in a Circuit

Moving a conducting wire along a U-shaped rail in a magnetic field creates a closed conducting loop (circuit).
Charges in the moving wire are pushed by the magnetic force, creating an induced current.
A pulling force is required to maintain constant wire speed due to magnetic drag.
Magnitude of magnetic force: F = I l B sinθ

Magnetic Flux

Magnetic flux represents the amount of magnetic field passing through a loop.
Maximum flux when loop is perpendicular to the field.
Component of magnetic field perpendicular to the surface: B_{\perp} = B cos θ

Magnetic Flux Definition

Magnetic flux: \Phi = B A cos θ
A is loop area, \theta is angle between the normal to the loop and the magnetic field.
SI unit: Weber (Wb), 1 Wb = 1 T⋅m

Examples of Magnetic Flux Calculation

Circular loop example: \Phi = B A cos θ
Rectangular coil example: \Phi = B A cos θ for different angles.

Faraday's & Lenz's Law

Faraday's Observation: Current induced by any change in magnetic flux.
Lenz's Law: Induced current creates a magnetic field opposing the change in flux.

Lenz’s Law

Changing flux induces current; induced current generates own B-field.
Flux changes via:
- Changing magnetic field.
- Changing loop area or angle.
- Loop moving in/out of the field.

Scenarios of Lenz’s Law

Six scenarios based on field direction (up/down) and flux change (increase/steady/decrease).

Tips For Using Lenz's Law

Determine applied B-field direction.
Determine how flux is changing (increasing, decreasing, or steady).
Determine direction of induced B-field to oppose flux change.
- Increasing flux: induced B-field opposes applied B-field.
- Decreasing flux: induced B-field aligns with applied B-field.
- Steady flux: no induced B-field.
Determine induced current direction using the right-hand rule.

Faraday’s Law of Electromagnetic Induction

Induced emf equals the time rate of change of magnetic flux. E = -N \frac{\Delta \Phi}{\Delta t}
N = number of loops.
SI Unit of Induced Emf: volt (V).
Changing magnetic flux due to change in B, A, or θ.

Examples of Faraday's Law

A coil of wire in an external magnetic field: E = -N \frac{\Delta \Phi}{\Delta t}
Flat coil rotated to determine the average induced EMF: E = -N \frac{\Delta \Phi}{\Delta t}

Lenz’s with Induced EMF

Induced emf drives current; the polarity leads to current direction where the induced magnetic field opposes the original flux change.

Examples: Motional EMF and Lenz's Law

A metallic loop moving through a magnetic field: Analyze the magnetic flux in the loop.
A square loop moving into & out of uniform magnetic field B: E = -N \frac{\Delta \Phi}{\Delta t}

Examples Two: 2018 VCE Q2 (a & B) and 2020 VCE Q6 (a)

Calculate the average EMF induced in the loop as it passes from just outside the magnetic field at position X to just inside the magnetic field at position Y: E = -N \frac{\Delta \Phi}{\Delta t}
Two Physics students hold a coil in a uniform magnetic field an determine the direction of the induced current: Decrease; as surface area of loop has decreased.

DC Generators

DC generators use a commutator (split ring) to maintain output voltage polarity.
Commercial DC generators use multiple coils and commutators to minimize output fluctuations.

Motors

Motors are generators operating in reverse.
Current supplied to the coil causes rotation via torque from a battery on a current-carrying coil.

Examples 2020 VCE Q5 (a) and (c)

Calculations include; Calculate the average EMF measured in the loop for the first quarter turn. and sketch the output EMF versus time for the first two rotations: E = -N \frac{\Delta \Phi}{\Delta t}

Examples with Lenz’s Law & EMF production

Apply the Right-Hand Grip Rule to determine Magnetic field and EMF production.
Copper Ring and Bar magnet example applying right hand grip rule and polarity determination in induced B field with current.
As the flux is increasing, current is induced to oppose change and vice versa.

Electric Generators

Electric generators convert mechanical work to electrical transmission.
AC generators connect loop ends to slip rings.
Varies Sinusoidally.

Electric AC Generators

Induced EMF can be calculated given angular speed (\omega) or rate of rotation plays an important role in determining induced emf in the coil: Emf, = \omegacos ($\Phi)
The magnitude of induced EMF can be determined through various examples with varying revolution rates in Faraday's Law.

Alternating Currents

AC source supplies sinusoidally varying voltage or current.
Sinusoidal voltage: v = V sin(\omega t)
v is the instantaneous voltage; V is the voltage amplitude; ω is the angular frequency.

RMS Voltage

RMS voltage: Root Mean Square of instantaneous voltage values.
RMS voltage is the DC equivalent of AC voltage.
Allows for power calculations in AC circuits.

RMS Voltage Formula

V{rms} = \frac{V{peak}}{\sqrt{2}} = V_{peak} \times 0.707
V{peak} = V{rms} \times \sqrt{2}

Formula Summary

Average voltage for sinusoidal waveform V{AVG} \approx 0.9 \times V{RMS}

Power in AC Circuits

Average power P is total energy dissipated per second.
RMS current: I{rms} = \frac{I{peak}}{\sqrt{2}}
Average power loss in a resistor: P{avg} = I{rms}^2 R
RMS voltage and emf: V{rms} = \frac{V{peak}}{\sqrt{2}}

AC circuit & Power

We want Average Power: Voltmeters, ammeters, and other AC measuring instruments are calibrated to give the rms value: P{avg} = V{rms}^2 R / \, I_{rms}^2/ R
Various Examples and Calculations are provided related power output and resistance calculations; a 100 W incandescent lightbulb, A stereo receiver applying a peak ac voltage of 34 V

Transformers

Transformers step up or down AC voltage.
Consist of primary (Np turns) and secondary (Ns turns) coils wound on an iron core.
Equations are provided to calculate transformer properties.

Transformers equation

Transformers: Es = - N \frac{\Delta \Phi}{\Delta t} with the ratio : \frac{Vs}{Vp} = \frac{Ns}{N_p}
Where s is the sent from secondary coil and p is the delivered power from the primary coils.
Transformers operates with AC not DC.

Transformers and Transmission

Transformers play a key role in electric power transmission.
Power companies use transformers to step up voltage and step down current to minimize power loss: The diagram shows one possible way of transmitting power, high-voltage power is sent over the long-distance transmission line: P_{loss} = I^2 R

Transformers Applications

Numerous real-world examples are provided; home owner uses a transformer at the house to reduce the voltage from 240 VRMS to 12 VRMS,
Power loss calculations, Transformer steps the voltage up to 500 kV RMS, Lighting examples, A home owner, large properties and backyard entertainment.
The purpose of the model is to operate the 4.0 V light globe by the physics students, transformer at a ratio of 4:1 and 8:1