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

• $V<em>{rms} = \frac{V</em>{peak}}{\sqrt{2}} = V_{peak} \times 0.707$
• $V<em>{peak} = V</em>{rms} \times \sqrt{2}$

Formula Summary

• Average voltage for sinusoidal waveform $V<em>{AVG} \approx 0.9 \times V</em>{RMS}$

Power in AC Circuits

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

AC circuit & Power

• We want Average Power: Voltmeters, ammeters, and other AC measuring instruments are calibrated to give the rms value: $P<em>{avg} = V</em>{rms}^2 R / \, I_{rms}^2/ R$
• 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: $E<em>s = - N \frac{\Delta \Phi}{\Delta t}$ with the ratio : $\frac{V</em>s}{V<em>p} = \frac{N</em>s}{N_p}$
• 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