Fundamentals of Electrical Engineering (4311101) - Winter 2024 Solution

Question 1(a) [3 marks]

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Define current, electric Power and energy.

Answer:

Mnemonic: “CPE: Charge-Per-second, Product-of-VI, Energy-over-time”

Question 1(b) [4 marks]

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Explain the effect of temperature on the value of resistance of pure metal, alloys and insulators.

Answer:

where α is temperature coefficient, T is temperature, and R is resistance

Mnemonic: “MAI: Metals Add, Alloys Increase-little, Insulators Invert”

Question 1(c) [7 marks]

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State and explain KCL and KVL with examples.

Answer:

Kirchhoff’s Laws:

graph TD; A((Node)); I1-->A; I2-->A; A-->I3; A-->I4; 

graph LR; A((+))-->B((-))); B-->C((+)); C-->D((+)); D-->A; linkStyle 0 stroke:red,stroke-width:2px; linkStyle 1 stroke:green,stroke-width:2px; linkStyle 2 stroke:blue,stroke-width:2px; linkStyle 3 stroke:orange,stroke-width:2px; 

Example:

• KCL: At node A, if I₁ = 5A and I₂ = 3A entering, then I₃ + I₄ = 8A must be leaving
• KVL: In a loop with battery 12V and resistors R₁(4Ω) and R₂(8Ω), 12V = I×(4Ω+8Ω)

Mnemonic: “CLAN: Currents Leave And eNter equally, Voltage Around Loop is Null”

Question 1(c) OR [7 marks]

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Explain series and parallel connections of resistors with necessary equations.

Answer:

graph LR; A---B[(R₁)]---C[(R₂)]---D[(R₃)]---E; 

graph TD; A---B; A---C[(R₁)]---B; A---D[(R₂)]---B; A---E[(R₃)]---B; 

• Series: Total resistance increases, current decreases
• Parallel: Total resistance decreases, current increases

Mnemonic: “SPARC: Series Plus All Resistors, parallel Combines with reciprocals”

Question 2(a) [3 marks]

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Write factors affecting the Resistance value.

Answer:

Mnemonic: “LAMT: Length Adds, Area Minimizes, Material matters, Temperature transforms”

Question 2(b) [4 marks]

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Draw power triangle and define active and reactive power.

Answer:

Power Triangle:

graph LR;
    A((O))-->B((P));
    A-->C((S));
    A-->D((Q));
    linkStyle 0 stroke:green,stroke-width:2px;
    linkStyle 1 stroke:red,stroke-width:2px;
    linkStyle 2 stroke:blue,stroke-width:2px;

Mnemonic: “PAWS: Power Active Works, Apparent is Slant-hypotenuse, reactive Qoscillates”

Question 2(c) [7 marks]

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Explain concept of cell and battery. List out various rating and types of battery.

Answer:

Cell vs Battery:

Battery Ratings:

Battery Types:

graph TD;
    A[Battery Types]-->B[Primary];
    A-->C[Secondary];
    B-->D[Alkaline];
    B-->E[Zinc-Carbon];
    B-->F[Lithium];
    C-->G[Lead-Acid];
    C-->H[Li-ion];
    C-->I[Ni-MH];

Mnemonic: “CAVE: Cells Are Voltage Elements, batteries Bundle And TallY Energy”

Question 2(a) OR [3 marks]

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Define the terms resistance, conductance and conductivity.

Answer:

where ρ is resistivity, l is length, and A is cross-sectional area

Mnemonic: “RCG: Resist Current Gladly, Conduct Generously, σ Gets current through”

Question 2(b) OR [4 marks]

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Prove that for pure inductive circuit, the current lags applied voltage by 90°.

Answer:

For pure inductive circuit:

graph LR;
    A((AC Source))-->B((L))

Mathematical Proof:

• Applied voltage: v = Vm sin(ωt)
• For inductor: v = L(di/dt)
• Therefore: L(di/dt) = Vm sin(ωt)
• Integrating: i = -(Vm/ωL)cos(ωt) = (Vm/ωL)sin(ωt-90°)

Waveform:

Mnemonic: “ELI: Voltage Leads current In inductor by 90 degrees”

Question 2(c) OR [7 marks]

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Describe Resistor, Inductor and Capacitor with their formula.

Answer:

graph LR; A---B[(___/\/\/\___)]---C

graph LR; A---B[(_mmmmm_)]---C

graph LR; A---B[(_⎥⎥_)]---C

Effect on AC Circuit:

• Resistor: Current in phase with voltage (cos θ = 1)
• Inductor: Current lags voltage by 90° (cos θ = 0)
• Capacitor: Current leads voltage by 90° (cos θ = 0)

Mnemonic: “RIC: Resistor Impedes Current, Inductor Catches current-changes, Capacitor Controls voltage-changes”

Question 3(a) [3 marks]

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Define and explain R.M.S value and average value of AC signal.

Answer:

Mnemonic: “RAM: Rms-Average Method: Root-mean-square And Mean-of-absolute”

Question 3(b) [4 marks]

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With necessary diagrams explain how alternating EMF is generated?

Answer:

Alternating EMF Generation:

graph TD;
    A[Rotating Coil]-->B[Magnetic Field];
    B-->C[EMF Induced];
    C-->D[Direction Changes];
    D-->E[AC Waveform];

Diagram:

• Coil rotates in uniform magnetic field
• EMF = NBAlω sin(ωt)
• As coil rotates, cutting flux changes direction
• Generating sinusoidal waveform e = Emax sin(ωt)

Mnemonic: “FARM: Flux And Rotation Make alternating voltage”

Question 3(c) [7 marks]

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Explain A.C analysis of purely resistive AC circuit.

Answer:

Purely Resistive Circuit:

graph LR;
    A((~))-->B[(R)]-->C

Waveform:

Mnemonic:“VIPS: Voltage In-Phase with current, Same waveform, Power always Positive”

Question 3(a) OR [3 marks]

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Alternating current is given by I = 28.28sin(2Π50t). Find R.M.S value of current.

Answer:

Given:

• I = 28.28sin(2Π50t)
• Therefore, Im = 28.28A

Solution:

Therefore, RMS value of current = 20A

Mnemonic:“PER: Peak to Effective by Root-2”

Question 3(b) OR [4 marks]

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Find maximum value and R.M.S value of sinusoidal voltage if Vav=60V.

Answer:

Given:

• Average value (Vav) = 60V

Solution:

Therefore, maximum value = 94.2V and RMS value = 66.6V

Mnemonic:“AVR: Average to peak Via multiplying by (π/2), Rms is peak/√2”

Question 3(c) OR [7 marks]

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Derive equation of line and phase voltage for balanced star connected load with help of phasor diagram.

Answer:

Star Connection:

graph TD;
A((R))-->N((N));
B((Y))-->N;
C((B))-->N;
R[Load]-->A;
Y[Load]-->B;
B[Load]-->C;

Phasor Diagram:

Derivation:

• Phase voltages: VRN, VYN, VBN (120° apart)
• Line voltages: VRY = VRN - VYN
• For balanced system with magnitude Vp for phase voltage:
• VRY = VRN - VYN = Vp∠0° - Vp∠-120° = Vp(1 - ∠-120°) = √3Vp∠30°

Relation:

• Line voltage (VL) = √3 × Phase voltage (Vp)
• Line voltage leads phase voltage by 30°

Mnemonic:“PALS: Phase to Line in Star: multiply by Square-root-3”

Question 4(a) [3 marks]

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Write statement of Faraday’s law and Lenz’s law with expression.

Answer:

Mnemonic:“FORC: Faraday’s flux Over Rate Change, Lenz Opposes the Reason for Change”

Question 4(b) [4 marks]

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State any four advantage of 3-phase supply over single-phase supply.

Answer:

Additional: More efficient transmission, reduced harmonics, balanced loading

Mnemonic:“PCCS: Power higher, Constant delivery, Copper less, Self-starting motors”

Question 4(c) [7 marks]

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Explain Fleming’s right-hand rule for generators and left-hand rule for motors.

Answer:

Fleming’s Hand Rules:

F ^
|
--+-- > M
|
v
C
``` |

|Left-Hand Rule (Motor)| Determines direction of motion/force |Thumb: Motion/Force
Forefinger: Field
Middle finger: Current |goat F ^ | --+-- > M | v C|

• Generator: Mechanical energy converted to electrical energy
• Motor: Electrical energy converted to mechanical energy

Mnemonic:“FBI-MFC: Field-B-Induced current for right hand, Motion-Field-Current for left”

Question 4(a) OR [3 marks]

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Describe phenomenon of electromagnetic induction.

Answer:

Electromagnetic Induction:

graph TD;
A[Changing Magnetic Field/Flux]-->B[Induces EMF in Conductor];
B-->C[Causes Current to Flow];
C-->D[Creates Secondary Magnetic Field];

Key Factors:

• Requires relative motion or changing flux
• EMF proportional to rate of change of flux
• Direction determined by Lenz’s law

Mnemonic:“MICE: Motion Induces Current via Electromagnetic induction”

Question 4(b) OR [4 marks]

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Explain the generation of 3-phase alternating EMF.

Answer:

3-Phase EMF Generation:

graph TD;
A[3 Coils at 120° Apart]-->B[Rotating Magnetic Field];
B-->C[3 EMFs Generated at 120° Phase Difference];
C-->D[Balanced 3-Phase Supply];

Three Phase Waveform:

• Three identical coils displaced 120° spatially
• Produces three identical EMFs displaced 120° in time
• EMFs: eR = Emax sin(ωt), eY = Emax sin(ωt-120°), eB = Emax sin(ωt-240°)

Mnemonic:“CPS: Coils Produce Shifted waveforms at 120 degrees”

Question 4(c) OR [7 marks]

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Differentiate statically and dynamically induced E.M.F.

Answer:

Mnemonic:“SMCE: Static-Moving, Change-External: static has changing flux, moving has constant flux”

Question 5(a) [3 marks]

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Differentiate HAWT and VAWT.

Answer:

Diagram:

Mnemonic:“HV-DIT: Horizontal-Vertical, Directional-Independent, Tall-lower”

Question 5(b) [4 marks]

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Classification of green energy.

Answer:

Green Energy Classifications:

graph TD;
A[Green Energy Sources]-->B[Solar Energy];
A-->C[Wind Energy];
A-->D[Hydro Energy];
A-->E[Geothermal];
A-->F[Biomass Energy];
A-->G[Tidal/Wave Energy];

Mnemonic:“SWHGBT: Sun Wind Hydro Geo Bio Tidal - Sources With Huge Green Benefits Today”

Question 5(c) [7 marks]

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Explain wind power system.

Answer:

Wind Power System:

graph LR;
A[Wind]-->B[Turbine];
B-->C[Gearbox];
C-->D[Generator];
D-->E[Transformer];
E-->F[Grid Connection];
D-->G[Controller];

Components:

• Wind Turbine: Converts wind energy to mechanical rotation
• Gearbox: Increases rotation speed for generator
• Generator: Converts mechanical to electrical energy
• Controller: Regulates output and safety functions
• Transformer: Steps up voltage for transmission
• Tower: Elevates turbine to capture stronger winds

Working Principle:

1. Wind turns blades (kinetic to mechanical)
2. Gearbox increases RPM
3. Generator produces AC power
4. Controller regulates output
5. Transformer prepares for grid connection

Mnemonic:“WINGER: Wind In, Gearbox Enhances Rotation, Generator outputs”

Question 5(a) OR [3 marks]

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List any three needs of green energy.

Answer:

Other Needs: Climate change mitigation, sustainable development, economic benefits

Mnemonic:“ECO: Environment protected, Conservation of resources, Oil-independence”

Question 5(b) OR [4 marks]

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Write short note on PV cell.

Answer:

Photovoltaic (PV) Cell:

graph TD;
A[Sunlight]-->B[PV Cell];
B-->C[DC Electricity];
B-->D[Construction: P-N Junction];
B-->E[Materials: Silicon, Thin Film];

Working Principle:

• Based on photovoltaic effect
• Converts sunlight directly to electricity
• Uses semiconductor material (usually silicon)
• Creates electron flow when photons hit P-N junction

Types: Monocrystalline, Polycrystalline, Thin-film

Efficiency: Typically 15-22% for commercial cells

Mnemonic:“SPEC: Sunlight Produces Electricity through Cells with p-n junctions”

Question 5(c) OR [7 marks]

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Explain solar system.

Answer:

Solar Power System:

graph TD;
A[Solar Panels]-->B[Charge Controller];
B-->C[Battery Bank];
C-->D[Inverter];
D-->E[AC Loads];
A-->F[On-Grid System]-->G[Grid Tie Inverter]-->H[Electric Grid];

Components:

• Solar Panels: Convert sunlight to DC electricity
• Charge Controller: Regulates battery charging
• Battery Bank: Stores electrical energy (off-grid)
• Inverter: Converts DC to AC for household use
• Distribution Panel: Connects to home electrical system

Types:

• Grid-Connected: Feeds excess power to grid
• Off-Grid: Independent with battery storage
• Hybrid: Combination of both systems

Applications:Home power, water pumping, street lighting, industrial use

Mnemonic:“SCBID: Solar Cells produce, Battery stores, Inverter converts, Distribution supplies”