Fundamentals of Electrical Engineering (4311101) - Winter 2023 Solution

Question 1(a) [3 marks]

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Define Power & Energy.

Answer:

• Power: Rate of doing work or energy consumption per unit time. Measured in Watts (W).
• Energy: Ability to do work or the work done. Measured in Joules (J) or Watt-hours (Wh).

Table: Power vs Energy

Mnemonic: “Power Performs, Energy Endures”

Question 1(b) [4 marks]

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Define current and electrical potential.

Answer:

Diagram:

flowchart LR
    A[Electron Flow] -->|Rate of Flow| B[Current]
    C[Potential Energy] -->|Per Unit Charge| D[Voltage]

• Current: Flow of electric charge per unit time. Measured in Amperes (A).
• Electrical Potential: Work done per unit charge to move a charge from one point to another. Measured in Volts (V).

Mnemonic: “Current Charges, Potential Pushes”

Question 1(c) [7 marks]

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Explain KCL and KVL with examples.

Answer:

Diagram:

Kirchhoff’s Current Law (KCL):

• Sum of currents entering a node equals sum of currents leaving it.
• Example: At node X, i1 + i2 = i3

Kirchhoff’s Voltage Law (KVL):

• Sum of voltage drops around any closed loop equals zero.
• Example: V1 - V(R1) - V(R2) = 0

Mnemonic: “Currents Come-Leave, Voltages Voyage-Loop”

Question 1(c) OR [7 marks]

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Explain different types of connections for Resistors.

Answer:

Diagram:

graph TD
    subgraph "Series Connection"
    A[R1] --- B[R2] --- C[R3]
    end
    subgraph "Parallel Connection"
    D[R1] 
    E[R2]
    F[R3]
    G --- D & E & F --- H
    end

Table: Series vs Parallel Connection

Mnemonic: “Series Sum, Parallel Parts”

Question 2(a) [3 marks]

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Define Resistance and Resistivity. Also state their unit of measurement.

Answer:

• Resistance: Opposition to current flow, measured in Ohms (Ω). R = V/I.
• Resistivity: Material property indicating resistance per unit dimension, measured in Ohm-meter (Ω·m). ρ = RA/L.

Mnemonic: “Resistance Restricts, Resistivity Relates to material”

Question 2(b) [4 marks]

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Define cell and write names of different types of cell.

Answer:

Diagram:

• Cell: Device that converts chemical energy into electrical energy creating a voltage.

Types of Cells:

1. Primary cells: Dry cell, Alkaline cell, Mercury cell
2. Secondary cells: Lead-acid, Nickel-Cadmium, Lithium-ion

Mnemonic: “Primary Produces once, Secondary Serves repeatedly”

Question 2(c) [7 marks]

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Calculate total equivalent resistance of the above circuit if R1=5Ω, R2=3Ω, R3=4Ω, R4=1Ω, R5=2Ω.

Answer:

Diagram:

Step-by-step solution:

1. R2 and R3 are in series: R23 = R2 + R3 = 3Ω + 4Ω = 7Ω
2. R23 and R4 are in parallel: 1/R234 = 1/7 + 1/1 = (1+7)/7 = 8/7 Therefore, R234 = 7/8 = 0.875Ω
3. R1, R234, and R5 are in series: Req = R1 + R234 + R5 = 5Ω + 0.875Ω + 2Ω = 7.875Ω

Therefore, equivalent resistance = 7.875Ω

Mnemonic: “Series-Sum, Parallel-Product over Sum”

Question 2(a) OR [3 marks]

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Find the cost of energy if 100W bulb operated 10 hours daily for 30 days. Rate of energy is Rupees 5/unit.

Answer:

Table: Energy Calculation

Therefore, cost of energy = Rs. 150

Mnemonic: “Energy × Rate = Electric bill fate”

Question 2(b) OR [4 marks]

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State ohm’s law and explain the use ohm’s law to calculate current in any circuit.

Answer:

Diagram:

graph LR
    A[Voltage] -->|"V = IR"| B[Current]
    C[Resistance] --> B

Ohm’s Law: Current flowing through a conductor is directly proportional to voltage and inversely proportional to resistance.

Formula: V = IR or I = V/R or R = V/I

Application: To find current in a circuit, measure voltage across a component and divide by its resistance (I = V/R).

Mnemonic: “Volts Invite current, Resistance Restricts”

Question 2(c) OR [7 marks]

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Show that the current in a purely capacitive circuit leads the applied voltage by 90° and the current in a purely inductive circuit lags the applied voltage by 90°.

Answer:

Diagrams:

graph TD
    subgraph "Capacitive Circuit"
    A[Voltage] --- B["Voltage = V sin(ωt)"]
    C[Current] --- D["Current = I sin(ωt + 90°)"]
    end
    subgraph "Inductive Circuit"
    E[Voltage] --- F["Voltage = V sin(ωt)"]
    G[Current] --- H["Current = I sin(ωt - 90°)"]
    end

For Capacitive Circuit:

• Voltage equation: v = V sin(ωt)
• Current: i = C × dv/dt = ωCV cos(ωt) = I sin(ωt + 90°)
• Current leads voltage by 90°

For Inductive Circuit:

• Voltage equation: v = L × di/dt = ωLI cos(ωt) = V sin(ωt + 90°)
• Current: i = I sin(ωt)
• Current lags voltage by 90°

Mnemonic: “ELI the ICE man” - In EL (inductor), I lags E; in ICE (capacitor), I leads E

Question 3(a) [3 marks]

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Define cycle, form factor and amplitude.

Answer:

Diagram:

• Cycle: One complete repetition of a waveform.
• Form Factor: Ratio of RMS value to average value. For sine wave = 1.11.
• Amplitude: Maximum displacement of a waveform from its mean position.

Mnemonic: “Cycles Complete, Form Factors Find ratio, Amplitude Achieves maximum”

Question 3(b) [4 marks]

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Define RMS and Average value. Write expression of RMS and average value of sinusoidal waveform.

Answer:

Table: RMS vs Average Value

• RMS (Root Mean Square): Equivalent DC value that produces same heating effect.
• Average Value: Mean of all instantaneous values over a half cycle.

Mnemonic: “RMS Relates to heating, Average Adds and divides”

Question 3(c) [7 marks]

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Explain the terms Apparent power, True Power and Reactive power. State their unit of measurement.

Answer:

Diagram:

graph TD
    subgraph "Power Triangle"
    A[True Power P] --- B[Apparent Power S]
    C[Reactive Power Q] --- B
    end

Table: Types of Power

Power Triangle: S² = P² + Q²

Mnemonic: “Active Performs work, Reactive Returns energy, Apparent Adds vectors”

Question 3(a) OR [3 marks]

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Write mathematical expressions of 3-phase voltages.

Answer:

Three-phase voltage expressions:

Table: 3-Phase Voltages

Where Vm is the maximum voltage and ω is the angular frequency.

Mnemonic: “Red phase Reference, Yellow lags 120°, Blue brings up 240°”

Question 3(b) OR [4 marks]

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Define crest factor and state value of crest factor for sine wave.

Answer:

Diagram:

• Crest Factor: Ratio of peak value to RMS value of a waveform.
• Formula: Crest Factor = Peak Value / RMS Value
• For sine wave: Crest Factor = 1/0.707 = 1.414

Mnemonic: “Crest Compares peak to RMS”

Question 3(c) OR [7 marks]

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Describe different three phase electrical connections.

Answer:

Diagram:

graph TD
    subgraph "Star Connection"
    A1[R] --- D[Neutral]
    B1[Y] --- D
    C1[B] --- D
    end
    
    subgraph "Delta Connection"
    A2[R] --- B2[Y]
    B2 --- C2[B]
    C2 --- A2
    end

Table: Star vs Delta Connection

Mnemonic: “Star Shows neutral, Delta Delivers higher current”

Question 4(a) [3 marks]

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Calculate the peak to peak value of a sinusoidal voltage if RMS value is 230V.

Answer:

Table: Calculation Steps

Therefore, peak-to-peak value = 650.54V

Mnemonic: “RMS to Peak - multiply by √2, Peak to Peak - double it”

Question 4(b) [4 marks]

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An alternating current is given by i=142.14sin628t find frequency and time period.

Answer:

Table: Calculation Steps

Therefore, frequency = 100 Hz and time period = 0.01 s

Mnemonic: “Frequency From omega divide 2π, Time takes inverse”

Question 4(c) [7 marks]

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State and explain Fleming’s left hand rule and right hand rule.

Answer:

Diagram:

Fleming’s Left Hand Rule (Motor):

• Used to determine direction of force on a current-carrying conductor in a magnetic field.
• Hold left hand with thumb, fore and middle fingers at right angles.
• Thumb: Motion (Force)
• Forefinger: Magnetic field
• Middle finger: Current

Fleming’s Right Hand Rule (Generator):

• Used to determine direction of induced current when a conductor moves in a magnetic field.
• Hold right hand with thumb, fore and middle fingers at right angles.
• Thumb: Motion of conductor
• Forefinger: Magnetic field
• Middle finger: Induced current

Mnemonic: “Left Lifts motors, Right Raises generators”

Question 4(a) OR [3 marks]

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A conductor of length 1 metre moves with speed of 30m/s in magnetic field of 0.6 Tesla making angle of 30° with the field. Calculate dynamically EMF induced in it. (use sin 30°=0.5)

Answer:

Table: Given Parameters

Formula: E = Blv sin θ

Calculation: E = 0.6 × 1 × 30 × 0.5 = 9 volts

Therefore, induced EMF = 9 volts

Mnemonic: “EMF Emerges from Field, velocity and Length with angle”

Question 4(b) OR [4 marks]

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State & explain Lenz’s law.

Answer:

Diagram:

Lenz’s Law: The direction of induced EMF or current is always such that it opposes the cause that produces it.

Application: When a magnet approaches a coil, induced current creates a magnetic field that repels the approaching magnet.

Mnemonic: “Lenz Likes to Oppose”

Question 4(c) OR [7 marks]

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Explain Statically and dynamically induced EMF.

Answer:

Table: Statically vs Dynamically Induced EMF

Mnemonic: “Static Stays but flux Changes, Dynamic Drives through field”

Question 5(a) [3 marks]

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Explain PV Cell.

Answer:

Diagram:

• PV Cell: Device that converts sunlight directly into electricity using photovoltaic effect.
• Working: Sunlight excites electrons in semiconductor material, creating voltage difference.
• Material: Typically made from silicon with P-N junction.

Mnemonic: “Photons Visit, Current Created”

Question 5(b) [4 marks]

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Explain the solar PV panel and arrays.

Answer:

Diagram:

graph LR
    A[Solar Cell] -->|"Multiple cells in series"| B[Solar Panel]
    B -->|"Multiple panels connected"| C[Solar Array]

Table: Solar System Hierarchy

Mnemonic: “Cells Combine into Panels, Panels Produce Arrays”

Question 5(c) [7 marks]

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Draw and explain block diagram of wind power system.

Answer:

Diagram:

flowchart LR
    A[Wind Turbine] -->|"Mechanical energy"| B[Gearbox]
    B -->|"High speed rotation"| C[Generator]
    C -->|"AC power"| D[Power Electronics]
    D -->|"Controlled output"| E[Transformer]
    E -->|"Grid-compatible power"| F[Grid/Load]
    G[Control System] -.-> A & C & D

Components of Wind Power System:

1. Wind Turbine: Converts wind energy to mechanical energy
2. Gearbox: Increases rotational speed for generator
3. Generator: Converts mechanical energy to electrical energy
4. Power Electronics: Controls and regulates electrical output
5. Transformer: Steps up/down voltage for transmission/distribution
6. Control System: Monitors and optimizes overall operation

Mnemonic: “Wind Turns Gears, Generating Electrical Returns”

Question 5(a) OR [3 marks]

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State the benefits of green energy.

Answer:

Table: Benefits of Green Energy

Mnemonic: “Clean Energy Creates Economic Salvation”

Question 5(b) OR [4 marks]

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Explain Solar PV applications in brief.

Answer:

Diagram:

graph TD
    A[Solar PV Applications] --> B[Residential]
    A --> C[Commercial]
    A --> D[Industrial]
    A --> E[Utility Scale]
    A --> F[Off-grid]

Solar PV Applications:

1. Residential: Rooftop systems, Solar water heaters
2. Commercial: Building integrated PV, Solar parking
3. Industrial: Process heating, Power generation
4. Utility Scale: Solar farms, Grid support
5. Off-grid: Rural electrification, Remote applications

Mnemonic: “Residences, Commerce, Industry Utilize Solar”

Question 5(c) OR [7 marks]

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Explain different types of Green energy.

Answer:

Table: Types of Green Energy

Diagram:

pie title "Green Energy Sources"
    "Solar" : 30
    "Wind" : 25
    "Hydro" : 20
    "Biomass" : 15
    "Geothermal" : 7
    "Tidal" : 3

Mnemonic: “Sun, Wind, Hydro, Biomass, Geothermal, Tidal - Simple Ways Humans Build Green Tomorrow”