EEE Theoretical Questions PYQ Solutions

1. DC Circuit Fundamentals and Basic Laws

Q: State and explain the basic laws of electrical engineering. (2016) Answer: The two fundamental laws upon which electric circuit theory is based are Ohm’s Law and Kirchhoff’s Laws.

Ohm’s Law: States that the voltage $v$ across a resistor is directly proportional to the current $i$ flowing through the resistor. Mathematically, $v = i R$ , where $R$ is the resistance,.
Kirchhoff’s Current Law (KCL): Based on the conservation of charge, KCL states that the algebraic sum of currents entering a node (or a closed boundary) is zero ( $\sum i = 0$ ). Alternatively, the sum of currents entering a node equals the sum of currents leaving the node,.
Kirchhoff’s Voltage Law (KVL): Based on the conservation of energy, KVL states that the algebraic sum of all voltages around a closed path (or loop) is zero ( $\sum v = 0$ ). Alternatively, the sum of voltage drops equals the sum of voltage rises,.

Q: Explain Ohm’s law. What are the limitations of Ohm’s law? (2017) Answer:

Explanation: Ohm’s law states that the voltage across a resistor is directly proportional to the current flowing through it ( $v \propto i$ ), with resistance $R$ as the constant of proportionality ( $v = i R$ ).
Limitations:
1. Ohm’s law applies only to linear resistors, which have a constant resistance.
2. It does not apply to nonlinear resistors (elements whose resistance varies with current), such as light bulbs and diodes, where the $i - v$ graph is not a straight line.
3. (External Information): It is not applicable to non-metallic conductors (e.g., electrolytes, semiconductors) or under varying physical conditions like changing temperature.

Q: State and explain Kirchhoff’s current law (KCL) and voltage law (KVL). (2023, 2024) Answer:

KCL: The algebraic sum of currents entering a node is zero ( $\sum_{n = 1}^{N} i_{n} = 0$ ). It implies that charge cannot accumulate at a node; the total current entering must equal the total current leaving,.
KVL: The algebraic sum of all voltages around a closed path (loop) is zero ( $\sum_{m = 1}^{M} v_{m} = 0$ ). It implies that the energy required to move a unit charge around a closed loop is zero.

Q: Classify energy sources (ideal and practical characteristics). (2016) Answer: Energy sources are classified as Independent and Dependent sources,.

Ideal Independent Voltage Source: An active element that provides a specified voltage completely independent of the current flowing through it. Ideally, it has zero internal resistance.
Ideal Independent Current Source: An active element that provides a specified current completely independent of the voltage across it. Ideally, it has infinite internal resistance.
Dependent (Controlled) Sources: An active element where the source quantity is controlled by another voltage or current in the circuit.

(External Information on Practical Characteristics): Practical voltage sources have a small internal resistance in series, causing terminal voltage to drop as load current increases. Practical current sources have a large internal resistance in parallel.

Q: Classify dependent sources. (2024) Answer: There are four possible types of dependent sources,:

Voltage-controlled voltage source (VCVS): The source voltage depends on a control voltage ( $V = a V_{x}$ ).
Current-controlled voltage source (CCVS): The source voltage depends on a control current ( $V = d i_{x}$ ).
Voltage-controlled current source (VCCS): The source current depends on a control voltage ( $I = b V_{x}$ ).
Current-controlled current source (CCCS): The source current depends on a control current ( $I = d i_{x}$ ).

Q: Differentiate between primary cell and secondary cell. (2016, 2018, 2019) Answer: (External Information - Not in provided sources)

Primary Cell: A non-rechargeable battery. The chemical reaction is irreversible (e.g., Zinc-carbon batteries). Once the chemical energy is converted to electrical energy, it is exhausted.
Secondary Cell: A rechargeable battery. The chemical reaction is reversible (e.g., Lead-acid, Lithium-ion). Electrical energy can be applied to reverse the chemical reaction, storing energy for later use.

Q: Write down the properties of open and short circuits. (2017) Answer:

Short Circuit: A circuit element with resistance approaching zero ( $R = 0$ ). The voltage across a short circuit is zero ( $V = 0$ ), but the current can be any value,.
Open Circuit: A circuit element with resistance approaching infinity ( $R = \infty$ ). The current through an open circuit is zero ( $i = 0$ ), but the voltage can be any value,.

Q: Distinguish between Active/Passive, Bilateral/Unilateral, Linear/Nonlinear. (2018) Answer:

Active vs. Passive: An active element is capable of generating energy (e.g., generators, batteries, op-amps). A passive element cannot generate energy (e.g., resistors, capacitors, inductors).
Linear vs. Nonlinear: A linear element has a linear relationship between cause and effect (e.g., a resistor where $v = i R$ forms a straight line through the origin). A nonlinear element does not obey this linear relationship (e.g., a diode),.
Bilateral vs. Unilateral: (External Information) A bilateral element conducts current equally well in both directions (e.g., Resistor). A unilateral element conducts current differently depending on polarity (e.g., Diode).

Q: What is the basic difference between DC and AC? (2017) Answer:

Direct Current (DC): Current flows only in one direction and can be constant or time-varying, but does not reverse polarity.
Alternating Current (AC): Current changes direction with respect to time. It reverses at regular time intervals,.
Key Advantage: AC allows for long-distance transmission at high voltage and low current to reduce power loss, which is cost-effective,.

2. Network Theorems and Analysis Concepts

Q: Why is the Maximum Power Transfer (MPT) condition important for communication engineering? (2016, 2018, 2019, 2023) Answer: In communication systems (and other areas like electronics), it is desirable to maximize the power delivered to a load (e.g., a loudspeaker or antenna) from a source with known internal losses. While this results in only 50% efficiency, maximizing the signal strength/power at the receiving end is often more critical than efficiency in these applications,.

Q: Write some applications of the maximum power transfer theorem. (2017) Answer:

Communications: Matching a radio transmitter to an antenna or an amplifier to a speaker to ensure maximum signal power transfer.
Circuit Design: Selecting load resistance $R_{L}$ equal to the Thevenin resistance $R_{T h}$ to maximize power ( $R_{L} = R_{T h}$ ),.
Car Engines: Matching the starter motor to the battery.

Q: What is a supernode? (2018) Answer: A supernode is formed by enclosing a (dependent or independent) voltage source connected between two nonreference nodes and any elements connected in parallel with it. It is treated as a generalized node where both KCL and KVL are applied to solve for node voltages,.

Q: Describe the Y to $Δ$ and $Δ$ to Y conversion process. (2017) Answer: This technique replaces 3-terminal networks to simplify analysis,.

$Δ$ to Y Conversion: Each resistor in the Y network is the product of the resistors in the two adjacent $Δ$ branches, divided by the sum of the three $Δ$ resistors ( $R_{a} + R_{b} + R_{c}$ ).
- Example: $R_{1} = \frac{R _{b} R _{c}}{R _{a} + R _{b} + R _{c}}$ .
Y to $Δ$ Conversion: Each resistor in the $Δ$ network is the sum of all possible products of Y resistors taken two at a time, divided by the opposite Y resistor.
- Example: $R_{a} = \frac{R _{1} R _{2} + R _{2} R _{3} + R _{3} R _{1}}{R _{1}}$ .

3. Magnetic Circuits and Properties

Q: What are the basic differences between an electric circuit and a magnetic circuit? (2016, 2017, 2019, 2023) Answer:

Electric Circuit	Magnetic Circuit
Current ( $I$ ) flows.	Magnetic Flux ( $Φ$ ) flows.
EMF (Electromotive Force) drives current.	MMF (Magnetomotive Force) drives flux.
Resistance ( $R = \frac{ρ L}{A}$ ) opposes current.	Reluctance ( $R = \frac{L}{μ A}$ ) opposes flux.
Current density ( $J = I / A$ ).	Flux density ( $B = Φ/ A$ ).
Conductivity ( $σ$ ).	Permeability ( $μ$ ).

Q: State and explain Ampere’s circuital law. (2017, 2019, 2022, 2023) Answer: Ampere’s law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It states that the line integral of magnetic field intensity $H$ around a closed path is equal to the current enclosed by the path. Mathematically (for a long straight conductor): $H = \frac{I}{2 π r}$ , where $H$ is the magnetic field intensity, $I$ is current, and $r$ is the distance from the conductor.

Q: State and explain Biot-Savart law. (2017, 2019) Answer: The Biot-Savart law describes the magnetic flux density produced by a current-carrying conductor. It states that the magnetic flux density $B$ is directly proportional to the current $I$ and inversely proportional to the distance $S$ . Mathematically: $B = \frac{μ I}{2 π S}$ , where $μ$ is permeability and $S$ is the separation/distance.

Q: Write down some applications of magnetic circuits. (2019) Answer: Magnetic circuits are used in:

Transformers: To transfer energy between circuits.
Electric Motors and Generators: For electromechanical energy conversion.
Relays and Magnetic Levitation: For switching and actuation.
Storage: Electromagnets and computer memory elements.

Q: Explain hysteresis loss and eddy current loss. How can these be minimized? (2016, 2018, 2022) Answer: (External Information)

Hysteresis Loss: Energy lost as heat due to the repeated magnetization and demagnetization of the magnetic core material as AC flows. It occurs because the magnetic domains resist realignment.
- Minimization: Use “soft” magnetic materials like silicon steel which have a narrow hysteresis loop.
Eddy Current Loss: Circulating currents induced within the conductive magnetic core material itself by the changing magnetic field, causing resistive heating ( $I^{2} R$ ).
- Minimization: Use a laminated core (thin sheets of steel insulated from each other) instead of a solid block. This increases the resistance of the path for eddy currents.

Q: What is a hysteresis loop? Show the difference between soft and hard materials. (2023) Answer: (External Information) A hysteresis loop (or B-H curve) plots Magnetic Flux Density ( $B$ ) vs. Magnetic Field Intensity ( $H$ ) during a cycle of magnetization. The area inside the loop represents the energy dissipated as heat.

Soft Materials: Have a narrow hysteresis loop (low retentivity and coercivity). They are easily magnetized and demagnetized (e.g., Soft Iron). Used in transformers.
Hard Materials: Have a broad/wide hysteresis loop (high retentivity and coercivity). They retain magnetism well (e.g., Steel). Used in permanent magnets.

4. AC Fundamentals and Power

Q: Why is the generation of alternating current necessary? (2016, 2017, 2022) / Advantages of AC over DC. (2018, 2019) Answer:

Ease of Generation: AC generation via rotating generators is mechanically simpler and more efficient than DC generation.
Voltage Transformation: AC voltages can be easily stepped up or down using transformers. This allows power transmission at very high voltages (reducing current and $I^{2} R$ losses) and distribution at safe low voltages,.
Economy: Because of high-voltage transmission, thinner and lighter cables can be used, reducing material costs,.

Q: What is phase? (2018) Answer: Phase is the argument of the sinusoid function ( $ω t + ϕ$ ). It describes the position of a point within a wave cycle. In the expression $v (t) = V_{m} cos (ω t + ϕ)$ , $ϕ$ is the phase angle, indicating whether the wave leads or lags a reference wave,.

Q: Explain the physical significance of form factor and crest factor. (2019, 2022) Answer:

Form Factor: The ratio of the RMS (effective) value to the Average value of a wave ( $K_{f} = I_{r m s} / I_{a vg}$ ). For a pure sine wave, it is 1.11. It indicates the “peakiness” or shape of the waveform relative to a DC equivalent.
Crest (Peak) Factor: The ratio of the Maximum (Peak) value to the Effective (RMS) value ( $K_{c} = V_{m} / V_{r m s}$ ). For a pure sine wave, it is $2 \approx 1.414$ . It indicates the extreme stress (voltage stress) insulation must withstand.

Q: What is a power triangle? (2017) Answer: The power triangle is a graphical representation of Complex Power ( $S$ ), Real Power ( $P$ ), and Reactive Power ( $Q$ ). It is a right-angled triangle where:

Hypotenuse: Apparent Power ( $S$ in VA).
Base: Real/Average Power ( $P$ in Watts).
Height: Reactive Power ( $Q$ in VAR).
Angle: The power factor angle ( $θ$ ).

Q: Describe the sign convention of power with an example. (2022) Answer: The passive sign convention is used.

If current enters the positive polarity of the voltage, $p = + v i$ , and power is absorbed by the element (e.g., a resistor).
If current enters the negative polarity (or leaves the positive), $p = - v i$ , and power is supplied by the element (e.g., a battery discharging).

Q: Explain how power factor can be improved (using power triangle). (2017, 2018) Answer: Power factor correction is the process of bringing the power factor closer to unity. Most industrial loads are inductive (lagging pf).

Method: A capacitor is installed in parallel with the load.
Power Triangle Explanation: The capacitor supplies a leading reactive power ( $Q_{C}$ ) that opposes the lagging reactive power of the inductive load ( $Q_{1}$ ). This reduces the total reactive power to $Q_{2} = Q_{1} - Q_{C}$ .
Since the total apparent power $S$ decreases (hypotenuse shortens) while real power $P$ remains constant, the phase angle $θ$ decreases, and the power factor ( $cos θ$ ) increases,.

Q: “Multiplication and division operations of phasors are suitable in polar form”—justify the statement. (2018) Answer: In polar form ( $z = r ∠ ϕ$ ), multiplication and division involve simple arithmetic:

Multiplication: Multiply magnitudes, add angles ( $z_{1} z_{2} = r_{1} r_{2} ∠ (ϕ_{1} + ϕ_{2})$ ).
Division: Divide magnitudes, subtract angles ( $z_{1} / z_{2} = (r_{1} / r_{2}) ∠ (ϕ_{1} - ϕ_{2})$ ). In rectangular form, these operations require complex algebraic expansion and rationalization, which is much more tedious.

5. AC Resonance

Q: Write down the significance of Quality factor / Describe its effect on bandwidth. (2022, 2023) Answer:

Significance: The Quality Factor ( $Q$ ) measures the “sharpness” of resonance or the selectivity of the circuit. It relates the maximum energy stored to the energy dissipated per cycle ( $Q = 2 π \frac{Peak Energy Stored}{Energy Dissipated}$ ).
Effect on Bandwidth: $Q$ is inversely proportional to bandwidth ( $B$ ). $Q = ω_{0} / B$ . A higher $Q$ results in a narrower bandwidth (higher selectivity), while a lower $Q$ results in a wider bandwidth.

Q: Write down the condition for resonance in an AC circuit. (2018, 2022, 2023) Answer: Resonance occurs when the imaginary part of the transfer function or impedance is zero, resulting in a purely resistive impedance.

Condition: The inductive reactance equals the capacitive reactance ( $X_{L} = X_{C}$ ) or $ω L = 1/ ω C$ .
Resonant Frequency: $ω_{0} = \frac{1}{L C}$ ,.

Q: Explain the effects of varying capacitance on the voltages and currents in a series RLC circuit. (2018) Answer: In a series RLC circuit, varying capacitance ( $C$ ) changes the capacitive reactance ( $X_{C} = 1/ ω C$ ) and the resonant frequency ( $ω_{0} = 1/ L C$ ).

If $C$ is adjusted such that $X_{C} = X_{L}$ , the circuit resonates, impedance is minimum ( $Z = R$ ), and current is maximum ( $I = V_{m} / R$ ).
If $C$ moves away from this value, impedance increases, current decreases, and the voltages across the inductor and capacitor ( $V_{L}, V_{C}$ ) become unequal,.

Q: Describe the use of an RLC series circuit as a selector. (2018) Answer: An RLC series circuit acts as a Band-Pass Filter. Because the impedance is minimum at the resonant frequency $ω_{0}$ , it allows signals near $ω_{0}$ to pass with high current (and high output voltage across the resistor) while attenuating frequencies outside the bandwidth. This selectivity allows it to “tune in” to specific stations in radio receivers.

Q: What are the conditions for series and parallel resonance? (2024) Answer:,

Series: Impedance is minimum ( $Z = R$ ). Current is Maximum. $X_{L} = X_{C}$ . Voltage and Current are in phase.
Parallel: Impedance is maximum. Voltage is Maximum. The current flowing through the inductor and capacitor cancel each other out in the main line. $X_{L} = X_{C}$ .

Q: Write down applications of resonance. (2024) Answer:

Radio/TV Tuning: Selecting a specific frequency channel.
Filters: Designing Band-pass or Band-stop filters.
Oscillators: Generating specific AC frequencies.

6. Three-Phase Systems

Q: What are the advantages of using a $3Φ$ system over a $1Φ$ system? (2017, 2019, 2023, 2024) Answer:

Economy: For the same amount of power transmitted, a 3-phase system uses less conductor material (wire) than an equivalent single-phase system (about 25% less),.
Constant Power: The instantaneous power in a balanced 3-phase system is constant (not pulsating), leading to smoother operation and less vibration in motors,.
Efficiency: 3-phase motors and generators are more efficient and have better starting torque than single-phase motors.

Q: Explain the two-lamp method of determining the phase sequence of a $3Φ$ system. (2016, 2018, 2019) Answer: (External Information - Standard Engineering Practice) To determine phase sequence (RYB or RBY):

Connect two lamps and an inductor in a Star (Y) configuration. One leg has the inductor, the other two have lamps.
Connect this test load to the 3-phase supply.
Because the inductor creates a phase shift, the voltages across the lamps will become unequal.
Result: One lamp will glow brighter than the other. If the lamp connected to the phase leading the inductor’s phase is brighter, the sequence can be determined based on the specific wiring diagram (commonly: Bright-Dim indicates one sequence, Dim-Bright indicates the reverse).

Q: How can phase sequence be determined (voltmeter method)? (2017, 2023) Answer: (External Information) Similar to the lamp method, but replaces lamps with a voltmeter.

An inductor (or capacitor) and a resistor are connected in series across two lines.
A voltmeter is measured from the junction of these components to the third line.
The magnitude of the voltage reading will differ depending on the phase sequence, allowing identification of the sequence order.

007_index