BEE (Bachelor of Electrical Engineering) Exam — Questions and Answers

Question 1: In a power system protection scheme, what is the purpose of a 'zone of protection'?

To define the geographic boundary of a utility's service territory
To identify the section of the system that a specific relay is responsible for isolating during faults (Correct answer)
To specify the voltage level at which a relay operates
To limit the number of circuit breakers that must operate for a given fault

Correct answer: To identify the section of the system that a specific relay is responsible for isolating during faults

A protection zone defines the electrical boundary within which a relay detects faults and initiates breaker tripping to isolate only the faulted section.

Question 2: In a common-emitter amplifier, what is the effect of adding an unbypassed emitter resistor?

Decreases both voltage gain and input impedance
Decreases voltage gain and increases input impedance (Correct answer)
Increases both voltage gain and input impedance
Increases voltage gain and decreases input impedance

Correct answer: Decreases voltage gain and increases input impedance

An unbypassed emitter resistor introduces negative feedback, which reduces voltage gain but increases input impedance and improves stability.

Question 3: The power spectral density (PSD) of a wide-sense stationary (WSS) random process is the Fourier transform of its:

Probability density function
Autocorrelation function (Correct answer)
Mean function
Cross-correlation function

Correct answer: Autocorrelation function

By the Wiener-Khinchin theorem, the PSD is the Fourier transform of the autocorrelation function.

Question 4: In a p-n junction solar cell, what generates the photocurrent?

Electron-hole pairs created in or near the depletion region (Correct answer)
Thermionic emission over the barrier
Tunneling through the junction barrier
Majority carrier drift in the bulk

Correct answer: Electron-hole pairs created in or near the depletion region

Photons absorbed in or near the depletion region create electron-hole pairs that are swept by the built-in electric field, producing photocurrent.

Question 5: Which Boolean expression is correctly simplified using De Morgan's theorem: NOT(A AND B)?

NOT(A) OR NOT(B) (Correct answer)
NOT(A) AND NOT(B)
NOT(A OR B)
A OR B

Correct answer: NOT(A) OR NOT(B)

De Morgan's theorem states that NOT(A·B) = NOT(A) + NOT(B), converting NAND to OR of complements.

Question 6: Downsampling a discrete-time signal x[n] by factor M produces y[n] = x[Mn]. This operation in the frequency domain causes the spectrum to be:

Multiplied by M
Expanded by M with aliasing if not bandlimited (Correct answer)
Compressed by M
Shifted by M

Correct answer: Expanded by M with aliasing if not bandlimited

Downsampling by M expands the spectrum by M and introduces aliasing unless the signal is bandlimited to π/M.

Question 7: In DMA (Direct Memory Access) data transfer, what role does the CPU play during the transfer?

The CPU pre-loads the DMA buffer
The CPU and DMA share alternating bus cycles
The CPU is bypassed; the DMA controller handles the transfer (Correct answer)
The CPU manages each data word transfer

Correct answer: The CPU is bypassed; the DMA controller handles the transfer

DMA allows the DMA controller to transfer data directly between memory and I/O without CPU intervention, freeing the CPU for other tasks.

Question 8: In digital logic, glitches (hazards) in combinational circuits are caused by:

Too many gate inputs
Incorrect Boolean expressions
Unequal propagation delays through different paths (Correct answer)
Insufficient fan-out

Correct answer: Unequal propagation delays through different paths

Glitches occur when signal transitions take different amounts of time through alternate paths, causing momentary incorrect output values.

Question 9: Parseval's theorem for continuous-time signals states that:

∫|x(t)|²dt = (1/2π)∫|X(jω)|²dω (Correct answer)
∫x(t)dt = X(0)
∫x(t)h(t)dt = X(jω)H(jω)
∫|X(jω)|dω = ∫|x(t)|dt

Correct answer: ∫|x(t)|²dt = (1/2π)∫|X(jω)|²dω

Parseval's theorem equates signal energy in time and frequency domains with the 1/2π normalization factor.

Question 10: In a three-phase synchronous generator, what happens when the field excitation is increased beyond the value needed for unity power factor?

The generator operates at lagging power factor
The generator absorbs reactive power from the grid
The generator operates at leading power factor
The generator supplies reactive power to the grid (Correct answer)

Correct answer: The generator supplies reactive power to the grid

Over-excitation causes the synchronous generator to supply reactive power (VAR) to the grid, appearing as a lagging power factor source.

Question 11: If the voltage across a 5 Ω resistor is 20 V, what is the power dissipated?

4 W
80 W (Correct answer)
100 W
25 W

Correct answer: 80 W

P = V²/R = 400/5 = 80 W.

Question 12: A delta (Δ) network has resistors R_AB = 30 Ω, R_BC = 30 Ω, R_CA = 30 Ω. What is the equivalent star (Y) resistance at each node?

90 Ω
10 Ω (Correct answer)
30 Ω
15 Ω

Correct answer: 10 Ω

For a balanced delta, R_Y = R_Δ / 3 = 30 / 3 = 10 Ω at each node.

Question 13: The Z-transform of δ[n - k] for k > 0 is:

z^k
1
z^(-k) (Correct answer)
k·z^(-1)

Correct answer: z^(-k)

By the time-shifting property of the Z-transform, δ[n-k] ↔ z^(-k).

Question 14: A designer needs to create a circuit that sequences through a specific series of states, but the transitions between states should only occur on the rising edge of a clock signal. Which of the following is the most fundamental building block for this type of circuit?

A flip-flop (Correct answer)
A multiplexer
An AND gate
A comparator

Correct answer: A flip-flop

Sequential circuits, which change state based on a clock signal, use memory elements to store their current state. The fundamental building block for clocked sequential circuits is the flip-flop, which is a bistable multivibrator that can store one bit of information and change its state only at a specific edge of a clock pulse.

Question 15: During a load flow analysis using the Newton-Raphson method, PQ buses have which quantities specified?

Voltage magnitude and angle
Real power and reactive power (Correct answer)
Reactive power and voltage angle
Real power and voltage magnitude

Correct answer: Real power and reactive power

At PQ (load) buses, both real power P and reactive power Q are specified, while voltage magnitude and angle are calculated.

Question 16: Which flip-flop is commonly used to eliminate metastability issues in clock domain crossing designs?

SR latch
JK flip-flop
Two-stage synchronizer using D flip-flops (Correct answer)
T flip-flop

Correct answer: Two-stage synchronizer using D flip-flops

A two-stage synchronizer with back-to-back D flip-flops allows the potentially metastable output of the first stage to settle before being sampled by the second.

Question 17: A discrete-time system is stable if all poles of its transfer function H(z) lie:

On the unit circle
Inside the unit circle (Correct answer)
On the imaginary axis
Outside the unit circle

Correct answer: Inside the unit circle

Discrete-time BIBO stability requires all poles to be strictly inside the unit circle in the z-plane.

Question 18: What is the Boolean simplification of the expression AB + AB'?

A (Correct answer)
A'
AB
B

Correct answer: A

AB + AB' = A(B + B') = A·1 = A by the complement and identity laws.

Question 19: A transmission line with a characteristic impedance of 50 Ω is terminated with a load impedance of 100 Ω. What is the Voltage Standing Wave Ratio (VSWR) on the line?

0.333
0.5
2.0 (Correct answer)
1.5

Correct answer: 2.0

First, calculate the reflection coefficient (Γ) using the formula: Γ = (ZL - Z0) / (ZL + Z0). Here, ZL = 100 Ω and Z0 = 50 Ω. So, Γ = (100 - 50) / (100 + 50) = 50 / 150 = 1/3. Next, calculate the VSWR using the formula: VSWR = (1 + |Γ|) / (1 - |Γ|). VSWR = (1 + 1/3) / (1 - 1/3) = (4/3) / (2/3) = 2.0. A VSWR of 2.0 indicates a mismatch where the maximum voltage on the line is twice the minimum voltage.

Question 20: Which instrument is best suited for measuring very low resistances (below 1 Ω) accurately?

Wheatstone bridge
Kelvin double bridge (Correct answer)
Megohmmeter
Schering bridge

Correct answer: Kelvin double bridge

The Kelvin double bridge eliminates the error due to lead and contact resistance by using a second set of ratio arms, making it ideal for milliohm measurements.

Question 21: State feedback control with full state feedback u = -Kx can place all closed-loop poles arbitrarily if and only if the system is:

Observable
Minimum phase
Controllable (Correct answer)
Stable

Correct answer: Controllable

Arbitrary pole placement via state feedback is possible if and only if the system is completely controllable (the controllability matrix has full rank).

Question 22: A power system has a total spinning reserve of 500 MW. If the largest online generating unit is rated at 600 MW, what reliability concern exists?

The frequency will increase uncontrollably
The transmission lines will become overloaded
Voltage collapse is imminent
The system cannot cover the loss of its largest unit (Correct answer)

Correct answer: The system cannot cover the loss of its largest unit

Spinning reserve of 500 MW is insufficient to cover the 600 MW loss from the largest unit trip, violating the N-1 contingency criterion.

Question 23: What type of semiconductor material results when silicon is doped with phosphorus?

Intrinsic semiconductor with no net charge
p-type, with holes as majority carriers
n-type, with electrons as majority carriers (Correct answer)
Degenerate insulator

Correct answer: n-type, with electrons as majority carriers

Phosphorus has five valence electrons; donating one to the lattice creates a free electron, making the silicon n-type.

Question 24: In Boolean algebra, what does the consensus theorem state about the term AB + A'C + BC?

It equals A'C + BC
It equals AB + BC
It equals AB + A'C (Correct answer)
It equals BC

Correct answer: It equals AB + A'C

The consensus theorem states that BC is redundant when both AB and A'C are present, so AB + A'C + BC = AB + A'C.

Question 25: In a power system, HVDC transmission is preferred over HVAC for very long distances primarily because:

DC lines require more conductors
DC systems have lower capital costs for short distances
There are no reactive power or skin effect losses, reducing overall transmission losses (Correct answer)
DC transformers are more efficient than AC transformers

Correct answer: There are no reactive power or skin effect losses, reducing overall transmission losses

HVDC eliminates reactive power losses, capacitive charging, and skin effect, making it more efficient for distances beyond the breakeven point (~600–800 km).

Question 26: The built-in potential (contact potential) of a p-n junction at thermal equilibrium is caused by:

Minority carrier injection
Generation-recombination in the depletion region
Applied external voltage
Diffusion of majority carriers and resulting charge separation (Correct answer)

Correct answer: Diffusion of majority carriers and resulting charge separation

Diffusion of holes into the n-side and electrons into the p-side creates charge separation, establishing the built-in potential.

Question 27: The unit of capacitance is:

Ohm
Henry
Watt
Farad (Correct answer)

Correct answer: Farad

Capacitance is measured in Farads (F). Common values are in µF, nF, or pF.

Question 28: The continuity equation ∇ · J + ∂ρ/∂t = 0 expresses conservation of:

Energy
Magnetic flux
Momentum
Electric charge (Correct answer)

Correct answer: Electric charge

The continuity equation is the mathematical statement of charge conservation, linking current density to charge density.

Question 29: The resolution of a 12-bit DAC with a full-scale output of 5 V is approximately:

4.88 mV
2.44 mV
9.77 mV
1.22 mV (Correct answer)

Correct answer: 1.22 mV

Resolution = Full-scale / (2ⁿ − 1) = 5 V / 4095 ≈ 1.22 mV, representing the smallest output voltage step.

Question 30: What is the primary architectural difference that distinguishes a Von Neumann architecture from a Harvard architecture in microprocessors?

The organization of memory and buses for instructions and data. (Correct answer)
The use of a RISC versus a CISC instruction set.
The speed of the system clock.
The number of processing cores available.

Correct answer: The organization of memory and buses for instructions and data.

The key difference lies in the memory structure. A Von Neumann architecture uses a single, shared memory and a common bus for both program instructions and data. In contrast, a Harvard architecture uses physically separate memories and separate buses for instructions and data, which allows the CPU to fetch an instruction and access data simultaneously, potentially overcoming the 'Von Neumann bottleneck'.

Question 31: For a second-order underdamped system, the peak overshoot Mp in the step response is determined by:

Neither ωn nor ζ
Both ωn and ζ
Damping ratio ζ only (Correct answer)
Natural frequency ωn only

Correct answer: Damping ratio ζ only

Peak overshoot Mp = exp(−πζ/√(1−ζ²)) depends solely on the damping ratio ζ, not on the natural frequency.

Question 32: In a Wheatstone bridge circuit at balance condition, what is the current through the galvanometer?

Maximum
Half of supply current
Equal to supply current
Zero (Correct answer)

Correct answer: Zero

At balance, the potential difference across the galvanometer is zero, so no current flows through it.

Question 33: Where the voltage division issue appears

Both series and parallel resistors.
Series connected resistors (Correct answer)
When resistors are equal
Parallel connected resistors

Correct answer: Series connected resistors

Voltage division occurs when resistors are connected in series. In a series circuit, the total voltage across the combination is divided among the individual resistors in proportion to their resistance values. The current, however, remains the same through all series components.

Question 34: In a CMOS inverter, static power dissipation is nearly zero because:

The supply voltage is very low
Both transistors are always in saturation
Both transistors have identical threshold voltages
Only one transistor conducts at a time in steady state (Correct answer)

Correct answer: Only one transistor conducts at a time in steady state

In steady state, either the PMOS or NMOS is OFF, creating no DC path from VDD to GND and eliminating static power.

Question 35: Which semiconductor material has a bandgap energy of approximately 1.12 eV at room temperature?

Gallium arsenide
Silicon carbide
Germanium
Silicon (Correct answer)

Correct answer: Silicon

Silicon has a bandgap energy of approximately 1.12 eV at 300 K, which is fundamental to its widespread use in electronics.

Question 36: Faraday's law of electromagnetic induction states that the induced EMF is proportional to the:

Rate of change of magnetic flux (Correct answer)
Magnitude of the magnetic field
Resistance of the circuit
Velocity of the conductor only

Correct answer: Rate of change of magnetic flux

Faraday's law: EMF = -dΦ/dt; the induced EMF equals the rate of change of magnetic flux linkage.

Question 37: Which interrupt in the 8085 microprocessor is non-maskable?

RST 6.5
INTR
TRAP (Correct answer)
RST 7.5

Correct answer: TRAP

TRAP is the only non-maskable interrupt in the 8085, meaning it cannot be disabled by software and always gets serviced.

Question 38: In a purely capacitive AC circuit, the current leads the voltage by:

180°
45°
0°
90° (Correct answer)

Correct answer: 90°

In a purely capacitive circuit, the current leads voltage by 90° (or π/2 radians).

Question 39: By _________, inductance control is attained.

using R5
using R4
using R2 (Correct answer)
using Lx

Correct answer: using R2

In many AC bridge circuits used for inductance measurement, such as the Maxwell or Hay bridge, the unknown inductance (Lx) is balanced by adjusting a variable resistance in one of the bridge arms. Often, this variable resistance is denoted as R2, which directly influences the balance equation for inductance. Thus, adjusting R2 allows for control and measurement of inductance.

Question 40: The group delay of a system is defined as:

dφ(ω)/dω
φ(ω)/ω
-dφ(ω)/dω (Correct answer)
-φ(ω)/ω

Correct answer: -dφ(ω)/dω

Group delay τ_g(ω) = -dφ(ω)/dω, representing the delay experienced by a narrowband signal centered at ω.

Question 41: The sensitivity of a voltmeter is expressed in:

Ohms per volt (Correct answer)
Volts per ohm
Watts per volt
Amperes per volt

Correct answer: Ohms per volt

Voltmeter sensitivity (Ω/V) indicates how much resistance the meter presents per volt of full-scale deflection; higher is better.

Question 42: The transfer function of an ideal PD controller is:

Kp(1 + 1/(Ti·s) + Td·s)
Kp(1 + Td·s) (Correct answer)
Kp/(Ti·s)
Kp/(1 + Ti·s)

Correct answer: Kp(1 + Td·s)

A PD controller adds proportional and derivative action, yielding the transfer function Kp(1 + Td·s).

Question 43: A PI controller introduces which of the following into the open-loop transfer function?

Two poles at the origin
A pair of complex poles
An additional pole at the origin and a zero in the LHP (Correct answer)
An additional zero at the origin and a pole in the LHP

Correct answer: An additional pole at the origin and a zero in the LHP

A PI controller C(s) = Kp + Ki/s = (Kp·s + Ki)/s adds a pole at s=0 (integrator) and a zero at s = -Ki/Kp in the left-half plane.

Question 44: The discrete Fourier transform (DFT) of a sequence of length N has how many unique frequency components?

N/2
N-1
2N
N (Correct answer)

Correct answer: N

The N-point DFT produces exactly N complex-valued frequency coefficients.

Question 45: An inductor of 0.5 H carries a current that changes from 2 A to 6 A in 0.1 s. What is the induced voltage across it?

40 V
5 V
20 V (Correct answer)
10 V

Correct answer: 20 V

V = L × (ΔI/Δt) = 0.5 × (4/0.1) = 20 V.

Question 46: What is the time constant of an RC circuit with R = 10 kohm and C = 100 microfarads?

0.01 second
0.1 second
10 seconds
1 second (Correct answer)

Correct answer: 1 second

The time constant tau equals R times C, so 10,000 ohms multiplied by 0.0001 farads equals 1 second.

Question 47: Creep in an energy meter refers to:

Vibration of the moving parts
Slow rotation under rated load
Backward rotation of the disc
Continuous rotation of the disc with no load applied (Correct answer)

Correct answer: Continuous rotation of the disc with no load applied

Creep is the slow continuous rotation of the energy meter disc when voltage is applied but no load current flows, causing measurement error.

Question 48: Thevenin's theorem allows a complex circuit to be represented as:

A current source in parallel with resistance
A voltage source in series with resistance (Correct answer)
An ideal transformer
A single resistor

Correct answer: A voltage source in series with resistance

Thevenin equivalent: open-circuit voltage source (Vth) in series with Thevenin resistance (Rth).

Question 49: A PD controller applied to a second-order plant primarily has what effect on the closed-loop system?

Adds a zero that increases damping ratio (Correct answer)
Increases steady-state error
Reduces bandwidth
Introduces an integrator

Correct answer: Adds a zero that increases damping ratio

The derivative term of the PD controller adds a zero to the open-loop transfer function, which increases damping and reduces overshoot.

Question 50: Norton's theorem states that any linear two-terminal DC network can be replaced by:

A voltage source in series with a resistance
A current source in series with a resistance
A voltage source in parallel with a resistance
A current source in parallel with a resistance (Correct answer)

Correct answer: A current source in parallel with a resistance

Norton's theorem represents any linear circuit as an equivalent current source in parallel with an equivalent resistance.

Question 51: Which of the following is a digital electronic example?

Computers
All of the mentioned (Correct answer)
Digital cameras
Information appliances

Correct answer: All of the mentioned

Digital electronics deals with devices that process information in discrete, binary formats. Digital cameras capture and store images as digital data, computers operate entirely on digital instructions and data, and information appliances like smartphones are essentially specialized digital computing devices. All these examples fundamentally rely on digital circuits and principles for their operation.

Question 52: What is the purpose of a power system stabilizer (PSS) installed on a synchronous generator excitation system?

Maintain terminal voltage at the scheduled setpoint
Control real power output according to the dispatch schedule
Damp low-frequency electromechanical oscillations to improve small-signal stability (Correct answer)
Limit fault current contribution from the generator

Correct answer: Damp low-frequency electromechanical oscillations to improve small-signal stability

A PSS adds a supplementary signal to the voltage regulator to provide damping torque, suppressing rotor oscillations (typically 0.1–2 Hz) that can destabilize interconnected systems.

Question 53: The phase margin of a stable feedback system is measured at the frequency where the open-loop magnitude is:

Equal to the phase crossover frequency
+3 dB
0 dB (unity gain) (Correct answer)
−3 dB

Correct answer: 0 dB (unity gain)

Phase margin is the additional phase lag at the gain crossover frequency (where |G(jω)H(jω)| = 1, or 0 dB) before the system becomes unstable.

Question 54: In a Nyquist plot, what does an encirclement of the point (-1, 0) indicate?

The system is always overdamped
The system has zero steady-state error
The closed-loop system may be unstable (Correct answer)
The gain margin is infinite

Correct answer: The closed-loop system may be unstable

Encirclements of the (-1, 0) point relate to closed-loop poles in the right-half plane via the Nyquist stability criterion.

Question 55: What is the purpose of the program counter (PC) in a microprocessor?

Stores the result of arithmetic operations
Holds the address of the next instruction to fetch (Correct answer)
Counts the number of executed instructions
Controls the ALU operation mode

Correct answer: Holds the address of the next instruction to fetch

The program counter holds the memory address of the next instruction to be fetched and executed.

Question 56: A current source of 5 A is connected in parallel with a 10 Ω resistor. What is the voltage across the resistor?

50 V (Correct answer)
0.5 V
2 V
25 V

Correct answer: 50 V

Using Ohm's law, V = I × R = 5 A × 10 Ω = 50 V.

Question 57: When a system follows the laws of linear dynamics, it is referred to

both scaling and additivity (Correct answer)
homogeneity
scaling
additivity

Correct answer: both scaling and additivity

A system is considered linear if it satisfies two fundamental properties: additivity and homogeneity (also known as scaling). Additivity means that the response to a sum of inputs is the sum of the responses to individual inputs. Homogeneity means that scaling the input by a constant factor results in the output being scaled by the same factor. Both properties must hold for a system to be classified as linear.

Question 58: What type of motor uses a commutator and brushes for operation?

Stepper motor
DC motor (Correct answer)
Synchronous motor
Induction motor

Correct answer: DC motor

DC motors use a commutator and brushes to reverse current direction in the armature windings for continuous rotation.

Question 59: An overhead transmission line has a distributed capacitance to ground. Under steady-state AC operation, this capacitance causes the line to:

Absorb reactive power (lagging)
Generate reactive power (leading) (Correct answer)
Have no effect on reactive power
Reduce active power transfer

Correct answer: Generate reactive power (leading)

Shunt capacitance generates leading reactive power (VArs), which can raise voltage levels along the line.

Question 60: For an ideal op-amp, which of the following is true?

Infinite input impedance, zero output impedance, infinite open-loop gain (Correct answer)
Zero input impedance, infinite output impedance, finite gain
Finite input impedance, zero output impedance, finite gain
Infinite input and output impedance, unity gain

Correct answer: Infinite input impedance, zero output impedance, infinite open-loop gain

An ideal op-amp has infinite input impedance, zero output impedance, and infinite open-loop differential gain.

Question 61: According to Kirchhoff's Current Law, what is the sum of currents entering a node?

Always zero
Equal to the supply current
Equal to the sum of currents leaving the node (Correct answer)
Dependent on the resistance values

Correct answer: Equal to the sum of currents leaving the node

Kirchhoff's Current Law states that the algebraic sum of currents at any node is zero, meaning currents in equal currents out.

BEE (Bachelor of Electrical Engineering) Exam

The BEE (Bachelor of Electrical Engineering) Exam exam validates essential knowledge and skills required for certification or licensure in this field.

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