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

Question 1: What is the primary advantage of a digital multimeter over an analog multimeter?

Higher input impedance and better accuracy (Correct answer)
Faster response time for transient signals
Lower cost and simpler construction
Ability to measure only AC quantities

Correct answer: Higher input impedance and better accuracy

Digital multimeters offer higher input impedance (typically 10 MΩ or more) and superior accuracy compared to analog meters, reducing loading effects on the circuit under test.

Question 2: Which of the following correctly defines the phase margin in the context of a Bode plot analysis?

The amount of additional gain required to make the system marginally stable at the phase crossover frequency.
The frequency at which the phase angle is -180 degrees.
The difference between the system's phase angle and -180 degrees at the gain crossover frequency. (Correct answer)
The phase angle at the frequency where the magnitude plot crosses 0 dB.

Correct answer: The difference between the system's phase angle and -180 degrees at the gain crossover frequency.

The phase margin is a measure of relative stability. It is found at the gain crossover frequency (where the magnitude plot is 0 dB). The phase margin is the amount of additional phase lag required to make the system unstable, calculated as the difference between the system's phase at that frequency and -180 degrees.

Question 3: Which error results from the loading effect of a voltmeter on a circuit?

Gross error
Random error
Observational error
Systematic error (Correct answer)

Correct answer: Systematic error

Loading error is a systematic error because it consistently affects every measurement in the same direction due to the meter's finite input impedance.

Question 4: Which material is most commonly used as a conductor in residential electrical wiring in the United States?

Aluminum
Silver
Copper (Correct answer)
Gold

Correct answer: Copper

Copper is the standard conductor for US residential wiring due to its excellent conductivity, ductility, and cost-effectiveness.

Question 5: In a three-phase synchronous generator, what happens when the field excitation is increased beyond the value needed for unity 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)
The generator operates at lagging power factor

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 6: A system with transfer function G(s) = 5/(s² + 4s + 5) has poles at which locations?

-2 ± 2j
-4 ± j
-1 ± 2j
-2 ± j (Correct answer)

Correct answer: -2 ± j

Using the quadratic formula on s² + 4s + 5 = 0 gives s = -2 ± j1.

Question 7: In a series RLC circuit at resonance, which of the following is true?

The phase angle is 90 degrees
The impedance is purely resistive (Correct answer)
The current is at its minimum value
The impedance is at its maximum value

Correct answer: The impedance is purely resistive

At resonance, inductive and capacitive reactances cancel, leaving only resistance.

Question 8: An overhead transmission line has a distributed capacitance to ground. Under steady-state AC operation, this capacitance causes the line to:

Generate reactive power (leading) (Correct answer)
Have no effect on reactive power
Absorb reactive power (lagging)
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 9: The term 'dead zone' in an instrument refers to:

The maximum overload the instrument can withstand
The frequency range where the instrument is inaccurate
The range of input values that produce no change in output (Correct answer)
The range where output is nonlinear

Correct answer: The range of input values that produce no change in output

The dead zone (or dead band) is the largest range of input change that fails to produce any detectable change in the instrument's output.

Question 10: A 120 V source has an internal resistance of 5 Ω. What is the maximum power that can be delivered to a load?

360 W
2880 W
1440 W
720 W (Correct answer)

Correct answer: 720 W

At maximum power transfer (R_L = R_s = 5 Ω), P_max = V_s²/(4R_s) = 14400/20 = 720 W.

Question 11: What physical law does Faraday's law in Maxwell's equations describe?

Electric charges produce electric fields
Magnetic monopoles do not exist
Moving charges create magnetic fields
A time-varying magnetic field induces an electric field (Correct answer)

Correct answer: A time-varying magnetic field induces an electric field

Faraday's law states that a changing magnetic flux through a surface induces a circulating electric field along its boundary.

Question 12: The most sensitive detector for a single frequency value is which one of the following?

headphone
oscillator
vibration galvanometer
tuned detector (Correct answer)

Correct answer: tuned detector

A tuned detector, such as a tuned amplifier or a resonant circuit, is designed to be highly sensitive to a specific frequency while rejecting others. This makes it the most sensitive choice for detecting a signal at a single, known frequency in bridge circuits or communication systems, as it can filter out noise and interference.

Question 13: What is the purpose of a priority encoder?

To select one of many data inputs based on a binary address
To generate a binary code corresponding to the highest-priority active input (Correct answer)
To detect and correct single-bit errors
To convert a decimal number to BCD

Correct answer: To generate a binary code corresponding to the highest-priority active input

A priority encoder accepts multiple inputs and outputs a binary code representing the highest-priority (typically highest-numbered) active input, resolving conflicts when multiple inputs are asserted.

Question 14: What is the divergence of the magnetic flux density B in free space?

∇·B = ρ/ε₀
∇·B = μ₀J
∇·B = 0 (Correct answer)
∇·B = ∂E/∂t

Correct answer: ∇·B = 0

Maxwell's equation states that magnetic monopoles do not exist, so the divergence of B is always zero.

Question 15: A 4-bit ripple carry adder adds two numbers in how many gate delays compared to a carry look-ahead adder?

Exactly twice the delays
More gate delays (Correct answer)
The same gate delays
Fewer gate delays

Correct answer: More gate delays

A ripple carry adder propagates carry serially through each stage, resulting in more gate delays than a carry look-ahead adder which computes carries in parallel.

Question 16: Which phenomenon causes sub-synchronous resonance (SSR) in power systems?

Overvoltage on lightly loaded cables
Resonance between transformer leakage inductance and bus capacitance
Harmonic injection from nonlinear loads
Interaction between series-compensated transmission lines and the torsional modes of nearby turbine-generator shafts (Correct answer)

Correct answer: Interaction between series-compensated transmission lines and the torsional modes of nearby turbine-generator shafts

Series capacitor compensation creates an LC resonant frequency below synchronous frequency; if this matches a shaft torsional mode, the shaft can experience growing oscillations and fatigue damage.

Question 17: Thevenin's theorem states that any linear circuit with sources and resistors can be replaced by:

A single resistor connected to ground
Two voltage sources connected in series
A single current source in parallel with a resistance
A single voltage source in series with a resistance (Correct answer)

Correct answer: A single voltage source in series with a resistance

Thevenin's theorem simplifies any linear two-terminal network into an equivalent circuit consisting of a single ideal voltage source (Vth) in series with a single resistance (Rth), making complex circuit analysis much simpler.

Question 18: Which addressing mode uses the content of a register as the memory address?

Direct
Register indirect (Correct answer)
Indexed
Immediate

Correct answer: Register indirect

Question 19: A 4-to-16 decoder can be constructed from:

Four 2-to-4 decoders with an enable input
One 2-to-4 decoder and one 3-to-8 decoder
Two 3-to-8 decoders with an enable input (Correct answer)
Two 2-to-4 decoders only

Correct answer: Two 3-to-8 decoders with an enable input

Two 3-to-8 decoders with enable lines can be combined — one upper address bit selects which 3-to-8 decoder is active, giving 16 total outputs.

Question 20: What relationship does the balance equation have to frequency?

varies by a factor of 2
independent (Correct answer)
depends on the supply magnitude
depends on the detector used

Correct answer: independent

For many AC bridge circuits, particularly those designed for measuring resistance or capacitance, the balance equation is independent of the supply frequency. This means that once the bridge is balanced, it remains balanced regardless of the frequency of the AC source. This characteristic simplifies measurements and ensures accuracy across different frequencies for these specific bridge types.

Question 21: In a p-n junction diode under forward bias, the depletion region width:

First increases then decreases
Increases
Remains unchanged
Decreases (Correct answer)

Correct answer: Decreases

Forward bias reduces the built-in electric field, causing the depletion region to narrow.

Question 22: What is the typical per-unit reactance range for a large power transformer used in a 500 kV transmission system?

0.005 to 0.02 per unit
0.50 to 0.80 per unit
1.0 to 1.5 per unit
0.08 to 0.15 per unit (Correct answer)

Correct answer: 0.08 to 0.15 per unit

Large EHV power transformers typically have leakage reactance in the range of 0.08 to 0.15 per unit on their own MVA base.

Question 23: The definition of a multiplier is

capacitive
non-capacitive
resistive
non-inductive (Correct answer)

Correct answer: non-inductive

In electrical measurement, a multiplier is a high resistance connected in series with a voltmeter to extend its voltage range. For accurate readings, especially with alternating current (AC) voltages, it is crucial that this resistance is non-inductive. Any significant inductance would introduce undesirable phase shifts and impedance changes with frequency, leading to errors in the voltage measurement.

Question 24: What does a zener diode primarily regulate in a circuit?

Voltage (Correct answer)
Power factor
Frequency
Current

Correct answer: Voltage

A zener diode operates in reverse breakdown to maintain a constant voltage across its terminals.

Question 25: Which of the following is a primary advantage of using CMOS (Complementary Metal-Oxide-Semiconductor) logic gates over TTL (Transistor-Transistor Logic) gates?

Significantly faster switching speed in all applications.
Much lower static power dissipation. (Correct answer)
Greater immunity to electrostatic discharge (ESD).
Simpler fabrication process.

Correct answer: Much lower static power dissipation.

The main advantage of CMOS technology is its very low static power dissipation. In a static state (output not changing), one of the complementary MOSFETs in a CMOS gate is always off, creating a high-impedance path from the power supply to ground and consuming negligible current. TTL gates, in contrast, draw a considerable amount of current even when their state is not changing.

Question 26: In a MOSFET, the threshold voltage VT is most directly affected by which parameter?

Channel length modulation
Drain-source voltage
Gate oxide thickness (Correct answer)
Minority carrier lifetime

Correct answer: Gate oxide thickness

Threshold voltage is directly related to oxide capacitance, which depends on gate oxide thickness (VT increases as tox increases).

Question 27: Which logic family offers the lowest power consumption in static conditions?

BiCMOS
ECL
CMOS (Correct answer)
TTL

Correct answer: CMOS

CMOS logic draws negligible static power because its complementary transistor pairs ensure one is always off in steady state.

Question 28: In a microprocessor's instruction cycle, which operation follows the fetch phase?

Execute
Memory access
Decode (Correct answer)
Write-back

Correct answer: Decode

After fetching the instruction from memory, the processor decodes it to determine the operation and operands.

Question 29: In Boolean algebra, what does the consensus theorem state about the term AB + A'C + BC?

It equals AB + A'C (Correct answer)
It equals AB + BC
It equals BC
It equals A'C + 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 30: When a P-N junction diode is forward-biased, what is the primary effect on the depletion region and the potential barrier?

The depletion region narrows, and the potential barrier is reduced. (Correct answer)
The depletion region and potential barrier remain unchanged.
The depletion region disappears completely, and the potential barrier inverts.
The depletion region widens, and the potential barrier increases.

Correct answer: The depletion region narrows, and the potential barrier is reduced.

Applying a forward-bias voltage (positive to P-type, negative to N-type) opposes the built-in potential barrier of the P-N junction. This opposition reduces the height of the potential barrier and causes the depletion region to become narrower, allowing majority charge carriers to cross the junction and current to flow easily.

Question 31: What is the skin depth δ for a good conductor with conductivity σ, permeability μ, at frequency f?

1/√(πfμσ)
√(2/ωμσ)
Both A and B are equivalent (Correct answer)
2π/√(μσf)

Correct answer: Both A and B are equivalent

Both 1/√(πfμσ) and √(2/ωμσ) are equivalent expressions for skin depth since ω = 2πf.

Question 32: In a three-phase induction motor running at slip s, the frequency of the rotor currents is:

f / s
(1 - s) × f
f (supply frequency)
s × f (Correct answer)

Correct answer: s × f

The rotor cuts flux lines at slip speed (s × Ns), so the frequency of rotor currents is s × f, where f is the supply frequency.

Question 33: According to the Biot-Savart law, the magnetic field dB due to a current element Idl at distance r is proportional to which quantity?

Idl × r̂ / r² (Correct answer)
Idl / r³
Idl · r̂ / r²
Idl × r̂ / r

Correct answer: Idl × r̂ / r²

The Biot-Savart law states dB = (μ₀/4π)(Idl × r̂)/r², showing an inverse-square dependence on distance.

Question 34: In a digital logic circuit, what is the primary functional difference between a combinational circuit and a sequential circuit?

Sequential circuits are constructed exclusively from AND, OR, and NOT gates, whereas combinational circuits incorporate memory elements like flip-flops.
Combinational circuits require a clock signal for operation, while sequential circuits are asynchronous and do not.
A combinational circuit's output depends solely on its current inputs, while a sequential circuit's output depends on both current inputs and its previous state. (Correct answer)
The speed of a combinational circuit is generally slower than that of a sequential circuit due to the lack of memory.

Correct answer: A combinational circuit's output depends solely on its current inputs, while a sequential circuit's output depends on both current inputs and its previous state.

A combinational circuit's output is a pure function of its present input values only, with no memory of past inputs. In contrast, a sequential circuit contains memory elements (like flip-flops or latches), and its output depends not only on the current inputs but also on the stored information from previous states.

Question 35: What is the time constant of a series RC circuit with R = 4.7 kΩ and C = 22 μF?

103.4 ms (Correct answer)
47.0 ms
22.0 ms
213.4 ms

Correct answer: 103.4 ms

τ = RC = 4700 × 22×10⁻⁶ = 0.1034 s = 103.4 ms.

Question 36: A Schmitt trigger is primarily used to:

Implement frequency division
Amplify high-frequency signals
Convert sine waves to square waves with hysteresis (Correct answer)
Generate sawtooth waveforms

Correct answer: Convert sine waves to square waves with hysteresis

A Schmitt trigger uses hysteresis (two threshold levels) to cleanly convert noisy analog signals into digital square waves.

Question 37: What principle does a thermocouple use to measure temperature?

Change in resistance with temperature
Piezoelectric effect
Seebeck effect (Correct answer)
Hall effect

Correct answer: Seebeck effect

A thermocouple generates a voltage based on the Seebeck effect, where a temperature difference between two dissimilar metal junctions produces an electromotive force.

Question 38: A 4-bit magnitude comparator has inputs A=1010 and B=1010. Which output is asserted?

A < B
A = B (Correct answer)
A > B
Both A>B and A<B

Correct answer: A = B

Since A and B are identical (both equal 10 in decimal), the A=B output of the comparator is asserted.

Question 39: Systems of this type, which have input and output quantized at specific levels, are referred to as

continuous
digital
analog
discrete (Correct answer)

Correct answer: discrete

A discrete system is characterized by signals that are defined only at specific, distinct points in time or space, and whose values are restricted to a finite or countably infinite set of levels. When input and output are 'quantized at specific levels,' it means their values can only be chosen from a predefined set, which is the defining characteristic of discrete-valued signals within a discrete system. This is distinct from continuous systems, where values can be any real number within a range.

Question 40: In an AC circuit, reactive power Q is measured in:

Watts (W)
Volt-Ampere Reactive (VAR) (Correct answer)
Volt-Ampere (VA)
Joules (J)

Correct answer: Volt-Ampere Reactive (VAR)

Reactive power, which represents energy oscillating between source and reactive elements, is measured in VAR.

Question 41: What is the maximum power transfer condition for a DC circuit with a source resistance of 50 ohms?

Load resistance is infinite
Load resistance equals 50 ohms (Correct answer)
Load resistance equals 100 ohms
Load resistance equals 25 ohms

Correct answer: Load resistance equals 50 ohms

Maximum power is transferred when the load resistance equals the source resistance.

Question 42: What happens to the capacitive reactance XC as frequency increases?

XC remains constant
XC decreases (Correct answer)
XC increases
XC becomes purely resistive

Correct answer: XC decreases

Capacitive reactance XC = 1/(2πfC), so as frequency increases, XC decreases.

Question 43: In a distribution system, what is the advantage of a ring (loop) network over a radial network?

Simpler protection coordination
Lower conductor cross-section requirement
Higher supply continuity and improved reliability (Correct answer)
Lower installation cost

Correct answer: Higher supply continuity and improved reliability

A ring network supplies each load from two directions, so a single fault or maintenance outage does not interrupt supply, improving reliability.

Question 44: Which parameter of a BJT is defined as the ratio of collector current to base current?

β (beta) (Correct answer)
α (alpha)
gm (transconductance)
Early voltage VA

Correct answer: β (beta)

β (hFE) = IC/IB is the common-emitter current gain of a BJT.

Question 45: How many control lines are required for a 16-to-1 multiplexer?

5
16
4 (Correct answer)
3

Correct answer: 4

A 16-to-1 MUX requires 4 select lines because 2^4 = 16, allowing selection of any one of the 16 inputs.

Question 46: The Miller effect in an inverting amplifier causes the input capacitance to appear as:

Cf · (1 + |Av|) (Correct answer)
Cf alone
Cf · |Av|
Cf / (1 + |Av|)

Correct answer: Cf · (1 + |Av|)

Miller's theorem shows that a feedback capacitor Cf across an inverting amplifier appears at the input as Cf·(1 + |Av|), significantly increasing effective input capacitance.

Question 47: Which Boolean algebra theorem states that A + A·B = A?

Idempotent theorem
De Morgan's theorem
Absorption theorem (Correct answer)
Consensus theorem

Correct answer: Absorption theorem

The absorption theorem states that a variable ORed with its AND combination with another variable simplifies to just the original variable.

Question 48: If the receiving end voltage is Vr0 and the power system network is at Vs, then the impedance of the TL is (R+j5). The ideal resistance value for maximum power transfer to the load should be .

3.45
5.2
1.732 (Correct answer)
0.33

Correct answer: 1.732

For maximum power transfer from a source with impedance Zs = R_s + jX_s to a load, the load impedance Z_L should be the complex conjugate of the source impedance, i.e., Z_L = R_s - jX_s. This means the ideal load resistance R_L should be equal to the source resistance R_s. If the transmission line impedance (R+j5) represents the source impedance, then for maximum power transfer, the ideal load resistance (R_L) would be R. Given the options, if R = 1.732, then the ideal load resistance is 1.732.

Question 49: The capacitance per unit length of a coaxial cable with inner radius a and outer radius b, filled with dielectric ε, is:

ε ln(b/a) / 2π
2πε(b-a)
πε / ln(b/a)
2πε / ln(b/a) (Correct answer)

Correct answer: 2πε / ln(b/a)

Applying Gauss's law to the coaxial geometry yields C/L = 2πε / ln(b/a).

Question 50: An ideal current source has:

Infinite internal resistance (Correct answer)
Resistance equal to 50Ω
Zero internal resistance
Resistance equal to the load

Correct answer: Infinite internal resistance

An ideal current source maintains constant current regardless of load, which requires infinite internal (parallel) resistance.

Question 51: Which of the following input-output relationships, y(t), describes a system that is linear but NOT time-invariant?

y(t) = x(t-2)
y(t) = x(t) * cos(2πt) (Correct answer)
y(t) = x(t) + 5
y(t) = x²(t)

Correct answer: y(t) = x(t) * cos(2πt)

The system y(t) = x(t) * cos(2πt) is linear because it satisfies the superposition principle: a*x1(t)*cos(2πt) + b*x2(t)*cos(2πt) = (a*x1(t) + b*x2(t))*cos(2πt). However, it is not time-invariant because a shift in the input, x(t-T), yields x(t-T)*cos(2πt), which is not the same as a shift in the output, y(t-T) = x(t-T)*cos(2π(t-T)). The cosine term is dependent on absolute time 't'.

Question 52: What is the main advantage of using HVDC transmission over HVAC for very long distance power transfer?

Lower transmission losses due to absence of reactive power losses and skin effect (Correct answer)
Lower initial installation cost for all distances
Easier voltage transformation at substations
Simpler protection and switchgear requirements

Correct answer: Lower transmission losses due to absence of reactive power losses and skin effect

HVDC transmission eliminates reactive power losses and skin effect present in AC systems, making it more efficient for very long distance power transfer.

Question 53: The Thevenin resistance R_th is found by:

Dividing the open-circuit voltage by the load current
Multiplying all resistances in the network
Connecting a test voltage and measuring current with all sources active
Dividing V_th by I_N from the Norton equivalent (Correct answer)

Correct answer: Dividing V_th by I_N from the Norton equivalent

R_th = V_th / I_N, which can also be found by deactivating all independent sources and measuring resistance at the terminals.

Question 54: What happens to the total resistance when resistors are connected in parallel?

It decreases below the smallest individual resistance (Correct answer)
It equals the sum of all resistances
It remains unchanged
It equals the largest resistance

Correct answer: It decreases below the smallest individual resistance

Parallel resistors always yield a total resistance smaller than the smallest individual resistor in the combination.

Question 55: Which of the following statements is true regarding a capacitor in a DC circuit after it has been fully charged?

Its voltage is zero.
It continuously draws maximum current from the source.
It acts as a short circuit.
It acts as an open circuit. (Correct answer)

Correct answer: It acts as an open circuit.

When a capacitor is connected to a DC source, it charges up. Once fully charged, the voltage across the capacitor equals the source voltage. At this point, the capacitor opposes any further flow of DC current, effectively behaving like an open circuit. No more current flows through the capacitor branch.

Question 56: The time constant (τ) of an RC circuit is:

R / C
C / R
R + C
R × C (Correct answer)

Correct answer: R × C

τ = RC (resistance × capacitance) in seconds.

Question 57: The gain margin of a control system is measured at which frequency?

The gain crossover frequency
DC (zero frequency)
The frequency where phase is -90°
The phase crossover frequency (Correct answer)

Correct answer: The phase crossover frequency

Gain margin is the additional gain allowable at the phase crossover frequency where the phase equals -180°.

Question 58: Voltage regulation of a transformer is correctly expressed as:

(VFL - VNL) / VFL × 100%
(VNL - VFL) / VNL × 100%
(VNL - VFL) / VFL × 100% (Correct answer)
VNL / VFL × 100%

Correct answer: (VNL - VFL) / VFL × 100%

Voltage regulation = (VNL − VFL) / VFL × 100%, measuring the change in secondary voltage from full-load to no-load relative to rated (full-load) voltage.

Question 59: In an economic dispatch problem, what condition must be satisfied for optimal allocation of real power generation among multiple units?

Reactive power output of each unit must match its real power output
All units operate at the same output in megawatts
Units with lowest capacity factor are loaded first
The incremental cost (λ) of each online unit must be equal (Correct answer)

Correct answer: The incremental cost (λ) of each online unit must be equal

Economic dispatch requires that the incremental fuel cost (∂F/∂P) be equal for all online generators, ensuring no cost savings are possible by shifting load between units.

Question 60: Which type of Analog-to-Digital Converter (ADC) operates by sequentially testing each bit from the most significant bit (MSB) to the least significant bit (LSB) to find the digital equivalent of an analog signal?

Successive-Approximation ADC (Correct answer)
Flash ADC
Dual-Slope ADC
Delta-Sigma ADC

Correct answer: Successive-Approximation ADC

A Successive-Approximation Register (SAR) ADC works by using a binary search algorithm. It starts by setting the MSB to 1 and compares the resulting analog voltage (from an internal DAC) to the input signal. Based on the comparison, the bit is either kept or cleared, and the process repeats for the next bit until the LSB is determined. This method allows for a good balance between speed and resolution.

Question 61: What is the bandwidth of a series RLC resonant circuit with f₀ = 1000 Hz and Q = 50?

50 Hz
20 Hz (Correct answer)
500 Hz
100 Hz

Correct answer: 20 Hz

Bandwidth BW = f₀/Q = 1000/50 = 20 Hz, representing the range of frequencies within 3 dB of the resonant peak.

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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