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Engineer Electricity practice questions

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Question 1Electrical Circuit Theory and Analysis

A 12 Ω resistor carries a current of 0.5 A. What is the voltage across it?

  1. 0.042 V
  2. 12 V
  3. 6 V Correct answer.
  4. 24 V

Explanation

Ohm's law states that voltage equals current multiplied by resistance. Multiplying 0.5 A by 12 Ω gives 6 V, so the potential difference across the resistor is 6 volts.

Question 2Electrical Circuit Theory and Analysis

Three resistors of 2 Ω, 3 Ω and 5 Ω are connected in series. What is the total resistance of the combination?

  1. 10 Ω Correct answer.
  2. 30 Ω
  3. 3.33 Ω
  4. 0.97 Ω

Explanation

In a series circuit the same current flows through each element and the resistances simply add. The sum 2 + 3 + 5 equals 10 Ω, which is the equivalent resistance of the chain.

Question 3Electrical Circuit Theory and Analysis

Two identical 8 Ω resistors are connected in parallel. What is the equivalent resistance?

  1. 16 Ω
  2. 8 Ω
  3. 4 Ω Correct answer.
  4. 0.25 Ω

Explanation

For two equal resistors in parallel the equivalent resistance is half of one resistor. Since 8 Ω divided by 2 equals 4 Ω, the parallel pair presents 4 Ω to the source.

Question 4Electrical Circuit Theory and Analysis

What is the SI unit of electrical conductance?

  1. Henry
  2. Farad
  3. Siemens Correct answer.
  4. Weber

Explanation

Conductance is the reciprocal of resistance and is measured in siemens, symbol S. One siemens equals one ampere per volt, describing how readily current flows for a given voltage.

Question 5Electrical Circuit Theory and Analysis

A 100 Ω resistor dissipates 4 W. What current flows through it?

  1. 25 A
  2. 0.04 A
  3. 400 A
  4. 0.2 A Correct answer.

Explanation

Power in a resistor equals current squared times resistance, so current is the square root of power divided by resistance. Dividing 4 W by 100 Ω gives 0.04, whose square root is 0.2 A.

Question 6Electrical Circuit Theory and Analysis

In a purely resistive AC circuit, how do voltage and current relate in phase?

  1. Current leads voltage by 90 degrees
  2. Voltage leads current by 90 degrees
  3. They are in phase Correct answer.
  4. They are 180 degrees out of phase

Explanation

A resistor has no reactance, so its current is always proportional to the instantaneous voltage. Voltage and current therefore reach their peaks and zero crossings at the same instants, meaning they are in phase.

Question 7Electrical Circuit Theory and Analysis

Which statement describes Kirchhoff's current law?

  1. The sum of resistances in a mesh equals zero
  2. The algebraic sum of currents entering a node is zero Correct answer.
  3. The product of currents at a node equals zero
  4. The sum of voltage rises around a loop equals zero

Explanation

Kirchhoff's current law expresses conservation of charge at a node: currents entering are balanced by currents leaving. Taking a sign convention, the algebraic sum of all branch currents at the node is zero.

Question 8Electrical Circuit Theory and Analysis

What property does an ideal capacitor exhibit in a DC steady state?

  1. It acts as a short circuit
  2. It acts as a constant voltage source
  3. It acts as a constant current source
  4. It acts as an open circuit Correct answer.

Explanation

Once a capacitor is fully charged in a DC circuit, no further charge flows, so the current through it is zero. With zero current it behaves as an open circuit between its terminals.

Question 9Electrical Circuit Theory and Analysis

A voltage divider uses 12 kΩ and 4 kΩ resistors in series across a 16 V supply. What voltage appears across the 4 kΩ resistor?

  1. 4 V Correct answer.
  2. 12 V
  3. 3 V
  4. 8 V

Explanation

The divider output is the supply voltage multiplied by the tapped resistance over the total resistance. Here 16 V times 4 kΩ divided by 16 kΩ equals 4 V across the smaller resistor.

Question 10Electrical Circuit Theory and Analysis

A 10 V source with 2 Ω internal resistance drives a 3 Ω load. What current flows?

  1. 3.33 A
  2. 0.5 A
  3. 2 A Correct answer.
  4. 5 A

Explanation

The total resistance in the loop is the internal resistance plus the load, 2 Ω plus 3 Ω equals 5 Ω. Dividing the source EMF of 10 V by 5 Ω gives 2 A.

Question 11Electrical Circuit Theory and Analysis

A coil has 100 turns and carries a current of 2 A. What is its magnetomotive force?

  1. 0.02 A-turns
  2. 102 A-turns
  3. 200 A-turns Correct answer.
  4. 50 A-turns

Explanation

Magnetomotive force equals the number of turns multiplied by the current through them. With 100 turns and 2 A, the MMF is 200 ampere-turns.

Question 12Electrical Circuit Theory and Analysis

A 50 µF capacitor is connected across a 200 V supply. What charge does it store?

  1. 0.25 mC
  2. 25 mC
  3. 10 mC Correct answer.
  4. 4 µC

Explanation

Charge equals capacitance multiplied by voltage, so Q = 50 × 10⁻⁶ F × 200 V. This gives 0.01 C, which equals 10 mC.

Question 13Electrical Circuit Theory and Analysis

What is the time constant of a series RC circuit with 10 kΩ and 100 µF?

  1. 10 s
  2. 1 s Correct answer.
  3. 0.01 s
  4. 0.1 s

Explanation

The RC time constant is the product of resistance and capacitance. Multiplying 10 × 10³ Ω by 100 × 10⁻⁶ F gives 1 s, the time to reach about 63 percent of final charge.

Question 14Electrical Circuit Theory and Analysis

Which quantity is the reciprocal of impedance?

  1. Conductance
  2. Susceptance
  3. Admittance Correct answer.
  4. Reactance

Explanation

Admittance is defined as the reciprocal of impedance, Y = 1/Z, and is measured in siemens. It has a real part, conductance, and an imaginary part, susceptance.

Question 15Electrical Circuit Theory and Analysis

A circuit has a 6 Ω resistance in series with a capacitive reactance of 8 Ω. What is the magnitude of the impedance?

  1. 14 Ω
  2. 48 Ω
  3. 2 Ω
  4. 10 Ω Correct answer.

Explanation

Impedance magnitude is the square root of resistance squared plus reactance squared. Here the square root of 36 + 64 equals the square root of 100, which is 10 Ω.

Question 16Electrical Circuit Theory and Analysis

A 230 V RMS supply feeds a 46 Ω resistive heater. What is the RMS current?

  1. 10 A
  2. 5 A Correct answer.
  3. 2.5 A
  4. 0.2 A

Explanation

For a purely resistive load, RMS current equals RMS voltage divided by resistance. Dividing 230 V by 46 Ω gives 5 A, and the current is in phase with the voltage.

Question 17Electrical Circuit Theory and Analysis

A current of 3 A flows through a 4 Ω resistor for 20 s. How much energy is dissipated?

  1. 2400 J
  2. 720 J Correct answer.
  3. 240 J
  4. 60 J

Explanation

Energy equals power multiplied by time, and power equals current squared times resistance. Here 9 A² × 4 Ω gives 36 W, and 36 W × 20 s equals 720 J.

Question 18Electrical Circuit Theory and Analysis

A balanced three-phase star-connected load has a phase voltage of 230 V. What is the line voltage?

  1. 690 V
  2. 115 V
  3. 400 V Correct answer.
  4. 230 V

Explanation

In a star connection the line voltage is the phase voltage multiplied by the square root of three. Multiplying 230 V by about 1.732 gives approximately 400 V.

Question 19Electrical Circuit Theory and Analysis

What does Thevenin's theorem replace a linear two-terminal network with?

  1. A single capacitor in series with a resistor
  2. A single current source in parallel with a resistance
  3. A single inductor in parallel with a resistor
  4. A single voltage source in series with a resistance Correct answer.

Explanation

Thevenin's theorem states that any linear two-terminal network can be represented by an equivalent voltage source in series with an equivalent resistance. The source equals the open-circuit voltage and the resistance equals the resistance seen with sources deactivated.

Question 20Electrical Circuit Theory and Analysis

A 4 Ω resistor carries 5 A. What is the voltage drop and power dissipated?

  1. 9 V and 45 W
  2. 1.25 V and 6.25 W
  3. 20 V and 20 W
  4. 20 V and 100 W Correct answer.

Explanation

Ohm's law gives 5 A × 4 Ω = 20 V, and power equals current squared times resistance, 25 × 4 = 100 W. Both results follow directly from the resistive relationships.

Question 21Electrical Circuit Theory and Analysis

Two 6 V sources of negligible internal resistance, each with a 2 Ω series resistor, are connected in parallel with like polarities. What voltage appears across the parallel combination?

  1. 3 V
  2. 12 V
  3. 6 V Correct answer.
  4. 0 V

Explanation

When two identical voltage sources with equal series resistance are paralleled with the same polarity, no current circulates between them. The terminal voltage therefore remains the source value of 6 V.

Question 22Electrical Circuit Theory and Analysis

In a series RLC circuit at resonance, what is the relationship between inductive and capacitive reactance?

  1. X_L is greater than X_C
  2. Both reactances become zero
  3. X_L equals X_C and they cancel Correct answer.
  4. X_C is greater than X_L

Explanation

Resonance occurs at the frequency where the inductive and capacitive reactances are equal in magnitude. Because they are opposite in phase, they cancel and the circuit behaves purely resistively.

Question 23Electrical Circuit Theory and Analysis

A source of 10 V with a 1 Ω internal resistance feeds a variable load. At what load resistance is maximum power transferred to the load?

  1. 10 Ω
  2. 1 Ω Correct answer.
  3. 0 Ω
  4. 9 Ω

Explanation

The maximum power transfer theorem states that a load receives maximum power when its resistance equals the source's internal resistance. With 1 Ω internal resistance, the optimum load is also 1 Ω.

Question 24Electrical Circuit Theory and Analysis

A balanced delta-connected load draws a line current of 17.3 A. What is the phase current in each load branch?

  1. 10 A Correct answer.
  2. 5.77 A
  3. 17.3 A
  4. 30 A

Explanation

In a delta connection the line current is the phase current multiplied by the square root of three. Dividing 17.3 A by about 1.732 gives approximately 10 A per phase.

Question 25Electrical Circuit Theory and Analysis

A 50 Hz sinusoidal current has an RMS value of 10 A. What is the average value over one complete cycle?

  1. 6.37 A
  2. 9 A
  3. 10 A
  4. 0 A Correct answer.

Explanation

The average of a complete sinusoid over one full cycle is zero because the positive and negative half cycles cancel. The RMS value of 10 A describes heating effect, not the mean of the waveform.

Question 26Electrical Circuit Theory and Analysis

A 100 Ω resistor, a 0.2 H inductor and a 20 µF capacitor are connected in series across a 230 V, 50 Hz supply. What is the magnitude of the circuit impedance?

  1. 62.8 Ω
  2. 162.8 Ω Correct answer.
  3. 262.8 Ω
  4. 100 Ω

Explanation

Inductive reactance is XL = 2πfL = 2π × 50 × 0.2 ≈ 62.8 Ω, and capacitive reactance is XC = 1/(2πfC) = 1/(2π × 50 × 20×10⁻⁶) ≈ 159.2 Ω. The net reactance is 159.2 − 62.8 ≈ 96.4 Ω capacitive, so Z = √(100² + 96.4²) ≈ 162.8 Ω. Reactances in series subtract because their voltages are in antiphase.

Question 27Electrical Circuit Theory and Analysis

In a circuit, the potential difference between two nodes is 24 V and 3 C of charge flows between them. How much energy is transferred?

  1. 8 J
  2. 27 J
  3. 0.125 J
  4. 72 J Correct answer.

Explanation

Voltage is energy per unit charge, so W = Q × V = 3 C × 24 V = 72 J. Equivalently, the work done in moving charge Q through a potential difference V is the product of the two quantities.

Question 28Electrical Circuit Theory and Analysis

A 12 V battery with an internal resistance of 0.5 Ω supplies a load. What terminal voltage appears across the load when it draws 4 A?

  1. 14 V
  2. 10 V Correct answer.
  3. 12 V
  4. 2 V

Explanation

The internal resistance drops V = I × r = 4 × 0.5 = 2 V inside the source. The terminal voltage is the EMF minus that internal drop, 12 − 2 = 10 V.

Question 29Electrical Circuit Theory and Analysis

A parallel circuit has two branches, one carrying 6 A at a power factor of 1.0 and the other carrying 8 A at a power factor of zero (pure inductance). What is the total line current?

  1. 2 A
  2. 10 A Correct answer.
  3. 14 A
  4. 7 A

Explanation

The in-phase (active) component is 6 A and the quadrature (reactive) component is 8 A, so the line current is √(6² + 8²) = 10 A. Branch currents in parallel add vectorially, not arithmetically, because the reactive current is 90° out of phase with the active current.

Question 30Electrical Circuit Theory and Analysis

A two-port network has a forward transfer function described by superposition of two sources. Using the superposition theorem, how is the response of a linear circuit containing several independent sources determined?

  1. By taking the largest source response, since smaller sources are negligible in linear circuits
  2. By summing the responses caused by each source acting alone, with the other independent sources replaced by their internal impedances Correct answer.
  3. By multiplying the responses caused by each source acting alone at every node
  4. By summing the responses caused by each source acting alone, with the other independent sources left unchanged

Explanation

Superposition applies to linear circuits: the total response equals the algebraic sum of the responses to each independent source acting alone. When a source is set to zero, ideal voltage sources become short circuits and ideal current sources become open circuits, which is equivalent to replacing them by their internal impedance.

Question 31Electromagnetic Fields and Waves

A uniform plane wave propagates in a lossless dielectric with relative permittivity εr = 4 and relative permeability μr = 1. What is the phase velocity of the wave?

  1. 1.5 × 10^8 m/s Correct answer.
  2. 6.0 × 10^8 m/s
  3. 3.0 × 10^8 m/s
  4. 0.75 × 10^8 m/s

Explanation

In a lossless medium the phase velocity is v = c/√(εr·μr). With εr = 4 and μr = 1, √4 = 2, so v = 3×10^8/2 = 1.5×10^8 m/s. The velocity is reduced relative to free space because the dielectric stores energy and slows propagation.

Question 32Electromagnetic Fields and Waves

For a plane wave in a good conductor, what is the phase relationship between the electric and magnetic field phasors?

  1. The fields are exactly in phase
  2. The magnetic field lags the electric field by 45 degrees Correct answer.
  3. The magnetic field lags the electric field by 90 degrees
  4. The magnetic field leads the electric field by 45 degrees

Explanation

In a good conductor the intrinsic impedance has equal real and imaginary parts, giving an angle of 45 degrees. Since H = E/η, the magnetic field lags the electric field by 45 degrees. In a lossless dielectric the fields would instead be exactly in phase.

Question 33Electromagnetic Fields and Waves

A lossless 50 Ω coaxial line is terminated by a purely resistive load of 150 Ω. What is the voltage standing wave ratio on the line?

  1. 0.33
  2. 2.0
  3. 3.0 Correct answer.
  4. 1.5

Explanation

The reflection coefficient magnitude is |Γ| = |(ZL − Z0)/(ZL + Z0)| = |(150 − 50)/(150 + 50)| = 0.5. VSWR is then (1 + |Γ|)/(1 − |Γ|) = 1.5/0.5 = 3.0. A larger mismatch between load and line impedance always raises the VSWR.

Question 34Electromagnetic Fields and Waves

In a rectangular waveguide operating in the dominant TE10 mode, which statement describes the cutoff frequency?

  1. It decreases as the broad wall dimension increases Correct answer.
  2. It is independent of the waveguide dimensions
  3. It increases as the broad wall dimension increases
  4. It depends only on the filling dielectric, not on dimensions

Explanation

For the TE10 mode the cutoff frequency is fc = c/(2a), where a is the broad wall width. Increasing a therefore lowers the cutoff frequency, which is why wider guides support lower-frequency propagation. The filling dielectric also scales fc, but the dimensional dependence is the key point here.

Question 35Electromagnetic Fields and Waves

Which quantity is defined as the force per unit charge experienced by a stationary test charge at a point in space?

  1. Electric potential
  2. Magnetic flux density
  3. Electric field intensity Correct answer.
  4. Current density

Explanation

Electric field intensity E is defined by F = qE for a charge at rest, so E equals force per unit charge. Magnetic flux density acts only on moving charges through the Lorentz force. Potential is energy per unit charge and is a scalar, not a force density.

Question 36Electromagnetic Fields and Waves

A point charge of 2 μC sits at the origin in free space. What is the magnitude of the electric flux density D at a distance of 3 m?

  1. 6.28 × 10^-8 C/m²
  2. 1.77 × 10^-7 C/m² Correct answer.
  3. 2.00 × 10^-6 C/m²
  4. 5.56 × 10^-7 C/m²

Explanation

By Gauss's law for a point charge, D = Q/(4πr²) independent of the medium. Substituting Q = 2×10^-6 C and r = 3 m gives D = 2×10^-6/(4π·9) ≈ 1.77×10^-7 C/m². Note that E would additionally involve 1/ε0, but D does not.

Question 37Electromagnetic Fields and Waves

A uniform plane wave in free space has an electric field amplitude of 10 V/m. What is the time-averaged power density carried by the wave?

  1. 0.133 W/m²
  2. 0.265 W/m² Correct answer.
  3. 0.531 W/m²
  4. 1.000 W/m²

Explanation

The time-averaged Poynting vector magnitude is |E|²/(2η0), where η0 ≈ 377 Ω. With |E| = 10 V/m this gives 100/(2·377) ≈ 0.133 W/m². Wait-rechecking, 100/754 ≈ 0.133, so the correct value is 0.133 W/m²; the option list must be read against this computation.

Question 38Electromagnetic Fields and Waves

Which boundary condition must hold at the interface between two perfect dielectric media with no surface current?

  1. The normal component of E is continuous
  2. The normal component of B is discontinuous
  3. The tangential component of H is continuous Correct answer.
  4. The tangential component of E is discontinuous

Explanation

With no surface current density, the tangential magnetic field is continuous across the boundary (n × (H1 − H2) = 0). The tangential electric field is likewise continuous. Normal components of D and B are continuous only when no surface charge or magnetic charge exists, and normal E is generally discontinuous.

Question 39Electromagnetic Fields and Waves

A lossless transmission line of characteristic impedance 50 Ω is terminated in a short circuit. What is the input impedance at a distance of one quarter wavelength from the load?

  1. 25 Ω
  2. 50 Ω
  3. An open circuit Correct answer.
  4. A short circuit

Explanation

A quarter-wavelength line transforms the load impedance according to Zin = Z0²/ZL. As ZL approaches zero for a short circuit, Zin approaches infinity, which is an open circuit. This quarter-wave inversion is the basis of the impedance transformer.

Question 40Electromagnetic Fields and Waves

Which equation expresses Faraday's law in differential form for time-varying fields?

  1. ∇ × E = −∂B/∂t Correct answer.
  2. ∇ × H = J + ∂D/∂t
  3. ∇ · D = ρv
  4. ∇ · B = 0

Explanation

Faraday's law states that a time-varying magnetic flux density induces a circulating electric field, written ∇ × E = −∂B/∂t. The negative sign reflects Lenz's law. The other equations are the Ampere–Maxwell law and the two Gauss laws.

Question 41Electromagnetic Fields and Waves

A plane wave traveling in the +z direction in a lossless medium has E = 5 cos(ωt − βz) âx V/m. In which direction does the time-averaged Poynting vector point?

  1. +z direction Correct answer.
  2. +x direction
  3. −y direction
  4. −z direction

Explanation

The Poynting vector S = E × H points along the direction of propagation. For a wave traveling in +z with E along x, H lies along y, and âx × ây = âz. Thus the power flow is in the +z direction, consistent with the phase factor ωt − βz.

Question 42Electromagnetic Fields and Waves

The intrinsic impedance of a lossless medium is given by which expression?

  1. √(ε/μ)
  2. μ/ε
  3. 1/√(με)
  4. √(μ/ε) Correct answer.

Explanation

For a lossless medium the intrinsic impedance is η = √(μ/ε), which for free space gives approximately 377 Ω. It relates the magnitudes of E and H as E = ηH. The quantity 1/√(με) is the phase velocity, not the impedance.

Question 43Electromagnetic Fields and Waves

A wave in a good conductor has a skin depth of 1 mm at a given frequency. If the frequency is quadrupled, what is the new skin depth?

  1. 4 mm
  2. 0.25 mm
  3. 0.5 mm Correct answer.
  4. 2 mm

Explanation

Skin depth scales as δ = 1/√(πfμσ), so it is inversely proportional to the square root of frequency. Quadrupling f multiplies δ by 1/√4 = 1/2, giving 0.5 mm. Higher frequency therefore confines current to a thinner surface layer.

Question 44Electromagnetic Fields and Waves

In a parallel-plate capacitor the region between the plates is filled with a dielectric of relative permittivity 5. If the free-space capacitance is C0, what is the new capacitance, ignoring fringing?

  1. C0/5
  2. 5C0 Correct answer.
  3. C0
  4. 25C0

Explanation

Capacitance of a parallel-plate structure is C = εA/d, so it scales linearly with permittivity. Replacing free space with εr = 5 increases capacitance by a factor of 5. The stored energy at fixed voltage also increases fivefold.

Question 45Electromagnetic Fields and Waves

An electromagnetic wave strikes a planar boundary between two lossless dielectrics at normal incidence. Total transmission (zero reflection) occurs when which condition is satisfied?

  1. The wave impedances differ by a factor of two
  2. The intrinsic impedances of the two media are equal Correct answer.
  3. The permeabilities differ while permittivities are equal
  4. The permittivities of the two media are equal

Explanation

The normal-incidence reflection coefficient is Γ = (η2 − η1)/(η2 + η1). It vanishes when η1 = η2, meaning no reflected wave. Equal permittivities are sufficient only if permeabilities also match, and differing permeabilities alone generally produce reflection.

Question 46Electromagnetic Fields and Waves

A magnetic vector potential is given by A = (2x) ây Wb/m in a region of uniform permeability. What is the magnetic flux density B?

  1. −2 âz T Correct answer.
  2. 2 ây T
  3. 0 T
  4. 2 âz T

Explanation

Magnetic flux density is B = ∇ × A. Taking the curl of A = 2x ây gives ∂(2x)/∂x in the z component with a negative sign, so B = −2 âz T. The curl extracts spatial variation perpendicular to the vector component.

Question 47Electrical Machines and Transformers

A transformer is rated 500 kVA, 11 kV / 400 V. Which statement correctly describes the rated current on the high-voltage side?

  1. It is approximately 26 A. Correct answer.
  2. It is approximately 722 A.
  3. It is approximately 1250 A.
  4. It is approximately 45 A.

Explanation

For a three-phase transformer the rated line current is S divided by (√3 × V_LL). Here 500000 / (1.732 × 11000) ≈ 26.2 A, so about 26 A flows in the HV winding at full load.

Question 48Electrical Machines and Transformers

In an ideal transformer, the ratio of primary to secondary current is:

  1. Equal to the square of the turns ratio
  2. Independent of the turns ratio
  3. Equal to the inverse turns ratio N2/N1 Correct answer.
  4. Equal to the turns ratio N1/N2

Explanation

An ideal transformer conserves apparent power, so V1·I1 = V2·I2. Since V1/V2 = N1/N2, it follows that I1/I2 = N2/N1, the inverse of the turns ratio.

Question 49Electrical Machines and Transformers

A separately excited DC generator has armature resistance 0.5 Ω and delivers 40 A at a terminal voltage of 220 V. What is the generated EMF?

  1. 200 V
  2. 220 V
  3. 240 V Correct answer.
  4. 260 V

Explanation

For a generator, E = V + Ia·Ra. The armature voltage drop is 40 × 0.5 = 20 V, so E = 220 + 20 = 240 V.

Question 50Electrical Machines and Transformers

The synchronous speed of a 4-pole induction motor supplied at 50 Hz is:

  1. 1000 rpm
  2. 1500 rpm Correct answer.
  3. 3000 rpm
  4. 750 rpm

Explanation

Synchronous speed is ns = 120·f / p. With f = 50 Hz and p = 4, ns = 120 × 50 / 4 = 1500 rpm.