I85PREP
⌘ K
PE Electrical study materials
PE Electrical study resources

PE Electrical practice questions

One question at a time. Build your PE Electrical understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1General Power Engineering

In a single-phase AC circuit, the apparent power delivered to a load is calculated as which of the following?

  1. The arithmetic sum of the real and reactive powers
  2. The product of RMS voltage and RMS current Correct answer.
  3. The real power divided by the reactive power
  4. The product of peak voltage and peak current

Explanation

Apparent power is the magnitude of the complex power, S = V_rms x I_rms, and is expressed in volt-amperes. Real power equals S cos(theta) and reactive power equals S sin(theta). The individual components must be combined as phasors, not added directly.

Question 2General Power Engineering

For a balanced three-phase load with line-to-line voltage V_L and line current I_L, the total real power is given by which expression?

  1. 3 x V_L x I_L x cos(theta)
  2. Square root of 3 x V_L x I_L x cos(theta) Correct answer.
  3. V_L x I_L x cos(theta)
  4. Square root of 3 x V_L x I_L x sin(theta)

Explanation

Using line quantities, total three-phase real power is the square root of 3 times line voltage times line current times the displacement cosine. The equivalent phase-quantity form is 3 times phase voltage times phase current times cosine, and the square root of 3 accounts for the conversion between the two.

Question 3General Power Engineering

In the per-unit system, base impedance on a given side of a transformer is defined as which of the following?

  1. The square of the base power divided by the base voltage
  2. The base voltage divided by the base power
  3. The base power divided by the square of the base voltage
  4. The square of the base voltage divided by the base power Correct answer.

Explanation

Base impedance is defined as the base voltage squared divided by the base power, using line-to-line volts and three-phase volt-amperes consistently. A measured ohmic impedance is then divided by this base value to obtain per-unit impedance.

Question 4General Power Engineering

The percent impedance of a distribution transformer is used most directly to estimate which of the following?

  1. The no-load core loss of the transformer
  2. The secondary short-circuit current Correct answer.
  3. The insulation dielectric strength of the windings
  4. The magnetizing current drawn at rated voltage

Explanation

Transformer percent impedance is the per-unit voltage drop at rated current, so short-circuit current is approximately rated current divided by the per-unit impedance. It also sets the magnitude of voltage regulation under load.

Question 5General Power Engineering

A four-pole induction motor supplied at 60 Hz runs at 1750 r/min. Its percent slip is closest to which value?

  1. 5.6 percent
  2. 1.4 percent
  3. 2.8 percent Correct answer.
  4. 3.3 percent

Explanation

Synchronous speed is 120 times frequency divided by poles, or 1800 r/min for four poles at 60 Hz. Slip is the difference between synchronous and actual speed divided by synchronous speed, so 50 divided by 1800 equals about 2.8 percent.

Question 6General Power Engineering

The primary purpose of a substation grounding grid is to do which of the following?

  1. Maintain the generator neutral at its rated insulation level
  2. Limit step and touch voltages and carry fault current to earth Correct answer.
  3. Reduce the harmonic content of the station service supply voltage
  4. Limit the magnetizing inrush current drawn by the station transformer

Explanation

A grounding grid provides a low-impedance return path for fault current and controls the potential differences appearing at the earth surface. Step and touch voltage limits are the primary safety criterion in its design.

Question 7General Power Engineering

The power factor of an AC load is defined as which ratio?

  1. Reactive power divided by apparent power
  2. Real power divided by reactive power
  3. Apparent power divided by real power
  4. Real power divided by apparent power Correct answer.

Explanation

Power factor is real power divided by apparent power, which equals the cosine of the impedance angle for a sinusoidal load. It ranges from zero at purely reactive loading to unity at purely resistive loading.

Question 8General Power Engineering

Symmetrical component analysis resolves an unbalanced set of three-phase phasors into which of the following?

  1. A single balanced set plus a harmonic series
  2. Three separate single-phase quantities with no phase relationship
  3. Two balanced sets and one DC offset
  4. Positive-, negative-, and zero-sequence balanced sets Correct answer.

Explanation

Fortescue's theorem states that any unbalanced set of three phasors can be decomposed into three balanced sequence sets: positive, negative, and zero. Each set can be analyzed with ordinary per-phase techniques and the results superimposed.

Question 9General Power Engineering

A plant draws 500 kW at a lagging power factor of 0.80. What capacitor rating is required to raise the power factor to 0.95 lagging?

  1. About 375 kvar
  2. About 164 kvar
  3. About 211 kvar Correct answer.
  4. About 125 kvar

Explanation

Initial reactive power is 500 times the tangent of 36.87 degrees, or 375 kvar. Final reactive power is 500 times the tangent of 18.19 degrees, or 164 kvar, so the capacitor must supply the difference of about 211 kvar.

Question 10General Power Engineering

A balanced three-phase feeder supplies 200 A at 480 V line-to-line. If the conductor resistance is 0.05 ohm per phase and reactance is negligible, the line-to-line voltage drop is closest to which value?

  1. 17.3 V Correct answer.
  2. 34.6 V
  3. 5.8 V
  4. 10.0 V

Explanation

For a balanced three-phase circuit with negligible reactance, line-to-line voltage drop is the square root of 3 times line current times resistance per phase. That gives 1.732 times 200 times 0.05, or about 17.3 V, roughly 3.6 percent of 480 V.

Question 11General Power Engineering

A generator has a subtransient reactance of 0.15 per unit on a 10 MVA, 13.8 kV base. Expressed on a 100 MVA, 13.8 kV base, the reactance is which value?

  1. 0.15 per unit
  2. 15.0 per unit
  3. 1.50 per unit Correct answer.
  4. 0.015 per unit

Explanation

Changing base requires multiplying by the new MVA base over the old MVA base and by the square of the old voltage over the new voltage. With voltage unchanged, the reactance becomes 0.15 times 100 divided by 10, or 1.50 per unit.

Question 12General Power Engineering

A 1000 kVA, 480 V three-phase transformer has 5.0 percent impedance. Neglecting source and conductor impedance, the bolted three-phase secondary fault current is closest to which value?

  1. 1.2 kA
  2. 12 kA
  3. 24 kA Correct answer.
  4. 4.8 kA

Explanation

Rated secondary current is 1000 kVA divided by the square root of 3 times 0.480 kV, about 1203 A. Fault current is approximately rated current divided by the per-unit impedance, so 1203 divided by 0.05 gives about 24 kA.

Question 13General Power Engineering

A 200 kW mechanical load is driven by a motor that is 92 percent efficient and runs 6000 hours per year. At 0.08 dollars per kWh, the annual energy cost is closest to which value?

  1. $104,000 Correct answer.
  2. $113,000
  3. $88,000
  4. $96,000

Explanation

Electrical input power is the shaft power divided by efficiency, 200 divided by 0.92, or about 217.4 kW. Multiplying by 6000 hours and by 0.08 dollars per kWh gives roughly 104,000 dollars per year.

Question 14General Power Engineering

When coordinating two inverse-time overcurrent relays in series, a coordinating time interval is maintained so that which of the following occurs?

  1. Both relays trip at the same instant to clear the fault more quickly
  2. The upstream relay always trips first to protect the downstream cable
  3. The downstream relay trips first and the upstream relay provides backup Correct answer.
  4. The relays respond only to ground faults and ignore phase faults

Explanation

Selective coordination requires the relay nearest the fault to operate first, with the upstream device delayed long enough to serve only as backup. The coordinating time interval accounts for breaker clearing time plus relay and CT error.

Question 15General Power Engineering

The terminal voltage applied to an induction motor drops to 90 percent of rated. Its breakdown torque changes to approximately which fraction of the original value?

  1. 0.90
  2. 0.95
  3. 0.73
  4. 0.81 Correct answer.

Explanation

Induction motor torque at a given slip is proportional to the square of the applied voltage. Reducing voltage to 0.90 per unit reduces breakdown torque to 0.81 per unit, although the slip at which breakdown occurs also shifts.

Question 16General Power Engineering

A 1000 kVA transformer with 5 percent impedance feeds a plant that has a 1000 kvar capacitor bank. The parallel resonance between the bank and the source is closest to which harmonic order?

  1. The 2nd harmonic
  2. The 4.5th harmonic Correct answer.
  3. The 10th harmonic
  4. The 20th harmonic

Explanation

The resonant order equals the square root of the short-circuit MVA divided by the capacitor MVA. Short-circuit capacity is 1000 divided by 0.05, or 20,000 kVA, so the order is the square root of 20, about 4.5.

Question 17General Power Engineering

Two single-phase transformers are to be operated in parallel. Which condition is required to avoid excessive circulating current at no load?

  1. Identical kVA ratings stamped on both nameplates
  2. Matched polarity and nearly equal turns ratios Correct answer.
  3. Percent impedances that are both zero
  4. Equal core losses at rated voltage

Explanation

Circulating current at no load is driven by voltage differences between the secondary windings, so the polarities must be matched and the turns ratios nearly equal. Impedance mainly governs how load current divides once the units are paralleled.

Question 18General Power Engineering

A 4,160 V generator is resistance-grounded through a resistor rated 400 A for 10 seconds. The required resistor ohmic value is closest to which value?

  1. 2.4 ohms
  2. 10.4 ohms
  3. 6.0 ohms Correct answer.
  4. 3.5 ohms

Explanation

The resistor must drop the line-to-neutral voltage at the rated ground-fault current. Line-to-neutral voltage is 4160 divided by the square root of 3, about 2402 V, and 2402 V divided by 400 A gives about 6.0 ohms.

Question 19General Power Engineering

A conductor has a tabulated ampacity of 200 A. It is installed where the ambient temperature correction factor is 0.88, and three current-carrying conductors in a raceway give an adjustment factor of 0.80. The corrected ampacity is closest to which value?

  1. 200 A
  2. 176 A
  3. 160 A
  4. 141 A Correct answer.

Explanation

Ampacity correction factors for ambient temperature and for conductor bundling are applied multiplicatively to the tabulated value. Multiplying 200 A by 0.88 and then by 0.80 gives about 141 A.

Question 20General Power Engineering

A synchronous generator operates at a leading power factor while its real power output is held constant. Compared with unity power factor operation, which statement is true?

  1. The real power limit rises because the field is stronger
  2. Field current falls and stability margin shrinks Correct answer.
  3. Field current is higher and stator current is lower
  4. Both field current and stator current increase

Explanation

Leading power factor corresponds to underexcitation, so DC field current is reduced. With the field weakened, the machine moves closer to its steady-state stability limit, which is why underexcitation limiters are applied.

Question 21General Power Engineering

An unbalanced set of phase currents contains positive- and negative-sequence components but no zero-sequence component. Which condition is consistent with this?

  1. The three phase currents sum to zero Correct answer.
  2. The phase currents consist of third-harmonic components only
  3. The phase currents are balanced and equal in magnitude
  4. The neutral return current is at its maximum value

Explanation

Zero-sequence current equals one third of the phasor sum of the phase currents, so its absence means the three currents sum to zero. This is the situation in a delta-connected load or an ungrounded wye, where no neutral return path exists.

Question 22General Power Engineering

Two generating units are dispatched economically with no losses and no binding limits. The dispatch is optimal when which condition holds?

  1. Both units have equal average fuel cost per MWh
  2. The larger unit carries the entire load
  3. Both units operate at the same percentage of their rating
  4. Equal incremental fuel cost on both units Correct answer.

Explanation

Optimal economic dispatch equalizes the incremental, or marginal, cost of the generating units at the system lambda. Any other split can be improved by shifting load to the unit with the lower marginal cost.

Question 23General Power Engineering

A lossless overhead line has a surge impedance of about 400 ohms. For a 345 kV line, the surge impedance loading is closest to which value?

  1. 300 MW Correct answer.
  2. 890 MW
  3. 170 MW
  4. 100 MW

Explanation

Surge impedance loading equals line-to-line voltage squared divided by the surge impedance. Using 345 kV, that is 119,025 divided by 400, or about 298 MW, the loading at which the line's reactive losses and charging are balanced.

Question 24General Power Engineering

A single machine is connected to an infinite bus through a reactance. Steady-state power transfer reaches its maximum when which condition occurs?

  1. The rotor angle with respect to the infinite bus is zero
  2. The rotor angle with respect to the infinite bus is 90 degrees Correct answer.
  3. The rotor angle with respect to the infinite bus is 45 degrees
  4. The sending-end and receiving-end voltage magnitudes are equal

Explanation

Power transferred is the sending-end voltage times the receiving-end voltage divided by reactance, all multiplied by the sine of the rotor angle. The sine reaches unity at 90 degrees, which is therefore the steady-state maximum.

Question 25General Power Engineering

A 13.8 kV bus has a three-phase fault current of 20 kA with an X/R ratio of 15 at 60 Hz. The decaying DC offset in the fault current has a time constant closest to which value?

  1. About 8 ms
  2. About 16 ms
  3. About 40 ms Correct answer.
  4. About 2.7 ms

Explanation

The DC component decays with a time constant equal to X divided by 2 pi f R, which is the X/R ratio divided by 377 for a 60 Hz system. Dividing 15 by 377 gives about 0.040 s, or 40 ms.

Question 26General Power Engineering

In building load calculations, the demand factor is defined as which of the following?

  1. Average load divided by peak load
  2. Peak load divided by average load
  3. Connected load divided by maximum demand
  4. Maximum demand divided by connected load Correct answer.

Explanation

The demand factor expresses the maximum demand actually imposed on a system as a fraction of the total connected load, reflecting that not all connected equipment draws current simultaneously. Load factor, by contrast, relates average load to peak load over a period.

Question 27General Power Engineering

A transformer is designated with the cooling class ONAN. Which description matches this designation?

  1. Oil forced, air natural
  2. Oil natural, air natural Correct answer.
  3. Oil natural, air forced
  4. Oil forced, air forced

Explanation

The four-letter code identifies the internal and external cooling media and their circulation method. ONAN means the oil circulates by natural convection and the external air moves by natural convection over the radiators.

Question 28General Power Engineering

A four-wire wye system supplies balanced single-phase nonlinear loads whose current is dominated by third-harmonic content. The current in the neutral conductor is closest to which of the following?

  1. Zero
  2. Equal to one phase current
  3. 1.73 times one phase current
  4. Three times one phase current Correct answer.

Explanation

Triplen harmonics (third, ninth, and so on) in the three phases are in phase with one another, so they add arithmetically in the neutral instead of cancelling. The fundamental and non-triplen components still cancel, leaving a neutral current roughly three times the per-phase triplen magnitude.

Question 29General Power Engineering

A current transformer secondary must not be open-circuited while primary current is flowing because of which of the following?

  1. The secondary current would reverse and damage the primary winding
  2. The core would permanently lose all of its residual magnetism
  3. A dangerously high voltage would appear at the secondary Correct answer.
  4. The connected burden would draw excessive current from the source

Explanation

With the secondary open, the opposing ampere-turns vanish and the entire primary current acts as magnetizing current, driving the core deep into saturation. The rapidly changing flux induces a very high peak voltage across the open terminals, endangering personnel and insulation.

Question 30General Power Engineering

A squirrel-cage motor has a locked-rotor torque of 150 percent of rated torque at full voltage. It is started on a 65 percent autotransformer tap. The starting torque produced at the motor is closest to which value?

  1. 42 percent
  2. 98 percent
  3. 150 percent
  4. 63 percent Correct answer.

Explanation

Reduced-voltage starting lowers torque in proportion to the square of the applied voltage. Applying 0.65 per unit voltage yields 0.65 squared, or 0.4225, of the full-voltage torque, which is about 63 percent of rated torque.

Question 31General Power Engineering

A 125 V station battery supplies a constant 15 A for 6 hours and then 10 A for 2 hours. Neglecting aging and temperature correction, the ampere-hour capacity required is closest to which value?

  1. 130 Ah
  2. 150 Ah
  3. 90 Ah
  4. 110 Ah Correct answer.

Explanation

Ampere-hour capacity is the sum of each load current multiplied by its duration. The load is 15 A times 6 h, or 90 Ah, plus 10 A times 2 h, or 20 Ah, for a total of 110 Ah.

Question 32General Power Engineering

A single-phase 240 V feeder carries 100 A to a load. The one-way conductor resistance is 0.10 ohm and reactance is negligible. The voltage drop at the load is closest to which value?

  1. 4.2 percent
  2. 12.5 percent
  3. 8.3 percent Correct answer.
  4. 16.7 percent

Explanation

In a single-phase circuit the current flows out and back, so the drop is twice the one-way drop: 2 times 100 A times 0.10 ohm equals 20 V. Dividing 20 V by 240 V gives about 8.3 percent.

Question 33General Power Engineering

A transformer has a core loss of 2.0 kW and a full-load copper loss of 8.0 kW. Maximum efficiency occurs at what fraction of full load?

  1. 75 percent
  2. 100 percent
  3. 50 percent Correct answer.
  4. 25 percent

Explanation

Efficiency peaks where the variable copper loss equals the constant core loss. Since copper loss varies with the square of load, the load fraction is the square root of the ratio 2.0 divided by 8.0, which is one-half of full load.

Question 34General Power Engineering

For a small arcing fault treated as a point source of radiant energy, the incident energy at a worker's location varies in which way with distance from the arc?

  1. Independent of the distance
  2. Inversely with the cube of the distance
  3. Inversely with the distance
  4. Inversely with the square of the distance Correct answer.

Explanation

Radiant energy from a compact source spreads over a spherical area that grows with the square of the radius. Doubling the working distance therefore reduces the incident energy to roughly one quarter.

Question 35General Power Engineering

A 10 m by 20 m room is to be lit to 500 lux. Each luminaire provides 5000 lumens, the coefficient of utilization is 0.5, and the maintenance factor is 0.8. The number of luminaires required is closest to which value?

  1. 80
  2. 62
  3. 40
  4. 50 Correct answer.

Explanation

Required lumens equal 500 lux times 200 square meters, or 100,000 lumens. Each luminaire delivers 5000 times 0.5 times 0.8, or 2000 lumens to the work plane, so 100,000 divided by 2000 gives 50 luminaires.

Question 36General Power Engineering

A facility consumes 4,000,000 kWh in a year and registers a peak demand of 800 kW. Its annual load factor is closest to which value?

  1. 0.68
  2. 0.57 Correct answer.
  3. 0.46
  4. 0.38

Explanation

Average load is the annual energy divided by 8760 hours, giving about 457 kW. Load factor is average load divided by peak demand, or 457 divided by 800, which is about 0.57.

Question 37General Power Engineering

A generator with 5 percent speed droop is adjusted to produce 60 Hz at no load. At rated load, its steady-state frequency is closest to which value?

  1. 55.0 Hz
  2. 59.7 Hz
  3. 58.5 Hz
  4. 57.0 Hz Correct answer.

Explanation

Five percent droop means the frequency falls by 5 percent of rated frequency when the unit moves from no load to rated load. Five percent of 60 Hz is 3 Hz, so rated-load frequency is 57 Hz.

Question 38General Power Engineering

Kelvin's law for selecting the economic size of a distribution conductor states that the most economical cross-section is the one for which which condition holds?

  1. Annual conductor cost equals annual cost of energy lost Correct answer.
  2. First cost of the conductor is minimized
  3. Annual cost of energy lost is reduced to zero
  4. Voltage drop is held to the lowest practical value

Explanation

As conductor size grows, capital cost rises while the cost of the I-squared-R energy loss falls. The economic optimum occurs where the annual capital charge on the conductor equals the annual value of the energy dissipated in it.

Question 39General Power Engineering

A surge arrester has a discharge voltage of 60 kV at the protected equipment, whose basic impulse insulation level is 95 kV. The protective margin is closest to which value?

  1. 58 percent Correct answer.
  2. 63 percent
  3. 158 percent
  4. 35 percent

Explanation

Protective margin compares the insulation strength remaining above the arrester discharge voltage. The difference is 35 kV, and 35 divided by 60 gives about 58 percent margin.

Question 40General Power Engineering

A distance relay's first zone is set to reach only about 80 to 90 percent of the protected line impedance primarily to accomplish which of the following?

  1. Detect high-resistance faults near the local bus
  2. Provide backup protection for the remote line
  3. Shorten the reset time of the carrier scheme
  4. Avoid overreaching because of measurement and line data errors Correct answer.

Explanation

Zone 1 must not operate for faults beyond the remote terminal, because it trips without intentional delay. Errors in relay measurement, current and voltage transformers, and line impedance data can make the measured impedance appear smaller than actual, so the reach is deliberately shortened.

Question 41Circuit Analysis

Three resistors of 10 Ω, 20 Ω, and 30 Ω are connected in series. What is the equivalent resistance of the combination?

  1. 6.0 Ω
  2. 20 Ω
  3. 30 Ω
  4. 60 Ω Correct answer.

Explanation

In a series connection the same current flows through every element, so the equivalent resistance is the arithmetic sum of the individual resistances. Here 10 + 20 + 30 = 60 Ω.

Question 42Circuit Analysis

Two 12 Ω resistors are connected in parallel. What is the equivalent resistance of the pair?

  1. 12 Ω
  2. 6 Ω Correct answer.
  3. 0.167 Ω
  4. 24 Ω

Explanation

For two equal resistors in parallel the equivalent resistance is half of one resistor: (12 × 12)/(12 + 12) = 6 Ω. The general product-over-sum rule gives the same result.

Question 43Circuit Analysis

A 24 V ideal voltage source is connected across an 8 Ω resistor. What current flows through the resistor?

  1. 192 A
  2. 32 A
  3. 0.33 A
  4. 3 A Correct answer.

Explanation

Ohm's law states that current equals voltage divided by resistance. Dividing 24 V by 8 Ω gives 3 A.

Question 44Circuit Analysis

A 10 µF capacitor is connected across a 60 Hz sinusoidal source. What is the magnitude of its impedance?

  1. 26.5 Ω
  2. 60 Ω
  3. 2.65 kΩ
  4. 265 Ω Correct answer.

Explanation

Capacitive reactance is Xc = 1/(2πfC). Substituting 60 Hz and 10 µF gives 1/(2π × 60 × 10⁻⁵) ≈ 265 Ω, and an ideal capacitor has no resistive part.

Question 45Circuit Analysis

A 100 mH inductor is connected to a 50 Hz sinusoidal source. What is the magnitude of its inductive reactance?

  1. 31.4 Ω Correct answer.
  2. 50 Ω
  3. 314 Ω
  4. 3140 Ω

Explanation

Inductive reactance is XL = 2πfL. With 50 Hz and 0.1 H, XL = 2π × 50 × 0.1 ≈ 31.4 Ω.

Question 46Circuit Analysis

A 4 Ω resistor carries a current of 3 A. How much power is dissipated in the resistor?

  1. 9 W
  2. 48 W
  3. 12 W
  4. 36 W Correct answer.

Explanation

Resistive power can be computed as P = I²R. Squaring 3 A and multiplying by 4 Ω gives 36 W.

Question 47Circuit Analysis

A 2 kΩ resistor and a 5 µF capacitor are connected in series. What is the time constant of the circuit?

  1. 0.1 s
  2. 10 ms Correct answer.
  3. 100 ms
  4. 2.5 ms

Explanation

The time constant of an RC circuit is τ = RC. Multiplying 2000 Ω by 5 × 10⁻⁶ F gives 0.01 s, or 10 ms.

Question 48Circuit Analysis

A 12 V source is in series with a 4 Ω resistor, and the load terminals are taken across the output of that series combination. What is the Thevenin voltage seen by the load?

  1. 12 V Correct answer.
  2. 0 V
  3. 9 V
  4. 6 V

Explanation

The Thevenin voltage is the open-circuit voltage at the load terminals. With the load removed no current flows, so there is no drop across the 4 Ω resistor and the full 12 V appears at the terminals.

Question 49Circuit Analysis

A 12 V source feeds a divider with a 6 kΩ series resistor and a 6 kΩ shunt resistor. A 6 kΩ load is connected across the shunt resistor. What voltage appears across the load?

  1. 8 V
  2. 3 V
  3. 6 V
  4. 4 V Correct answer.

Explanation

The load parallels the shunt resistor, giving 3 kΩ for that section. The total series resistance is then 9 kΩ, so the load voltage is 12 × 3/9 = 4 V, lower than the unloaded divider value.

Question 50Circuit Analysis

A node is fed by a 10 mA current source and connected to ground through a 2 kΩ resistor and, in parallel, a 3 kΩ resistor. What is the node voltage?

  1. 6 V
  2. 20 V
  3. 12 V Correct answer.
  4. 10 V

Explanation

Writing KCL at the node gives 0.01 = V/2000 + V/3000. The combined conductance is 8.333 × 10⁻⁴ S, so V = 0.01/8.333 × 10⁻⁴ = 12 V.