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Electrical Theory & Fundamentals — Electrician Practice Questions

44 questions · 9% of the Electrician exam

Worked questions

1. Three resistances of 5 ohms, 10 ohms, and 25 ohms are connected in series across a 120-volt source. What is the voltage measured across the 25-ohm resistance?

  • 75 volts
  • B120 volts

    Putting the whole supply across one element is what happens in a parallel arrangement. Series elements share the source voltage between them, so no single element can ever see the entire supply.

  • C40 volts

    This splits the source into three equal parts. Voltage divides in proportion to resistance, not by a head count, so equal shares occur only when all three resistances happen to be equal.

  • D30 volts

    This is the drop across the 10-ohm element rather than the 25-ohm one. Reading the proportion off the wrong resistance is an easy slip when three values are in play and the clock is running.

Why A is correct

Series means a single path, so every element carries the identical 3 amperes and each takes voltage in proportion to its own resistance. The 25-ohm element holds 25 of the 40 total ohms, so it takes 25 fortieths of 120 volts, which is 75 volts. The largest resistance takes the largest share of voltage and therefore produces the most heat.

What this question is testing

Two habits are being checked at once: totaling series resistances before doing anything else, and remembering that current is the quantity that stays constant. The distractors reward candidates who split the voltage evenly among the elements or who quietly assume a parallel arrangement, both common errors under time pressure.

On the job

Series wiring turns up in heating elements, control circuits, and, unintentionally, in every loose connection you will ever chase. A loose splice puts resistance in series with the load, claims its proportional share of the voltage, and turns that share into heat right at the joint. That is exactly why a bad termination glows while the equipment downstream runs low, and why voltage readings taken across a suspect connection find the fault so quickly.

Memory technique

Series shares current, parallel shares voltage.

Exam tip

Work series problems in order: total resistance first, then circuit current, then back to any individual drop. Jumping straight to the drop invites an even-split error.

Where to look it up

Closed-book theory with no article involved.

2. A single-phase load consists of 12 ohms of resistance in series with 5 ohms of inductive reactance. Impedance equals the square root of the sum of the squares of resistance and reactance, and power factor equals resistance divided by impedance. What is the power factor of this load?

  • A0.42

    This divides reactance by resistance, which is the tangent of the phase angle rather than the power factor. The power factor is the cosine of that angle.

  • 0.92
  • C1.08

    A power factor greater than one is impossible; it would mean the load consumes more real power than the source supplies. The error is inverting the ratio to impedance over resistance.

  • D0.38

    This divides reactance by impedance, which gives the reactive factor rather than the power factor. Power factor always uses the resistive side over the hypotenuse.

Why B is correct

Because resistance and reactance are 90 degrees apart, they combine as the sides of a right triangle: 12 and 5 give a hypotenuse of 13 ohms. Power factor is the ratio of the resistive side to the hypotenuse, so 12 divided by 13 gives 0.92 lagging.

What this question is testing

Tests whether you can combine resistance and reactance correctly using the right triangle relationship rather than adding them, and whether you know that power factor is the ratio of resistance to impedance rather than any of the other ratios available in the same triangle.

On the job

The practical payoff is understanding why a clamp meter and a voltmeter multiply out to more volt-amperes than a wattmeter reads on the same circuit. Motors, transformers, solenoids and ballasts all present inductive reactance, and the difference between the two readings is what utilities charge large customers for. It also explains why conductors and overcurrent devices are sized on current, which reflects apparent power, not on the watts the load actually converts.

Memory technique

Three, four, five and twelve, five, thirteen: the impedance triangle loves the same numbers a framer does.

Exam tip

Draw the right triangle: resistance on the bottom, reactance up the side, impedance across. Power factor is bottom over hypotenuse.

Where to look it up

Impedance and power factor are theory, but they explain why Code load calculations are done in volt-amperes rather than watts throughout Article 220.

3. A four-pole induction motor operates on a 60-hertz supply. Synchronous speed in revolutions per minute equals 120 times the supply frequency divided by the number of poles. What is the synchronous speed of that motor?

  • A3,600 rpm

    Thirty-six hundred is the synchronous speed of a two-pole motor. It comes from dividing by 2 instead of by the four poles the problem specifies.

  • B1,200 rpm

    Twelve hundred corresponds to a six-pole motor. More poles means a slower field, and this motor has four rather than six.

  • 1,800 rpm
  • D900 rpm

    Nine hundred corresponds to an eight-pole motor, which is half again slower than the six-pole case.

Why C is correct

One hundred twenty times 60 hertz is 7,200, and dividing by the four poles gives 1,800 revolutions per minute for the rotating field. The rotor lags that field by the amount of slip needed to produce torque, which is why the nameplate speed sits a little below 1,800.

What this question is testing

Tests whether you know the relationship between supply frequency, pole count and synchronous speed, whether you apply it correctly, and whether you understand slip well enough to explain the gap between the calculated speed and a real nameplate value.

On the job

Motor speed is set by poles and frequency, not by voltage, which is the point most customers get wrong. That is also why variable frequency drives change speed by changing frequency rather than voltage alone. When you replace a motor, matching the nameplate speed matters as much as matching horsepower, because a two-pole replacement on a four-pole pump or fan will roughly double the flow demand and can overload the driven equipment and the circuit.

Memory technique

Twelve thousand divided by poles, then drop a zero: four poles gives eighteen hundred.

Exam tip

Two poles gives 3,600, four gives 1,800, six gives 1,200, eight gives 900. Double the poles, halve the speed.

Where to look it up

Motor speed is theory, but Article 430 uses horsepower and full-load current tables where the same motor characteristics show up in the sizing rules.

4. A 240-volt single-phase source supplies a load that draws 30 amperes. The total resistance of the complete conductor path, out and back, measures 0.25 ohm. What voltage appears at the load terminals?

  • 232.5 volts
  • B240 volts

    The source voltage appears at the load only when no current flows. Under load the conductors always take their share, which is why an unloaded measurement can look fine while the equipment still misbehaves.

  • C247.5 volts

    Adding the drop instead of subtracting it puts more voltage at the load than the source produces. Conductor resistance can only consume voltage.

  • D225 volts

    This doubles the 0.25 ohm as though it were a one-way figure. The problem already gives the total for both conductors, so applying the factor of two again overstates the drop.

Why A is correct

Thirty amperes through a quarter ohm of conductor resistance drops 7.5 volts, and that drop is subtracted from the 240-volt source to give 232.5 volts at the load. Because the problem states the resistance for the complete out-and-back path, the drop is calculated directly without doubling anything.

What this question is testing

Tests whether you can apply Ohm's law to conductor resistance as a series element, whether you subtract the drop from the source rather than adding it, and whether you read carefully enough to notice that the given resistance already covers both conductors.

On the job

This is what a voltmeter is really telling you when you meter at the panel and again at the equipment while the load is running. The difference is the conductor drop, and it appears only under load, which is why measuring a dead circuit proves nothing about voltage drop. The same arithmetic in reverse, measuring the drop and dividing by the current, gives you the resistance of a run and can locate a loose connection or a damaged conductor.

Memory technique

The wire takes its cut first, and the load gets what is left.

Exam tip

Read whether the resistance given is one way or for both conductors. Doubling something that is already doubled is the usual trap.

Where to look it up

Chapter 9, Table 8 gives conductor resistance per thousand feet, which is where a real total path resistance comes from. Voltage drop targets themselves are informational notes.

40 more in the bank

Answers and explanations for these are in the app.

  • A resistance heating element measures 9.6 ohms and is supplied from a 120-volt circuit. How much current does the element draw?
  • An appliance connected to a 208-volt supply draws a steady 16 amperes. What is the resistance of the load?
  • A branch-circuit conductor pair has a total resistance of 0.4 ohm and carries 24 amperes to a 120-volt load. How much power is dissipated as heat in the conductors?
  • An electric resistance heater is rated 4,800 watts at 240 volts. What is the resistance of its heating element?
  • Three loads of 10 ohms, 15 ohms, and 30 ohms are connected in parallel on the same 120-volt branch circuit. What total current does that circuit carry?
  • A single-phase transformer has a 480-volt primary and a 120-volt secondary. If the secondary supplies a load of 100 amperes, what current flows in the primary?
  • A standard 120-volt alternating-current receptacle is measured with a true-RMS meter. What is the approximate peak value of that sine wave voltage?
  • Alternating-current systems in the United States operate at 60 hertz, and system voltages are stated as RMS values. What does the RMS value of an alternating voltage represent?
  • On a 120/240-volt single-phase three-wire service, one ungrounded conductor carries 46 amperes of line-to-neutral load while the other carries 32 amperes of line-to-neutral load. How much current does the grounded neutral conductor carry?
  • A three-phase wye-connected system measures 277 volts from any ungrounded conductor to the grounded neutral. What is the voltage between any two ungrounded conductors?
  • A balanced three-phase delta-connected load draws 30 amperes through each of its windings. What current flows in each of the three line conductors feeding that load?
  • A single-phase 240-volt motor circuit draws 25 amperes while a wattmeter connected to that same circuit reads 4,800 watts. What is the power factor of the load?
  • A 45 kVA three-phase transformer has a 208Y/120-volt secondary. What is the full-load secondary current available from that transformer?
  • A facility adds several lightly loaded induction motors to an existing service. What happens to the power factor of that service and to the current in the feeder conductors?
  • A 120-volt single-phase circuit uses 12 AWG copper conductors and supplies a 16-ampere load located 100 feet from the panel. Using a copper K value of 12.9 and 6,530 circular mils for 12 AWG, what is the approximate voltage drop?
  • Transformers, generators and uninterruptible power supplies are rated in kilovolt-amperes rather than kilowatts. What does a kilovolt-ampere rating actually express about the equipment?
  • A 208Y/120-volt four-wire feeder supplies a floor full of switch-mode power supplies and electronic lighting drivers. A clamp meter reads about 40 amperes on each of the three ungrounded conductors and about 55 amperes on the grounded conductor. What explains that reading?
  • A three-phase delta-connected transformer secondary measures 240 volts between any two line conductors. What voltage appears across each individual transformer winding, and what is the reason?
  • A four-wire delta system with one winding center-tapped supplies a shop. Two of the ungrounded conductors measure about 120 volts to the grounded conductor and the third measures about 208 volts to it. What is the correct interpretation and what does the Code require?
  • The same 30-kilowatt resistive heating load can be supplied at 240 volts single phase or at 240 volts three phase. How does the current in each ungrounded conductor compare between the two arrangements?
  • A branch circuit is measured with about 4 percent voltage drop at full load. How does the National Electrical Code treat the 3 percent and 5 percent voltage drop figures that are so often quoted on the job?
  • Two conductors are the same size and the same length and are at the same temperature, but one is copper and the other is aluminum. How do their resistances compare, and what is the practical consequence for conductor selection?
  • Three heating elements are connected in series across a 240-volt supply. One element burns open. A voltmeter is placed across the terminals of that open element. What does the meter read, and what current flows in the circuit?
  • Several resistances of different values are connected in parallel across one branch circuit. Which statement correctly describes the total resistance of that combination and what happens when one of the branches opens?
  • A single-phase transformer has a 480-volt primary wound with 1,200 turns and a 120-volt secondary. Assuming the voltage ratio equals the turns ratio, how many turns are on the secondary winding?
  • A single-phase load operates at 240 volts and draws 62 amperes. Standard single-phase dry-type transformer ratings available include 7.5, 10, 15 and 25 kilovolt-amperes. What is the smallest standard transformer that will carry this load?
  • A three-phase motor drives a constant mechanical load. Because of a long feeder, the voltage at the motor terminals is about 10 percent below the nameplate value. What happens to the current the motor draws?
  • Capacitive reactance equals 1 divided by the product of 2, pi, the supply frequency and the capacitance in farads. If the frequency applied to a fixed capacitor doubles from 60 hertz to 120 hertz, what happens to the reactance and to the current the capacitor draws at the same voltage?
  • A 12 AWG uncoated copper conductor has a direct-current resistance of 1.93 ohms per 1,000 feet. A branch circuit uses two such conductors over a one-way distance of 130 feet. What is the total resistance of the conductor pair, counting both the outgoing and the returning conductor?
  • A single-phase 240-volt load draws 50 amperes at a power factor of 0.80 lagging. What is the reactive power in that circuit?
  • A four-pole induction motor runs on a 60-hertz supply, giving a synchronous speed of 1,800 revolutions per minute. Its nameplate full-load speed is 1,725 revolutions per minute. What is the percent slip at full load?
  • A three-phase transformer has a delta-connected primary at 480 volts and a wye-connected secondary. Each secondary winding develops 120 volts between its end and the neutral point. What is the voltage measured between any two secondary line conductors?
  • A 208Y/120-volt four-wire feeder supplies a perfectly balanced three-phase load drawing the same current in each line. The load is linear with no harmonic content. What current flows in the neutral conductor?
  • A feeder carries 30 amperes and its conductors dissipate 90 watts of heat. If the load increases so the same conductors carry 60 amperes, how much power will the conductors dissipate?
  • A three-phase supply measures 470, 480, and 490 volts between the three pairs of line conductors. Percent unbalance is the greatest deviation of any reading from the average, divided by the average. What is the percent voltage unbalance?
  • Capacitors are installed at a plant to correct a lagging power factor caused by its motors. What happens to the real power drawn by those motors and to the current in the service conductors?
  • A three-phase motor operating at 460 volts delivers 20 horsepower of mechanical output. Its efficiency is 90 percent and its power factor is 0.85. Using 746 watts per horsepower, what is the approximate line current drawn from the supply?
  • Chapter 9, Table 8 lists stranded uncoated copper 10 AWG as having an area of 10,380 circular mils and a direct-current resistance of 1.24 ohms per 1,000 feet. The resistivity constant used in voltage drop work is found by multiplying the resistance per 1,000 feet by the circular mil area and dividing by 1,000. What constant does this conductor produce?
  • An existing 240-volt circuit wired in 10 AWG copper, area 10,380 circular mils, shows a measured drop of 9.6 volts under load. The same load will be reconnected over the same distance using 6 AWG copper with an area of 26,240 circular mils. Voltage drop is inversely proportional to circular mil area when current and length are unchanged. What drop should the larger conductors produce?
  • A technician measures 121.4 volts at the panel and 113.8 volts at the receptacle at the end of the run, both readings taken with the load operating. Percentage voltage drop is the difference between the two readings divided by the voltage at the source. What is the percentage drop on this circuit?

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