Third Year Practice Questions

How many conductors from the source to a service are required in a single-phase 120/240 V system?

Three conductors (L1, L2, N)

The number of _______ determines the number of phases

windings

What type of three-phase system does 240 V, 3-phi identify?

A delta connected service

Three-phase circuits are three single-phase circuits combined into one circuit with either three or four conductors

True

What is the minimum number of coils in an ac generator required for producing a three-phase supply?

Three

What is the effect on output voltage of an alternator if the magnetic field strength is increased?

Egen increases

An alternator is constructed so that all three windings have a common connection to one point. This is known as a _______ connection

wye

What happens when a coil cuts the magnetic lines of force?

A voltage is induced in the coil cuts the magnetic lines of forces

As the turns of a coil rotate in an alternator, when is the induced voltage maximum?

The induced voltage is maximum when the turns of the coil are at 90 degrees to the magnetic lines of force

As the turns of a coil rotate in an alternator, when is the induced voltage zero?

The induced voltage is zero when the turns of the coil are moving parallel with the magnetic lines of force

Why is the phase sequence CAB the same as the ABC phase sequence?

The Terminals 1, 2, and 3 still see an ABC sequence and a counterclockwise rotation

The BAC phase sequence is the same as the ABC phase sequence

False

In what two ways can the phase sequence of voltages at a piece of equipment be changed?

The phase sequence can be changed by either reversing the rotation of the alternator supplying the equipment or by interchanging any two line conductors to the equipment

List three methods of observing a phase sequence

1. an oscilloscope

2. a phase sequence indicator

3. a phase rotation meter

List 3 advantages of three-phase systems over single-phase systems

1. constant power

2. smaller equipment for equivalent capacity

3. better efficiency

In which of the following systems would you expect less vibration?

A three-phase system

In which of the following systems would approximately 25% more copper be used for a feeder for the same capacity?

A single-phase system

When does the voltage induced in an alternator coil reach its maximum

When the coil is moving at 90 degrees to the magnetic lines of force

How many mechanical degrees apart are the coils in the most basic three-phase alternator?

120 degrees

How many electrical degrees apart are the voltages produced by three-phase ac generator?

120 degrees

Which of the following is considered a positive phase rotation?

BCA

How should the phase rotation of equipment be confirmed before energizing?

by using a phase rotation meter

What equipment is required to run a three-phase lathe on a single-phase farm service?

phase converter

State the mathematical relationship between phase and line voltage in a wye connection

VL = VP x 1.732 and VL leads VP by 30 degrees

Calculate the line voltage in a wye-connected load when the phase voltage is 347 V

600 V

Calculate the phase voltage when three light bulbs are connected in wye and the supply voltage is three-phase, four-wire, 415 V

239.6 V

What is the angle measurement between phase and line voltage in a wye-connected load?

30 degrees

What is the angle measurement between the phase voltages in a wye-connected load?

120 degrees

What is the relationship between line current and phase current in a wye-connected system?

The phase and line currents in a wye-connected circuit are equal

What is the angle measurement between the line current and line voltage in a wye connection at unity power factor?

At unity power factor the angle between line current and line voltage is 30 degrees

In a wye-connected load, the phase voltage is 200 V and the resistance of each phase is 20 ohms. Calculate the line current.

10 A

If the line voltage of a three-phase wye-connected load is 208 V and the resistance of each phase is 5 ohms. Calculate the phase current.

24 A

What are the two main purposes of a neutral conductor in a three-phase, four-wire wye connected system

1. To maintain phase voltages

2. To carry unbalanced current

What is the angle measurement between phase voltage and line voltage in a wye-connected circuit?

30 degrees

What two conditions must be present for a three-phase wye system to be balanced?

1. Currents must be equal in magnitude

2. Power factor of each phase must be the same

In a three-phase, four-wire unbalanced circuit the phase voltages are equal

True, the neutral conductor maintains voltages from line to neutral

An unbalanced load consisting of 10 ohms (Phase A), 5 ohms (Phase B). and 20 ohms (Phase C) are wye-connected across 120/208 V supply. Calculate the neutral current.

15.87 A

One single-phase motor is connected in each phase of a three-phase, four-wire system, with values shown below. Calculate the current in the neutral.

Phase A: M1 has 20 A at 0.866 pf

Phase B: M2 has 15 A at 0.707 pf

Phase C: M3 has 10 A at 0.5 pf

9.41 A

A three-phase wye connected ac generator produces a phase voltage of 240 V. What is the measured voltage from Line B to Line C?

416 V

A phasor diagram for a three-phase wye connected generator with a positive phase rotation uses V_AN as a reference. What is the angle between V_AN and V_CA?

150 degrees

A three-phase wye connected 480 V motor draws a line current of 88 A with a power factor of 0.85 lag. What is the phase current of the motor?

88 A

Three 19 ohm resistors are connected in wye on a 600 V line-to-line supply. What is the current flowing through each resistor?

18.3

What is one purpose of a neutral conductor in a three-phase wye connected load?

Maintain phase voltages

If the neutral conductor were to become disconnected, which phase will experience the highest volt drop in unbalanced wye connected circuit? Phase A has a 25 ohm load, Phase B has a 16 ohm load, and Phase C has a 32 ohm load.

Phase C

Three 10 ohm resistors are connected in wye. What is the phase angle of Phase B?

0 degrees

Three 8 ohm capacitors are connected in wye to a 120/208 V supply. Using V_AN as the reference. what is the angle of the I_B phasor?

330 degrees

In a delta-connected system, a voltmeter is connected between Lines A and B (E_AB). If the voltmeter is then connected across E_Cc what would the meter reading be?

The same

When connecting three coils to complete a three-phase delta-connected system, an open corner test reveals that the voltmeter reads twice the phase voltage. What is the problem? How would you solve it?

The problem is that a coil has been connected in reverse with respect to the other coils. De-energize the system and check the leads/labels.

When creating a phasor diagram for a delta-connected load, which phasor is referred to as the reference phasor? At what angle is drawn in the phasor diagram?

By convention, V_AB is drawn on the horizontal axis (0 degrees) and is used as a reference phasor

A delta connected source has a line voltage of 600 V. What is the phase voltage?

The phase voltage is 600 V because in a delta connection line voltage is equal to phase voltage

If a delta-connected load has devices that have equal impedances at the same power factor, what is the circuit said to be?

Balanced

When a delta-connected load is balanced, the phase currents are 120 degrees out of phase with each of the other phase currents unless they all have a lagging power factor

False, if the delta-connected load is balanced, the phase currents are always 120 degrees out of phase with each of the other phase currents no matter what the power factor is

What is the equation to calculate the line current that can be used on any balance delta-connected load?

I_Line = I_Phase x 1.732

The following formulas can only be used on unbalanced delta-connected systems:

I_A = I_AB + I_AC

I_B = I_BC + I_BA

I_C = I_CA + I_CB

False, these formulas work for balanced or unbalanced systems

A 60 Hz, three-phase delta-connected source with a line voltage of 600 V supplies a balanced delta-connected load consisting of three 12 ohm resistors.

Calculate the phase currents I_AB, I_BC, I_CA

Calculate the line currents I_A, I_B, I_C

All three phase currents are 50 A

All three line currents are 86.6 A

For a balanced delta load consisting of three 20 ohm impedances at 10 degrees lag

Calculate phase currents I_AB, I_BC, I_CA

Calculate the line currents I_A, I_B, I_C

All phase currents are 30 A

All line currents are 51.96 A

In a balanced delta-connected load, the line current is equal to the phasor sum of its phase currents.

What is the relationship between the magnitude of the line current and the magnitude of the phase current?

The line currents are displaced from each other by _____ degrees

I_L = I_P x 1.732

the line currents are displaced from each other by 120 degrees

For any balanced delta-connected load, what is the phase angle difference between the line currents and their line voltages at unity power factor?

The line currents lag their line voltages by 30 degrees

For any balanced delta-connected load, what is the phase angle difference between the line currents and their line voltages at a lagging power factor of 0.9659?

45 degrees (15 + 30 = 45)

The line current is always 1.732 greater than any phase current

False, the impedance and power factor must be the same to use the formula I_L = I_P x 1.732

The line currents are not equal to each other

True, line currents are calculated from the phasor sum of the appropriate phase currents

An unbalanced delta load can never have equal phase currents

False, an unbalanced delta load can have equal phase currents at different power factors

The line current can be calculated by the formula I_L = I_P x 1.732

False, I_L = I_P x 1.732 can only be used on balanced circuits

Answer the following questions using the unbalanced delta-connected load supplied by the 240 V three-phase generator where R_AB = 20 ohms, R_BC = 30 ohms, R_CA = 40 ohms.

Calculate phase voltages V_AB, V_BC, V_CA.

Calculate phase currents I_AB, I_BC, I_CA.

Calculate the line currents I_A, I_B, I_C.

V_AB = 240 V, V_BC = 240 V, V_CA = 240 V

I_AB = 12 A, I_BC = 8 A, I_CA = 6 A

I_A = 15.9 A at 340.9 degrees, I_B = 17.4 A at 203.4 degrees , I_C 12.2 A at 85.3 degrees

Answer the following questions using the unbalanced delta-connected load provided:

• 600 V three-phase, three-wire

• Z_AB = 30 ohms with pf = 0.8 lag

• Z_BC = 30 ohms with pf = 0.6 lag

• Z_CA = 30 ohms with pf = 1 (unity)

Calculate phase voltages V_AB, V_BC, V_CA.

Calculate phase currents I_AB, I_BC, I_CA.

Calculate the line currents I_A, I_B, I_C.

V_AB = 600 V, V_BC = 600 V, V_CA = 600 V

I_AB = 20 A with 36.9 degree lag, I_BC = 20 A with 53.1 degree lag, I_CA = 20 A

I_A = 39.2 A at 311.6 degrees, I_B = 37.1 A at 165 degrees , I_C 12 A at 63.5 degrees

A 4360 V three-phase delta motor has an FLA of 19 A. What is the phase current of the motor?

10.97 A

A balanced delta-connected load has a phase current on Phase AB or 20 A at 340 degrees. What is the magnitude and angle of Line B current?

I_Line = 34.64 A at 340 degrees

I_Line lags 30 degrees

I_AB at 340 degrees means I_A is at 310 degrees

Line currents are displaced by 120 degrees therefore I_B is at 190 degrees (310 - 120)

Calculate the line currents and complete the values for V_AB, V_BC, V_CA, I_AB, I_BC, I_CA, I_A, I_B, I_C for a delta-connected load with the following values:

• E_L = 600 V

• Z_AB = 36 ohms at 0.866 lag

• Z_BC = 24 ohm resistive load

• Z_CA = 60 ohms at 0.5 lag

V_AB = V_BC = V_CA = 600 V

I_AB = 16.67 A at 330 degrees, I_BC = 25 A at 240 degrees, I_CA = 10 A at 60 degrees

I_A = 19.44 A at 299 degrees, I_B = 30 A at 206.3 degrees, I_C = 35 A at 60 degrees

In a four-wire delta-connected supply, the high-leg should always be between Line A and Centre Tap N with the center tap connection between Lines B and C

True, the high-leg should always be between Line A and Centre Tap N with the center tap connection between Lines B and C as per the CE Code

Which of the following statements is correct when using a delta-connected system?

The line voltage and phase voltages are equal

Which of the following statements is correct when using a balanced delta-connected system?

The line current is equal to the phase current times 1.732

Which of the following statements is correct when using a delta-connected system?

Voltage V_AB leads voltage V_BC by 120 degrees

The phase currents of a delta-connected circuit are as follows:

• I_AB = 5 A at 0.766 lagging

• I_BC = 5 A at unity

• I_CA = 5 A at 0.927 lagging

Using the above information, what is the value of line current I_B?

6.4 A

In a three-phase four-wire high-leg delta system, which phase must be the high-leg?

Phase A

In a three-phase four-wire 240 V high-leg delta system, what is the voltage between Line A and neutral?

208 V

Using 0 degrees as the reference point, which of the following phase angles are equal?

120 degrees lagging and 240 degrees leading

When a balanced three-phase delta-connected load is reconnected into a wye-connected configuration, the voltage drop will be ___ times ____ (more/less). The current through each load will be ___ times ____ (more/less). The line current supplying the wye-connected loads will be ___ times ____ (lower/higher).

When a balanced three-phase delta-connected load is reconnected into a wye-connected configuration, the voltage drop will be 1.732 times less. The current through each load will be 1.732 times less. The line current supplying the wye-connected loads will be 1.732 times lower.

Three single-phase transformers have a voltage rating of 120 V each and a current rating of 50 A.

Which configuration (wye or delta) will provide the greatest line current capacity?

What will be the output voltage be for this configuration?

Delta will provide the greatest line current capacity.

The output voltage will be 120 V.

A three-phase wye-connected load has loads in each phase with different current values at different power factors of the other phases. If the neutral current is zero amperes, then the load is considered a balanced load.

False, it is mathematically possible for three unbalanced loads to have no current in the neutral.

Two balanced loads, one wye-connected and one delta-connected, are supplied from the same source. Phasor drawings are very useful to determine the line currents I_A, I_B, I_C that the source is supplying to these two loads. What is done with the phasor drawing for the wye-connected load and why?

The phasors for the wye-connected load are rotated 30 degrees clockwise from the way the phasors are normally drawn. This gives the wye-connected load phasors and the delta-connected load phasors the same reference, which is the line voltage.

Three single-phase transformers are delta-connected on the secondary to provide a line output voltage of 347 V. Is it possible to reconfigure the secondary to provide an output voltage of 600 V? Explain your answer.

Yes, if the single-phase transformers are reconnected in wye, the windings will still have 347 V induced onto them, and the line voltage will now be 600 V.

Two three-phase loads, one wye-connected and one delta-connected, are supplied from the same source. The voltage drop across one of the delta-connected loads is 208 V. What is the voltage drop across any of the wye-connected loads if the wye-connected circuit is unbalanced?

120 V

A three-phase alternator produces 277 V and 100 A per winding. If this alternator were connected in delta, what would the available line current be?

173 A

A three-phase alternator produces 277 V and 100 A per winding. If this alternator were connected in delta, what would the available line voltage be?

277 V

A delta connected three-phase supply has a line voltage of 48- V. If it were reconnected in wye, what would be the line voltage supplied by the source?

831 V

When a three-phase wye connected load is reconnected in delta, which value will not change on the load?

Phase impedance

A three-phase wye connected load draws 25 A of line current. If the load were reconnected in delta to the same source, what would the new line current be?

75 A

• Two loads are connected to a 600 V 60 Hz three-phase supply

• Load 1: Delta connected resistor bank with each phase drawing 10 A

• Load 2: Wye connected resistor bank with each phase drawing 10 A

What is the impedance of each phase in Load 2?

What is the line current on Load 1?

What is the total line current required from the supply?

34.7 ohms

17.3 A

27.3 A

• Two loads are connected to a 600 V 60 Hz three-phase supply

• Load 1: Wye motor with a line current of 20 A and a pf of 0.866 lag

• Load 2: Delta motor with a line current of 35 A and a pf of 0.707 lag

What is the phase current of Load 2?

What is the total line current required from the supply?

20.2 A

54.6 A

Which formula describes the reactive power of a single phase of a three-phase balanced circuit?

Q_P = V_P x I_P x sin(theta)

Which formula describes the power factor of a single phase of a three-phase balanced circuit?

pf = P/S

How does phase power compare to the total power of a three-phase wye-connected balanced load?

The phase power is only one-third of the total power

Which formula best describes the total apparent power of a three-phase balanced load?

S_T = V_L x I_L x 1.732

A three-phase induction delta-connected motor operates at 0.6 power factor and draws 34.64 A from a 240 V, 60 Hz, three-phase supply. Calculate the following values:

• True power for the circuit

• Reactive power for the circuit

• Apparent power for the circuit

• True power of one phase

• Reactive power of one phase

• Phase angle of the motor

• Power factor of one phase

• P_M = 8639.747 A

• Q_M = 11519.647 var (lag 53.13 degrees)

• S_M = 14399.578 VA

• P_P = 2880 W

• Q_P = 3840 var (lag 53.15 degrees)

• 53.15 degrees

• pf = 0.6 lag

A three-phase, 600 V, 60 Hz supply has a three-phase 40 kW oven and a 25 hp. 85% efficient, 60% power factor motor connected to it.

Calculate the motor load, oven load and the circuit totals.

Motor:

• Phase angle

• P_M

• Q_M

• S_M

Oven:

• Power factor angle

• P_O

• Q_O

• S_O

Circuit Totals:

• P_T

• Q_T

• S_T

• Phase angle

• pf

Motor:

• Phase angle = 53.13 degrees lag

• P_M = 21941.176 W

• Q_M = 29.25 kvar

• S_M = 36.57 kVA

Oven:

• Power factor angle = 0 degrees

• P_O = 40000 W

• Q_O = 0 var

• S_O = 40000 VA

Circuit Totals:

• P_T = 61.94 kW

• Q_T = 29.26 kvar

• S_T= 68.5 kVA

• Phase angle = 25.31 degrees

• pf = 0.904 lagging

There are three individual loads that are wye-connected to a 120/208 V, 60 Hz, three-phase, four-wire system.

• Phase A load is a motor that draws 15 A at 0.6 lagging power factor

• Phase B load is a heater and a motor that draws 18 A at 0.866 lagging power factor

• Phase C load is a capacitive circuit that draws 24 A at 0.5 lagging power factor

Calculate the phase and circuit total values.

Phase A:

• Phase angle

• P_A

• Q_A

• S_A

Phase B:

• Phase angle

• P_B

• Q_B

• S_B

Phase C:

• Phase angle

• P_C

• Q_C

• S_C

Circuit Totals:

• P_T

• Q_T

• S_T

• pf

Phase A:

• Phase angle = 53.13 degrees lag

• P_A = 1080 W

• Q_A = 1440 var lag

• S_A = 1800 VA

Phase B:

• Phase angle = 30 degrees lag

• P_B = 1870.615 W

• Q_B = 1080 var lag

• S_B = 2160 VA

Phase C:

• Phase angle = 60 degrees lead

• P_C = 1440 W

• Q_C = 2494.153 var lead

• S_C = 2880 VA

Circuit Totals:

• P_T = 4390.615 W

• Q_T= 25.847 var lag

• S_T = 4390.691 VA

• pf = 0.999 or 1