Three-phase motor questions

These questions on three-phase motors are from a Japanese examination for electricians (for second-class or junior electricians, in Japanese Denki Kouji-shi Dai-ni-shu Shiken, 電気工事士第二種試験). This exam needs to be passed to get a licence to do any kind of electrical work. All the questions on the written test are multiple-choice with four choices. The answers to the questions are at the bottom of the page.

Question 1

A three-phase induction motor has rated voltage $V$ [volts] and rated current $I$ [amps]. If it runs continuously for a fixed time $t$ [hours] at the rated values, its power consumption is $W$ kW$\cdot$h. What is the power factor of the motor?

$\displaystyle{W\over\sqrt3VIt}\times10^5$
$\displaystyle{W\over3VIt}\times10^5$
$\displaystyle{\sqrt3VI\over Wt}\times10^5$
$\displaystyle{3VI\over Wt}\times10^5$

This is question 5 from the 2016 first written exam.

Question 2

In the three phase circuit shown in the diagram, the current I (amps) is.

8.3
11.6
14.3
20.0

Question 3

In the three-phase circuit below, with source voltage E volts, the circuit is broken at the cross. In this case, the equation for the current flowing between a and c, I amps, is.

$\displaystyle {E\over 2R}$
$\displaystyle {E\over \sqrt3R}$
$\displaystyle {E\over R}$
$\displaystyle {3E\over 2R}$

This is question 5 from the 2015 first written exam.

Question 4

In the three-phase circuit below, if each supply line has a resistance of 0.15 Ω, and the line current is 10 A, what is the electrical loss in the circuit?

This is question 6 from the 2015 first written exam.

Question 5

In the three-phase circuit shown in the diagram, when a three-phase alternating voltage is applied, twenty amps flows in each line. The line voltage $E$ in volts is:

This is question 4 from the 2014 second written exam.

Question 6

What is the total power consumption of the illustrated three-phase circuit in kilowatts?

This is question 5 from the 2014 first written exam.

Question 7

In a three-phase circuit like the one in the diagram, if the resistance of each line is $r$, and the line current is $I$ amps, the equation for the power loss in watts is

$\displaystyle \sqrt3 I r$
$\displaystyle \sqrt3 I^2 r$
$\displaystyle 3 I r$
$\displaystyle 3 I^2 r$

This is question 7 from the 2013 second written exam.

Question 8

In the 200 volt three-phase circuit in the diagram, the resistor from c to o is cut. Which of these are the correct voltages before and after the cut?

Before: 116V
After: 100V
Before: 116V
After: 116V
Before: 100V
After: 116V
Before: 100V
After: 100V

This is question 5 from the 2013 first written exam.

Answers

1: イ
2: ロ
3: ニ
4: ニ
5: ハ
6: ハ
7: ニ
8: イ

Web links

Original Japanese examination papers