Threephase motor questions
These questions on threephase motors are from a Japanese examination for electricians (for secondclass or junior electricians, in Japanese Denki Koujishi Dainishu 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 multiplechoice with four choices. The answers to the questions are at the bottom of the page.
Question 1
A threephase 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 threephase 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 threephase 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?
 15
 26
 30
 45
This is question 6 from the 2015 first written exam.
Question 5
In the threephase circuit shown in the diagram, when a threephase alternating voltage is applied, twenty amps flows in each line. The line voltage $E$ in volts is:
 120
 173
 208
 240
This is question 4 from the 2014 second written exam.
Question 6
What is the total power consumption of the illustrated threephase circuit in kilowatts?
 2.4
 4.8
 7.2
 9.6
This is question 5 from the 2014 first written exam.
Question 7
In a threephase 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 threephase 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