EE331-15950 Test 4 - Preston -
Your name:_____________________________________
Closed book
1. (1 point each – 20 total) Write the answer to the left of each question.
right
__________Which
direction is the force on a current out of a page that is in a downward magnetic field?
0
__________What
is the intensity of the magnetic field inside a copper pipe with a uniform current I?
mutual
__________What
is the name of the inductance for two coils with a common magnetic field?
south
__________Would
we label the earth’s geographic north pole as a magnetic north or south pole?
hysteresis
__________What
kind of iron core losses are caused by reversing the direction of the B field in the iron?
capacitor
__________What
kind of component can be used to cancel a lagging power factor of a motor?
induction
__________What
kind of AC motor has rotor slip?
synchronous
__________What kind of AC motor does not have rotor slip?
stator
__________The
name of the mechanical part of a motor that does not rotate?
universal
__________What
kind of motor would you use in a portable vacuum cleaner (high speed)?
induction
__________What
kind of motor would you use in a refrigerator (for long life)?
DC
– series
__________What
kind of motor is used for the electric starter in a car?
the current
__________What
creates the magnetic field in a coil of wire?
reluctance
__________For
a magnetic circuit model, what is the resistance to the magnetic field called?
Lenz’s
Law
__________The
name of the law that says currents will be induced to resist a changing magnetic field?
permeability
__________What is material property μ called that is used in the formula B=μH?
ferrite
__________A
material commonly used in very high frequency toroid coils?
squirrel
cage
__________The
kind of motor that uses aluminum bars for the rotor?
universal
__________The
kind of AC motor with a wide range of speeds that is used commonly in households?
NEC
__________The
letters naming the construction code specifying grounding requirements in homes?
2. (10 points)
N
3. (10 points)
S
N
S
attract
+
-
-
+
See the discussion on page 3.
4. (12 points) A 60 Hz single phase AC fan motor runs at 3420 RPM (revolutions per minute). Answer
the questions below. Note that the slip = (3600 – rotor RPM) / 3600.
2
What are the number of poles?____________
induction
What type of motor is this?____________________
(3600-3420)/3600 = .05
What is the motor’s slip?________________
0
How many brushes does the motor have?_________
1
EE331-15950 Test 4 - Preston -
Your name:_____________________________________
Closed book
5. (12 points) An electronics company desires to construct a 50 H toroid inductor for a filter. The
toroid core uses a ferrite material which has a relative permeability μr of 203. It has an inside diameter Di
of 2.2 cm and an outside diameter Do of 3.5 cm. The ferrite toroid thickness is 1.2 cm. N will be ~ integer.
(.5)(.035-.022)(.012) = .000078 m2
Calculate the cross sectional area of the toroid in meters2: Acore = _____________________________
(.5)(.035+.022)π m = (.0285) π m
Calculate the path length of the B field in meters (use πD): lcore = _____________________________
Calculate the reluctance (μ0=4π x 10-7)
Using L = N 2/R core = 50 H
(.0285)π/[(4π)(10-7)(203)(7.8)(10-5)]=4499810
R core = lcore/(μ0μr Acore) = _____________________________
find the number of turns
[(50)(10-6)(4499810)]0.5 = 15 turns
N = _____________________________
6. (9 points) An electric rail gun is shown in Fig P16.26.
The projectile weighs 3 grams. When the switch is closed
a current will flow out of the + terminal, through the projectile and back into the – terminal. The electrical energy
in the capacitor is ½CV2 and if converted to ½mv2 kinetic
energy, the projectile will have considerable velocity. Use
MKS units of farads, volts, kilograms, and meters per sec.
to the right
Which direction is the force on the projectile?___________
-6
2
(.5)(1000x10 )(10000) = 50,000 Joules
The energy in the capacitor is? ______________________________________________
What is the maximum velocity the projectile could attain?_________________________
v = [(2)(50,000)/(.003)].5 = 5773 m/s
The maximum speed of a rifle bullet is about 1200 m/s.
7. (27 points) You are going to install a 0.25 horsepower 120 VAC 400 Hz single phase 6 pole induction
motor in an airplane for air circulation. It draws 1.9 amperes without power factor correction and uses
200 watts of power. You will also install a capacitor to correct the motor’s power factor.
(note that: 1 hp ≡ 746 watts, Q=V2/X, X=1/ωC, ω=2πf, P=VI, PF=P/VA)
120 x 1.9 = 228 volt amperes
What is the apparent power at 1.9 amps? _______________________________________________
(2282 – 2002).5 = 109.5 vars
What is the VAR reactive power (use VA2=P2+Q2 and solve for Q)? __________________________
200/228 = .877
What is the power factor PF of this motor (PF=P/VA)? _____________________________________
109.5 vars (of a shunt capacitor)
How many VARs are needed to correct the PF? ___________________________________________
C = Q/(V22πf) = 109.5/(12022π400) = 3 μF
What shunt capacitance is needed to correct the PF? ________________________________________
(.25)(746)/200 = .9325
What is the efficiency of the motor? _____________________________________________________
200 - (.25)(746) = 13.5 watts
How much power is lost in all the losses? ________________________________________________
I = P/V = 200/120 = 1.67 amps
What is the current to the motor+capacitor after the capacitor is installed? _______________________
(400)(60)(.95)/3 = 7600 RPM
What is the speed of the fan in RPM if the slip is 5%?________________________________________
2
EE331-15950 Test 4 - Preston -
Your name:_____________________________________
Closed book
Discussion for problem 3 – first method:
Lenz’s law can be used to solve this problem:
+
–
–
+
Putting resistors on the terminals and adding currents (see the arrows above) that
tends to cancel the increasing Φ flux, shows that the voltage drop across the
resistors is as indicated.
Discussion for problem 3 – second method:
+
–
–
+
The first thing to do is observe that currents into the windings (as shown by the
arrows above) will add to the flux Φ. From this, we can put dots on the windings
(as shown above) and these dots automatically denote the voltage polarity. The +
is on the same sides as the dots (since Φ is increasing). If Φ had been decreasing,
then the dotted ends would have had a – voltage. Therefore, the correct answer is
+ – – + as shown above. Note that the field Φ could have come from a third
winding which would make this problem the same as the FE problem PC15 in
Lecture 36.
3