3211 EEL Fall 2011 Homework #4
1. The stators of two three phase motors are wired as shown below with Vaa= Vmsin(t), Vbb= Vmsin( t+120) and Vcc=
Vmsin(t-120).
Determine the direction of rotation for the resulting net magnetic flux density for each stator. Explain your answers.
At what frequency does the magnetic field of each stator rotate at if =377 radians/sec?
Determine the direction of rotation for the resulting net magnetic flux density if each stator were rewired by swapping
phases a and c. Explain your answers.
Determine the speed, in Revolutions Per Minute, that would result if these stators were used to make synchronous motors
assuming that =377 radians/sec. Repeat if =314 radians/sec.
Determine for each motor if the rotational speed is to equal 1000 rpm.
Figure 1
Figure 2
2. Figure 3 depicts a wire loop that is rotating in the clockwise direction about the axis labeled A in the presence of a constant
and uniformly distributed magnetic flux density B=0.1 wb/m2 in the direction shown. Given that L=0.5m, W=0.35m and
d=0.1m determine the instantaneous voltage V12, which is the voltage terminal at 1 with respect to terminal 2, if f=60 and the
loop is oriented as shown.
Determine the instantaneous values for V12 once the loop has rotated 45, 90, 135 and 180. How does V12 vary with
angular position?
Figure 3
3. For the configuration of problem 2, how would V12 vary if the loop were stationary and the direction the direction of the
magnetic field intensity rotated about the axis A instead? What would this be equivalent to?
4. The loop shown in figure 4 below has a current i=4 amps and a magnetic flux density B=0.045 wb/m2. Determine the
magnitude and the direction of the torque about axis A if L=0.2m, W=0.1m and d=0.03m.
Calculate the magnitude and direction of the torque about axis A of figure 5 assuming all the same dimensions, currents and
magnetic flux densities.
How would the torque vary for each case if the loop were to rotate about the axis A in the clockwise direction?
Figure 4
Figure 5
5. For the configurations of problem 4 how would the torque vary if the direction of the magnetic field intensities rotated
about the axis A and the loops remained stationary?