Problems on Electrical Engineering
ESO210/ESO203A: Introduction to Electrical Engineering
Assignment 4
Date of Submission: 20th March, 2013
1. The rotor shown in Fig.1 has two coils. The rotor is nonmagnetic and and is placed in a uniform magnetic field of magnitude B0 . The coil sides are of radius R and are uniformly spaced around the rotor surface. The first coil carrying a current I1 and second coil carrying a current I2 .
Assuming that the rotor is 0.30 m long, R=0.13 m, and B0 = 0.85 T, find the Θ directed torque as a function of rotor position α for (a) I1 =0A and I2 =5A, (b)I1 =5A and I2 =0A, and
(c)I1 =8A and I2 =8A.
Uniform magnetic field, B 0y
r
θ
Ι2
Ι1
R
α
ι
x
Figure 1:
2. An inductor has an inductance which is found experimentally to be of the form
L=
2L0
1+x/x0
where L0 =30 mH, x0 =0.87 mm, and x is the displacement of movable element. Its winding resistance is measured and found to equal 110 mΩ.
(a) The displacement x is held constant at 0.90 mm, and the current is increased from 0 to
6 A. Find the resultant magnetic stored energy in the inductor.
(b) The current is then held constant at 6 A, and the displacement is increased to 1.80 mm.
Find the corresponding change in magnetic stored energy.
3. The inductor of Problem 2 is driven by a sinusoidal current source of the form
i(t)=I0 sin(ω t)
Where I0 =5.5A and ω =100Π(50Hz). With the displacement held fixed atx = x0 , calculate
(a)the time- averaged magnetic stored energy (Wf ld ) in the inductor and (b)the time-averaged power dissipated in the winding resistance.
4. The inductance of a phase winding of a three-phase salient-pole motor is measured to be of the form
L(Θm )=L0 +L2 cos2Θm where Θm is the angular position of the rotor.
(a) How many poles are on the rotor of this motor?
(b) Assuming that all other winding currents are zero and that this phase is excited by a constant current I0 , find the torque Tf ld (Θ) acting on the rotor.
5. As shown in Fig.2 , an N -turn
Assignment 4
Date of Submission: 20th March, 2013
1. The rotor shown in Fig.1 has two coils. The rotor is nonmagnetic and and is placed in a uniform magnetic field of magnitude B0 . The coil sides are of radius R and are uniformly spaced around the rotor surface. The first coil carrying a current I1 and second coil carrying a current I2 .
Assuming that the rotor is 0.30 m long, R=0.13 m, and B0 = 0.85 T, find the Θ directed torque as a function of rotor position α for (a) I1 =0A and I2 =5A, (b)I1 =5A and I2 =0A, and
(c)I1 =8A and I2 =8A.
Uniform magnetic field, B 0y
r
θ
Ι2
Ι1
R
α
ι
x
Figure 1:
2. An inductor has an inductance which is found experimentally to be of the form
L=
2L0
1+x/x0
where L0 =30 mH, x0 =0.87 mm, and x is the displacement of movable element. Its winding resistance is measured and found to equal 110 mΩ.
(a) The displacement x is held constant at 0.90 mm, and the current is increased from 0 to
6 A. Find the resultant magnetic stored energy in the inductor.
(b) The current is then held constant at 6 A, and the displacement is increased to 1.80 mm.
Find the corresponding change in magnetic stored energy.
3. The inductor of Problem 2 is driven by a sinusoidal current source of the form
i(t)=I0 sin(ω t)
Where I0 =5.5A and ω =100Π(50Hz). With the displacement held fixed atx = x0 , calculate
(a)the time- averaged magnetic stored energy (Wf ld ) in the inductor and (b)the time-averaged power dissipated in the winding resistance.
4. The inductance of a phase winding of a three-phase salient-pole motor is measured to be of the form
L(Θm )=L0 +L2 cos2Θm where Θm is the angular position of the rotor.
(a) How many poles are on the rotor of this motor?
(b) Assuming that all other winding currents are zero and that this phase is excited by a constant current I0 , find the torque Tf ld (Θ) acting on the rotor.
5. As shown in Fig.2 , an N -turn