Vector Calculus Reference

I found an interesting website with interactive demonstrations of numerous vector calculus concepts HERE. It's well worth your time to review the material on this website, especially the upcoming material on Green's Theorem and Stokes' Theorem.

Friday's PA Session Versus the Midterm

Make sure you read my post about this issue.

Midterm Example Questions

Folks,

Here are some example questions, and here are some more. This is the formula sheet you will be given. Feel free to ask me more questions tomorrow. I'll be in my office tonight as usual as well.

Next PA Sessions

Folks, your next set of PA sessions will focus on the following:

Problems taken from:

Field and Wave Electromagnetics, Second Edition, by David K. Cheng.

P.4-1, P.4-6, P.4-7, P.4-8, P.4-14, P.4-18

P.4-12, P.4-15, P.4-16, P.4-18, P.4-23, P.4-27

New Version of Xfmr Lab

My server is still dead. I'm working on moving everything over to a new machine.

Meanwhile, the TAs have given me an updated version of the Xfmr Lab. You can find your updated lab for this week HERE, and a supplement for the lab HERE.

Hints for the Transformer Lab

Thanks to Arvind for coming up with the following:

ELEC 3105

Basic EM and Power Engineering

Lab 5- The Transformer

(Please make sure you have the latest lab theory + instruction booklet)

Description of Experiments and Hints

Experiment (a)

This is a simple experiment, where we measure the coil resistances R1 and R2 of the transformer, as shown in Fig. 3 using a multimeter. Please remove all connections on the Transformer before you make the measurements.

Experiment (b)

In this experiment, we measure the turns ratio of the given transformer, assuming its ideal. Connect the Wavetech source to the primary and the measure the output voltage amplitude at the secondary and evaluate the v1/v2 ratio.

Experiment (c)

In this experiment, we compute the input impedance and its components (resistance and reactance) with the secondary short circuited. Hence, the simplified equivalent circuit Fig. 5 comes into the picture. Using the set up in Fig. 7, you will measure the current and voltage in the primary. Hence the ration v1/i1 must give the input impedance. Note that this will be complex as we have the effect of a resistance and an inductance connected in series for this set up as shown in Fig. 5. The resitance being R1+ a² R2 and inductance being 2(1-k)L1.

But first, you must figure out how to calculate a resistance and an inductance part of a load when you know the voltage and the current through them. Once you derive the relationships as given in the booklet, proceed to measure the voltage and current amplitudes and relative phase.

Experiment (d)

The purpose of this experiment is to measure the eddy current losses (Rc) and kL1. For this we open circuit the secondary and hence, Fig. 6 comes into effect. As in the previous experiment, you shall measure v1 and i1. From that you can estimate the effective series resistance and the inductance of the circuit in Fig. 6 Rs and Ls as before.

From Fig. 6 you will see that these values depend upon R1, (1-k)L1, Rc and kL1. But we already know the values of R1 (Expt (a)) and (1-k)L1 (half the value of the inductance found in Expt (c)), so to find the remaining unknowns, (Rc and kL1), you must derive the relationship (10) and then use the values of Rs, Ls, R1 and (1-k)L1 to compute Rc and kL1.

Experiment (e) & (f)

You will repeat the above experiment for increasing frequencies and plot the behavior of Rc and kL1 against frequency. Beyond a certain point, you will see a drastic change in the Reactance of the equivalent circuit. Give an explanation for this behavior.

Hint: May be some assumptions made to construct Fig.6 that you so dearly followed for all your calculations isn’t that good after all!

Experiment (g) & (h)

This is again a repetition of the previous experments but with 2 small changes:

1. you will connect a 10 ohm load to the secondary
2. you will model the resulting equivalent circuit looking “into” the source v1 as a resistance and an inductance in PARALLEL as against serial, as you have been doing till now.

Now with v1 and i1, you figure out how to measure the resistance and inductance connected in parallel. Use these relationships (13) to measure the values of Rp and Lp. Compare it with the ideal model described in (5) and speculate why your results don’t satisfy that simple explanation, especially at low frequencies. Also the currents and the voltages distort at some value of v1 as you increase it. Note that point and explain why.

Hint: What do you remember of inductors, when it comes to DC currents and very high frequency AC currents?

Server Issue?

Hmmm.....my server seems to be dead, or at least the connection to it is dead. I'll fix it first thing tomorrow (fingers crossed). Meanwhile, you can find your lab for this week HERE, and a supplement for the lab HERE.

So what's this one about, you might ask....well, this week you'll look at transformers. I think it's safe to say that you've all dealt with transformers in some form in other courses, but in this course we will examine them using fundamental EM theory. We'll actually have to cover quite a bit of material before we're ready to give transformers the full EM treatment, but everyone can handle the lab this week because it is a measurements-type lab that you can later refer back to when we cover the theory. Hopefully the theory we develop will match the measurements.

Speaking about measurements and the value of measurement-based labs, consider this quote that I read recently on-line:

"One accurate measurement is worth a thousand expert opinions."
Author: Admiral Grace Hopper

(It's well worth your time to read about her.)

Labs this Week

Folks,

This week is a lab week, as originally planned. I'll post the lab later on this evening (as soon as I get my lap top up and running!).

Midterm Date

Folks,

In case you didn't come to class the few times we discussed this, the midterm has been scheduled for November 2nd (during class time). We'll discuss the contents of the midterm in class next week, likely on Wednesday.

First Injuries

You may have noticed that I wasn't lecturing today. I have a pulled periformus muscle, a pulled gluteus medius, and likely a pulled gluteus maximus. Talk about painful! Anyway, I had my first chiropractor session today, and already it feels "different" (not better yet, but at least a change). Hopefully I'll be back in the gym soon! ...oh yeah, and back to lecturing too :) .

Office Hours

Folks,

Some of you have been coming to my office during office hours, which is great! Just for the record, here are the office hours for myself and the TAs:

• Dr. MacEachern: Tuesdays, from 6pm-7pm. You can also try earlier (e.g 5:30pm) but no promises!
• Khaled: Khaled says just email him for an meeting, anytime! What an offer! His email address is: kmnay@doe.carlton.ca (spell Carleton correctly -- just trying to confuse the SPAMbots).
  
• Mark: 2pm-4pm Wednesdays in 5149ME
• Lado: 12pm-2pm Thursdays in 338AP
• Lidija: waiting for confirmation
• Barbora: 2pm to 3pm Wednesdays in 5169ME
• Arvind: 12pm-2pm Tuesdays in 6075MC
• Christopher: 10am-12pm Tuesdays in 7047MC

PA Sessions for the week of Oct. 15th

Folks,

Khaled is proposing the following questions from Cheng:

P.3-24, P.3-25, P.3-26, P.3-27, P.3-37, P.3-47, P.3-38, P.4-1, P.4-6, P.4-7, P.4-8, P.4-14, P.4-18

Plus, I've requested problems related to forces on conductors and also on image theory.

Lab #3 Download

You can find a PDF for Lab #3 HERE.

Note that it says "Lab #2", but don't fret, it's really Lab #3 for this year.

Give it a read, and have some fun with it tomorrow. It works rather well, and we'll be covering the material in class soon, so this gives you a good preview of what's to come in the course.

Lab #3

Hi Class,

I'll post up the materials for Lab #3 as soon as I get the "all clear" from your friendly neighbourhood TAs about the contents and functionality. It should be fine -- no changes from last year in any case.

Since today is a holiday, Section A1O is missing their lab for this week. No problem. You can do either of the following:

• Show up during any of the other sections this week, if you can fit the period into your schedule;
• Show up at the end of the term for a "make-up" lab period.

Enjoy the rest of the holiday!