An electrical puzzle

[marconi]

Attached is a circuit. It was a course problem I recently was involved with through long-term mentoring of a junior, bright member of the EF.

I thought others might like some mental fun too.

1. How much power is dissipated in R2?

2. Which is true? Both batteries supply energy? Only one battery supplies energy?

E1 = 45V E2 = 30V. R1 = 1800R R2 = 2200R R3 = 2700R R4 = 3900R

Assume batteries have zero internal resistance and are rechargeable types. Assume all wires and connections have negligible resistance.

Hint: Mesh analysis of dc circuits but there other ways of tackling this problem.

 

[Vortigern]

Wow, don't really know what you are talking about but it sounds really intelligent @Julie. While we did Rt calcs in serial and parallel in theory work we never approached that level of analysis/problem solving. I can't even really remember having to use most of the theory at all in the humdrum of daily installation work. Hence most of the theory has taken a back seat.

 

[Julie.]

Most of the analytical methods will not be taught to electricians, as it's pretty unnecessary tbh.

Most are covered at hnc/tec5 and all are covered in the first year of university.

The dc versions (here) are simpler and predominantly electronic applications, all are capable of working in the time-domain (eg ac analysis and other signal or control applications).

My speciality was power systems analysis, & protection systems; so I spent many years performing loads of studies on electrical networks, so basically the above sort of calculations, but with ac (so real and quadrature/reactive combination of currents, voltages, and impedances) and in 3 phase - using both software and a methodology called symmetrical components.

This latter methodology basically splits a three phase system into a system having positive phase sequence rotation (normal) plus negative phase sequence, plus zero phase sequence, you calculate each individually then summate.

It was interesting and a challenge at the time, but the pay was nowhere near as good as it should have been, general consultancy pays much better!

 

[marconi]

Julie is being too modest. It is all down to girl power ️

 

[pc1966]

Certainly I was taught the mesh method at Uni for such things many moons ago. For example as shown here:

MathOnWeb - Analysing Electric Circuits and Networks

Solve basic electric circuits with resistors in series and parallel. Solve electric networks using loop and nodal analysis.

www.mathonweb.com

These days for electronics work it is still important to grasp the basic "how" of such analysis, but the reality is if you have any sort of circuit of any non-trivial complexity you just use SPICE or some other analysis software to churn out the results. Then you need the sanity checking of the results to see if they are at all reasonable.

Why? Well even with such software tools you can end up with situations that are just hard to simulate. For example, I had one where some of the parts were RF transistors with GHz response times and the other bits were op-amps to set the bias with kHz times and the simulator just borked. Basically it was trying sub-ns time-steps for the RF bits and running out of time and precision when it came to multi-millisecond adjustments. If you are not already sufficiently bored reading this then you can search for "stiff equations" and find out more (with safe search on!) So basically had to do two simulations:

• First with op-amps and settings to force it to slow adjustment so it found the DC levels
• Then to replace the op-amp DC levels with equivalent voltage sources (ideal batteries) so the fast stuff could be done against a fixed background.

Software is not magic. It is like any other tool or item of test equipment that has its limits and you really need to have an idea of what/where they are.

 

[pc1966]

I can't even really remember having to use most of the theory at all in the humdrum of daily installation work. Hence most of the theory has taken a back seat.

Which is kind of how it should be. We have the OSG tables of standard circuits to make most choices simple, fast, and safe.

Except of course from time to time when you have something that is not standard, then it is time to brush up the calculation methods!

 

[Julie.]

Julie is being too modest. It is all down to girl power ️

Instantaneous sum of girl power is zero - back to Tellegen's theorem

 

[Julie.]

......
Software is not magic. It is like any other tool or item of test equipment that has its limits and you really need to have an idea of what/where they are.

Not just software tbh, I spent a short time teaching this rubbish at college and I couldn't believe how many couldn't use a calculator, but more importantly didn't understand whether the answer was slightly right or complete nonsense!

I guess 5-6 in one class when asked for the sin of 30 degrees, instead of getting 0.5 gave answers in the 10's if not hundreds!!! *

You should really have some understanding of the sort of answer, not just take it as read!

Even doing the shopping, I have an idea of what the bill should be!

*
Just for the pedants I know sin can go beyond +/- 1.0 if one looks at the complex domain - but this was a simple creation of a sine wave from 360 deg in steps, and a number couldn't even use a calculator for 10, 20,30,40..360 degrees!

 

[Lucien Nunes]

I got out my pen and paper, labelled i1 and i2 and started writing i1=...

Then I thought - I feel really good. I am having a pain-free morning, I have a museum to build, so I ought to get one with that. And I started work on a different electrical puzzle: Finding a 15,000 square foot building to fill with electrical machinery. That one, unfortunately, can't be solved by superposition!

 

[plugsandsparks]

This is going to sound really old... but when those casios scientific calculators first came out with the red leds that ate batteries, my friend at school bought one ( i could not afford one) so when in class i used to race him to the answers , me doing it either in my head or on paper, him bashing away at the keys. It was in the good old days when you had to show all your working out, so there was no time penalty effect for the way i did it. I carried on like this all through secondary school and local college but when i eventually went to Uni i had to buy one as the lecturer kindly informed me i had no chance in the exams without a calculator, i was gutted, lol

 

[Julie.]

My first "proper" calculator was a texas ti-58, I bought when I started university, you could write programs on it, and insert special (eprom) cartridges, at the time I think it was the only one that could use cosh, sinh and the like.

Although I have real difficulties using modern calculators tbh.

I think my way through equations, and that doesn't suit modern calculators, which expect the user to be copying an equation from a book.

So say I want to calculate the current into a load of two parallel resistors of 10 ohm, each supplied by 5v (not withstanding we can all do that in our heads), I would do the 10 + 10 part - do 1/x then x by 10 x 10 (which would give 5 ohm) then 1/x (0.2) then multiply by 5v to get 1A.

Just not possible now, instead you have to enter the equation v/(r1 x r2/(r1 + r2)) ans.

Not how my brain works!

 

[plugsandsparks]

My old school taught maths going from Lowest digit to highest, i..e from the right to the left. My brain does not like that so i have always done it from left to right. Sometimes i do wonder if schools realise there is more than one way to add up

 

[Baddegg]

Fair enough, if we don’t have a winning answer by Friday night you can give us a detailed explanation of how you worked it out ??

Friday nights a bit tricky for me….?

 

[Vortigern]

I sometimes see slide rules in the charity shops and it reminds me of precalculator. At school we were learning slide rules and using anti/log tables which I don't think they do nowadays do they? Slide rules, I just think they are so clever. I asked my teacher what was the answer to 10 x 10 to the power of 10. Mrs. White as I recall, a flurry of the log/anti log tables and she did it! I was captivated and impressed and determined to learn the mysteries of those pages, alas fair reader, I never did.

 

[ipf]

I sometimes see slide rules in the charity shops and it reminds me of precalculator. At school we were learning slide rules and using anti/log tables which I don't think they do nowadays do they? Slide rules, I just think they are so clever. I asked my teacher what was the answer to 10 x 10 to the power of 10. Mrs. White as I recall, a flurry of the log/anti log tables and she did it! I was captivated and impressed and determined to learn the mysteries of those pages, alas fair reader, I never did.

Ten to ten, ten to ten, ten to ten ten ten.......................Lone Ranger on his abacus??

 

[pc1966]

Although I have real difficulties using modern calculators tbh.

When I replaced my old Casio with a newer one I was really disappointed to see they revered the order of entry (oh-er matron!) as I was used to the older method when you used the function key to compute the action on the current display value.