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.

 

[Baddegg]

Anyone else fancy a stab before I jump in?……?

 

[Phil L]

Anyone else fancy a stab before I jump in?……?

No, over too you @Baddegg

 

[Baddegg]

No, over too you @Baddegg

Let’s give em a sporting chance Phil…..

 

[Phil L]

Let’s give em a sporting chance Phil…..

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 ??

 

[Dave OCD]

Erm, nah I'll only get it wrong. ?

 

[stevethesparks]

1= 0.102W
2= Both
added characters to allow posting

 

[Vortigern]

So we don't use Kirchoffs voltage law here just straightforward Ohms law then, what say you @Baddegg ? So split it into two then and getting a bit lost now come back to it in the morning when I'm a bit brighter. Might have to confer with @Badegg on this one a little though. I am a bit worried about the loops as E2 is in the middle which throws me a little but at least the current is going in the same direction and mesh at R2. Yeh let me thing about this one. Hang on we don't use Kirchoffs in the Branch current method. EDIT
I must say though, this should be in the Arms. It could cause a scandal when the general public realise the paucity of knowledge in the less educated among us running amok in peoples houses.?

 

[buzzlightyear]

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

10,600.

 

[Julie.]

Well this was something to wake up to...

Thought I would take a look whilst my coffee cools, I thought doing it by superposition would be quickest, which gives E1 as source, E2 as sink, and 4.8mW

But as it doesn't line up with previous answers, nor comes out with a nice round number as these things usually do, so I did it via Maxwell (kirchoffs ) which gives two unknowns from two equations, so just the mechanics of solving, however my coffee got to the right temperature, so just solved via wolfram!

Gives the same current, so I think it's right, unless I have made some stupid mistake - it being before the morning coffee to wake me up.

Scruffy calculations attached:

 

[Julie.]

Slurp now taken...

Plus some words - why?

 

[buzzlightyear]

Plus some words - why?

Not had your weetrbix yet then.

 

[Julie.]

Not had your weetrbix yet then.

Still in bed savoring what's left of my coffee!

Arguing with myself as to how long I can stay in bed without being late!

 

[marconi]

By Thevenin’s theorem or Tellegen’ theorem anyone?

 

[Julie.]

By Thevenin’s theorem or Tellegen’ theorem anyone?

Not a problem, but I would think a poor choice, if the question was to calculate the power/current/voltage of the load resistances Thevenin or Norton equivalents would be the first choice (Probably Millman would be best), Tellegen's wouldn't be my choice either - unless it was more complicated and I was using software - it's good for relatively short transmission network calculations.

My order of preference would be
Superposition
Maxwell (mesh )
Millman/Norton/Thelvenin

The ideal current methods I would use the 1800 & 2200 ohm resistances as internal resistances of the voltage sources as it's obviously not possible to get an ideal current source equivalent for an ideal voltage source.

And of course Millman uses Norton to start with.

Ahh well, back to the boring stuff, today is a work day ?

 

[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!