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 ?