Solve Superposition Theorem for R1, R2 Circuit

[leejohnson222]

Homework Statement

find current and voltage at r1, r2

Relevant Equations

KCL

i have this question and i just want to make sure i am on the right track as i know there are quite a few steps to this to get to the final soultions

i need to find Current at r1
voltage at r1
current at r2
voltage at r2

i have so far split this into 2 drawings so i am dealing with one power source at a time,
taking r1 and r2 as parallel i found 1/RT to be 2 ohms
so current being 30/2 = 15amps
voltage at r1 current x resistance = 15 x 3 = 45v
i understant now to get the complete answer i would need to do the same with the other power source and combine the figures
Is this correct or have i missed a step out ?

 

[scottdave]

Revisit how you arrive at R1 and R2 becoming parallel, when zeroing out one of the sources. Are you able to show your other drawings?

 

[DaveE]

Yes, please show us what you mean with some schematics.

Superposition doesn't work if you change the passive parts of the network. i.e. you can't add, move, remove, or change the value of the resistors. Where it does work is with setting all sources (voltage or current sources) to zero and solving the same network, with all sources still present but mostly having zero value. Then if you solve for each source value independently, you can add up the separate results to get the correct solution when all of the sources are active.

https://www.khanacademy.org/science...pic/ee-dc-circuit-analysis/a/ee-superposition

 

[leejohnson222]

yes this what i was going to do, work out both sides of this with different power sources
i havent drawn any thing i was going to make of results for each side

 

[DaveE]

yes this what i was going to do, work out both sides of this with different power sources
i havent drawn any thing i was going to make of results for each side

You should be able to have one schematic, since the network doesn't change. Just assign variables to each source value. Then sometimes those variables are zero in the analysis, sometimes they are non-zero.

 

[scottdave]

Note that you need to calculate the currents through resistor 3 to solve this, even though the question does not ask for it. It appeared that you were ignoring R3 in your initial post.

Also remember that the direction of each current is important. For example (I made up these numbers) if R1 has 10 amps "up" in one calculation, then 12 amps "down" in the other calculation, the superposition of these is 2 amps down.

 

[Babadag]

Millman theorem it is easier, I think

 

[DaveE]

Millman theorem it is easier, I think

Yes. But the question was about Superposition, I think.

I would have used Norton/Thevenin source transformations myself. Millman's theorem never excited me. There are several approaches to choose from.

 

[leejohnson222]

I wouldnt ignore R3 as when you short circuit the E2 R3 would be in series while R1, R2 are in
but when you short circuit E1, im not 100% sure i think 2 loops are created one going left and one going right, from positive to negative returning to the power source

to avoid making it too confusing i could draw 2 scematics to show each power source being used with values, then combine the two results, that is what i have read about the way to do this so far

 

[Babadag]

You have to put E1=0 and short the source and then calculate the currents as if you only had one source. Do the same with E2. And finally, sum the currents on each branch.

 

[scottdave]

You have to put E1=0 and short the source and then calculate the currents as if you only had one source. Do the same with E2. And finally, sum the currents on each branch.

And when you "sum" the currents, the directions of the currents are important.

 

[leejohnson222]

yes i understand that directions need to be taken into account at the end so you get the correct voltage depending on direction of each power source.

so far i have this for 45v source
r1//r1 = 2ohms
r3 = 3 oms
Current Total is 45v/5 = 9amps
then i need to find each current through each resistor

 

[DaveE]

yes i understand that directions need to be taken into account at the end so you get the correct voltage depending on direction of each power source.

so far i have this for 45v source
r1//r1 = 2ohms
r3 = 3 oms
Current Total is 45v/5 = 9amps
then i need to find each current through each resistor

Yes (except for the typo r1||r1...). Next you want to solve for the node voltages for this case.

 

[leejohnson222]

great sorry about typo, one question, when i am lookin at the 2nd voltage are all resistors all in series? since voltage will flow in 2 directions would any resistors be in parallel?
if i label the top node as node a voltage i have is 18v ? not sure i have this correct

 

[LvW]

Voltage does not "flow".
When E1 is shorted (0 volts) and only E2 is present, you only have to verify how (which way) the current - driven by E2 - will go. Through all the resistors - one after another? Or does it take different ways in parallel?

 

[leejohnson222]

sorry i mean current flow, when E2 is active and E1 is shorted out i looks to me like current will flow left and right, creating 2 loops, but if that is true then would R1 and R3 always be in parallel with R2 on each loop?

 

[scottdave]

When E1 is shorted, you can say that R1 is parallel to R3, since it shares a node at both top and bottom. When E1 is active, then R1 only shares 1 node with R2 or R3 so it is not parallel.

I hope that explanation makes sense.

Similar when talking about R2, when you short E2.

 

[DaveE]

if i label the top node as node a voltage i have is 18v ? not sure i have this correct

Yes. You have 9A flowing through R1, a 3Ω resistor, which will make a voltage drop of 9A⋅3Ω = 27V. You can subtract this from the E1 voltage drop, 45V (Note the polarities are really important!) to get a total drop across the E1-R1 branch of 18V.

The alternate way is to see that the 9A also flows through R2||R3, which is 2Ω. So that will make an 18V drop across those two resistors.

This is all with E2 set to 0V, of course.

 

[leejohnson222]

thank you so much, this makes quite a bit of sense now and i was able to get closer to my answers and follow why i was doin it also, thanks again