Simple Circuit: Find v1 and v2

[truettct]

Simple Circuit: Find "v1" and "v2"

Homework Statement

Using the circuit attached find the value of "v1" and "v2".

The values for

Is1=2.9A
R1=124 ohm
R2= 24 ohm
R3= 240 ohm
R4= 380 ohm
Is2= 3.2A.

Homework Equations

I approached this problem by putting R3 and R4 in parallel and setting the two unknown potentials as potentialm and potentialn. I put these potentials on either side of the R2 resistor.

With these two unknown potentials I was able to set up these two equations

for potentialm:

-Is1 - (potentialm / R1) + ((potentialn - potentialm) / R2)=0

for potentialn:

Is2 - (potentialn / R34) - ((potentialn-potentialm) / R2)=0

The Attempt at a Solution

Working out these equations and using algebra to solve for the potentials I get that potential m is 13.22V which is wrong, so there is no need to plug in for potential n.

Can someone help and show me where I went wrong or if I set up the equations wrong.

Thanks

 

[cepheid]

I think that your equations are right, although it was a bit of a pain to check them (why not just stick with the names v₁ and v₂)?

Here are the equations I got. For node 1, KCL says that current in = current out. The current in is the current across resistor R₂, coming into the node from the right. It is given by (v₂ - v₁)/R₂. The current coming out of the node (going to the left) is the sum of the current across R₁ and the source current I_s1. Hence, we have:

(v₂ - v₁)/R₂ = v₁/R₁ + I_s1

KCL for node 2 also says that current in = current out. The current going in (from the right) is just I_s2. The current coming out (to the left) is the sum of the currents across resistor R₂ and the parallel combination of R₃ and R₄. Hence, we have:

I_s2 = (v₂-v₁)/R₂ + v₂/(R₃ || R₄)

Perhaps you made an arithmetic error? I'll try working it out myself and get back to you.

 

[truettct]

I must be doing something wrong with my algebra, because I still cannot come up with the right answer.

 

[cepheid]

The algebra is ugly, so I may also have made a mistake. I get v1 = -10.7029296 volts. Is that right? I am assuming you have the answer since you seem to know that your result is wrong.

I started out by solving for v2 from the first equation, which gave me:

$$v_2 = v_1\left(\frac{R_2}{R_1} + 1\right) + R_2 I_{s1}$$

I then substituted that into the second equation, which gave me some pretty ugly expressions. Eventually I was able to isolate v1.

 

[cepheid]

Okay, yeah. Plugging in my answer for v1 into my equation for v2 gives me v2 = 56.8255356 volts. This handy dandy circuit program I have confirms that these are the right answers (see attached).

I have gone through all of the algebraic steps. Why don't you post your steps, and we can see where you went wrong?

 

[truettct]

Ok thanks so much for the help. I have many problems on my homework like this one and I didnt want to start the others one knowing I was getting the wrong answer. I was solving the equations wrong and I went back and got it figured out.

Thanks for the explanation.

What is the program you used to check your solutions because I would love to use a program similar to that.

Cheers

 

[cepheid]

Its called solve elec, and it is for Mac OS. I'm sure there are similar programs out there for many different platforms.