# Simple Circuit: Find v1 and v2

• Engineering
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

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cepheid
Staff Emeritus
Gold Member

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 Is1. Hence, we have:

(v2 - v1)/R2 = v1/R1 + Is1

KCL for node 2 also says that current in = current out. The current going in (from the right) is just Is2. 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:

Is2 = (v2-v1)/R2 + v2/(R3 || R4)

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

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

cepheid
Staff Emeritus
Gold Member

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
Staff Emeritus
Gold Member

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?

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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
Staff Emeritus