Did I count this current in a circuit correctly?

[Duc Anh Le]

This i a test question and we are not allowed to use a calculator, so I was wondering whether I did everything correctly, since the I1 = - 1/7. I am supposed to find out I3, but stopped at I1, since the result is a bit tricky.

1. Homework Statement
R1 = 10 ohm, R2 = 20 ohm, R3 = 40 ohm
I3 = ?

Homework Equations

I3 = I2 + I1
V1 = I1 * R1 + I3 * R3
V2 = R2 * I2 + I3 * R3

The Attempt at a Solution

10 = 20I1 + 40 I2 + 40I1
20 = 20I2 + 40I1 + 40I2
-10 = 70I1
I1 = -1/7

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[gneill]

The circuit in the image is very difficult to read the component labels. Please post a closeup or draw and photograph a larger version.

3. The Attempt at a Solution
10 = 20I1 + 40 I2 + 40I1
20 = 20I2 + 40I1 + 40I2
-10 = 70I1
I1 = -1/7

From what I can tell, the first term on the RHS should be 10I1 rather than 20I1. This is likely a transcription typo since your value for the current I1 looks good to me.

 

[Duc Anh Le]

The circuit in the image is very difficult to read the component labels. Please post a closeup or draw and photograph a larger version.

From what I can tell, the first term on the RHS should be 10I1 rather than 20I1. This is likely a transcription typo since your value for the current I1 looks good to me.

Here's a better picture

 

[gneill]

It is indeed much better! Thanks.

 

[verty]

This i a test question and we are not allowed to use a calculator, so I was wondering whether I did everything correctly, since the I1 = - 1/7. I am supposed to find out I3, but stopped at I1, since the result is a bit tricky.
...

I will show that $I_1$ is negative:

$$50 I_1 + 40 I_2 = 10;\ 40 I_1 + 60 I_2 = 20 \\
5 I_1 + 4 I_2 = 1; 2 I_1 + 3 I_2 = 1\\
3 I_1 + I_2 = 0$$
Note that $I_1$ and $I_2$ have different signs and that $I_3 = -2 I_1$, so $I_3$ and $I_1$ have different signs. And since $I_2$ is clearly positive, we know all the signs and $I_1$ is indeed negative.

 

[DaveE]

You are on the right track, good work so far!
Do you know about Thevinin & Norton equivalent circuit transformations yet? I think they make problems like this much easier to do.

 

[Duc Anh Le]

You are on the right track, good work so far!
Do you know about Thevinin & Norton equivalent circuit transformations yet? I think they make problems like this much easier to do.

Alright, thanks for the verification. So far we've only been taught ohm's and kirchhoff's laws.