# Solution of 2 Equations with 3 Variables

1. Jan 24, 2008

### m_niz

Hello there,

I have got the following equations, plz see the attached file.

Have to find Es, Einf and T. others are known. How to do that? Thanks.

#### Attached Files:

• ###### New Microsoft Word Document.doc
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Last edited: Jan 24, 2008
2. Jan 24, 2008

### HallsofIvy

Staff Emeritus
You should understand that most people will not open WORD files for fear of viruses. Since I have very strong virus protection, I took the chance. Of course, it took a while to load since it had to go through all the virus tests.

In any case, I am now embarassed that I did since I should have seen, from the title "New Microsoft Word Document" that the document is blank!

3. Jan 24, 2008

### Defennder

Yeah Halls is right, it's completely blank.

4. Jan 24, 2008

### m_niz

Very Sorry, I have loaded the correct file now! actually its a bit tricky to write these equations so I just attached the file. Thanks

5. Jan 24, 2008

### HallsofIvy

Staff Emeritus
The two equations, then, are
$$\epsilon'= \epsilon_\infty+ \frac{\epsilon_s- \epsilon_\infty}{1+ (\omega \tau)^2}$$
and
$$\epsilon"= \frac{(\epsilon_s- \epsilon_\infty)\omega\tau}{1+ (\omega \tau)^2}$$}

Of course, since there are only two equations in 3 unknown values, you cannot solve for all three. What you could do is solve for two of them in terms of the third.

You might, for example, multiply the first equation by $\omega\tau$, so that the two fractions are the same, and then subtract one equation from the other, eliminating the fractions:
$$\epsilon'- \epsilon"= \epsilon_\infty (\omega\tau)$$
Then
$$\epsilon_\infty= \frac{\epsilon'-\epsilon"}{\omega\tau}$$
so you have solved for $\epsilon_\infty$ in terms of $\tau$.

Replace $\epsilon_\infty$ by that in either of the two equations, and you can then also solve for $\epsilon_\infty$ in terms of $\tau$.

6. Jan 24, 2008

### m_niz

Thanks Hall! Can you write me a detailed solution. I am not very good in maths.