# Homework Help: Finding the absolute error for equation of total resistance

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1. May 29, 2017

1. The problem statement, all variables and given/known data
Prove the equation for ΔRC. (See the first attachment with the circuit schematic inside)

2. Relevant equations
(The equation for RC, in both attachments)

3. The attempt at a solution
You can see my attempt at a solution in the second attachment. I'm stuck at the step shown in the picture. Maybe that needs a bit algebra, or my attempt was incorrect.

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2. May 29, 2017

### BvU

I already have difficulty with the first step: If $R_C = R_{//} + R_3$ then it certainly is not so that $\log R_C = \log R_{//} + \log R_3$ !
And then the $\Rightarrow$ is also unjustified.

I suggest you try to find $\Delta R_{//}$ on its own...

3. May 29, 2017

### Staff: Mentor

ln(a+b) and ln(a) + ln(b) are not the same (first -> second line and also within the second line) and the result is wrong.

4. May 30, 2017

Thanks a lot, dear BvU! I tried your suggestion and it worked!
Yes, I had a big mistake in my first attempt as you mentioned.

What do you mean by this:
Is that because of my mistake in taking logarithms or it's generally not considered right to use in these equations?

5. May 30, 2017

### BvU

Transition from first line in attachment to second line was in error.
The transition from before the $\Rightarrow$ to after was also in error, hence my remark.
$$\ln{R_1 R_2\over R_1+R_2} =\ln R_1+\ln R_2-\ln(R_1+R_2)$$