Convert Equation to Linear form of y=mx+c

[kmmaran]

Homework Statement

I need to substitute eq1 to eq2, and obtain a linear relationship of S = ()d + () or S = ()lnd + (). I have tried a lot of method but non of them a successful one. I hope anyone can help to obtain the equation in linear form.

Deined parameters:
C = capacitance, d = distance, ε = permittivity, A = variable , ln - natural log , a = radius, W = width, S = space

Homework Equations

Equation 1 and 2 need to provide S = ()d + () or S = ()lnd + ()

C = (pi*ε)/(ln [d/a]) ...eq 1

C = A^1/2 / ([(60*pi)/ε^1/2] * (W/S^2)) ...eq 2

The Attempt at a Solution

I have attempt to find solution using expansion series but not working and I use different method of substitution to bring this two formula to linear function but I failed.

I hope anyone can help me with this problem.

Thanks

Kmmaran

 

[MostlyHarmless]

My first thought is to set them equal to each other. I'm assuming you have tried this. What kind of road block did you hit when trying to simplify it?

 

[HallsofIvy]

Yes, set the two different formulas for C equal to each other (you will have no "C" in the equation) and then solve for S. Show us how you are trying to do that.