# Slope of a semilog plot

1. Dec 19, 2011

### ShayanJ

We had an experiment of charging and dicharging a capacitor in a RC circuit.Our instructor asked us to plot our data in a semilogarithmic paper.Then told us the formula of calculting the slope of such a curve.It was:
$\frac {[the vertical distance between two points measured by a ruler]*2.3}{the distance of two successive ones]*[the difference of the two ponit's independent variables]}$
then asked us two prove that what is this slope I did the following:
$\frac{log \frac{i_{2}}{i_{1}} *ln{10}}{\Delta t}=\frac{ln{i_{2}}ln{i_{1}}}{\Delta t}$
And we have $ln{i} = ln{\frac{\Epsilon}{R}}-\frac{t}{RC}$
So we get that the slope is -1/RC.
But the instructor says this proof is incomplete.What's the problem?Can you tell what quantity does this slope idicate?
thanks

2. Dec 19, 2011

### Simon Bridge

Could it be the bit where you measure with a ruler?
Why is the delta-y of the slope 2.3 times the ruler distance?

Other than that you seem to have related the slope of ln(i) vs t properly.
Unless he wants you to explicitly find the derivative?

Tips:
you can write text inside the tex box by using \text{}
you can write the natural logarithm as \ln(i_1) etc.
The upper-case epsilon in just E

3. Dec 19, 2011

### ShayanJ

Ok.forget my first post's mess.
I just wanna know if I find the slope of the straight line in a semilog paper,what quantity does it mean.For example if I plot the formula
$y=a e^{b x}$
On a semilog paper and get a straight line,what will be the slope of that line?
thanks

Last edited: Dec 19, 2011
4. Dec 19, 2011

### Simon Bridge

When you plot $y=ae^{bx}$ on semi-log paper, the values on the vertical axis are not $\ln(y)$ are they?

You are actually plotting values of y, and adjusting the spacing to account for the logarithm.

The slope of ln(y) vs x will be b... which you know.

You have not been told you are wrong exactly, but that your explanation is incomplete. - what you are missing is the relationship between the semi-log paper and this equation. (That and maybe making the relationship between the derivative and the analytic equation for a line explicit.)

Remember: this is an exercise you have been set: I am not supposed to do it for you. Ergo: I cannot just give you the answer. I have to try to guide you to the answer, from the information you give me. If you want to know exactly what your instructor means, you'll have to ask him.

5. Dec 19, 2011

### Staff: Mentor

You could plot a few curves on your semilog paper, e.g., y=e0.3x, y=e0.6x and y=2e0.3x and see how these turn out.