What does the slope of a semilog plot indicate?

[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 calculating 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

 

[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

 

[ShayanJ]

Ok.forget my first post's mess.
I just want to 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

 

[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.

 

[NascentOxygen]

Ok.forget my first post's mess.
I just want to 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

You could plot a few curves on your semilog paper, e.g., y=e^0.3x, y=e^0.6x and y=2e^0.3x and see how these turn out.