How to calculate time constant tau for RL and RC circuits from their graph?

[6021023]

I made graphs of simple RC and RL circuits. We were told to mark off at 10% of the rise and 10% away from the max. This gives a delta. We were then supposed to use this information form the graph to calculate tau, and compare it with the theoretical value. I know how to calculate the theoretical value, for RC it's just tau = RC and for RL it's just tau = L/R. But then how do you calculate it from the graph?

 

[kuruman]

Did you make a plot with linear axes or a semi-log plot?

 

[6021023]

I guess I used linear axes, I don't know what that other thing is.

 

[kuruman]

Ok, so you have two separate times that you can read off the graph, t₁ when you get 0.1 (or 10%) of max and t₂ when you get 0.9 (or 90% of max). This gives two equations

0.1 = e^-t₁/τ
0.9 = e^-t₂/τ

What do you get if you divide the top equation by the bottom?