Physics 40 Resistivity and Resistance (16 of 32) Resistance of a Cylinder with Cut-Out

In this video I will find resistance of a cylinder with a truncated cone cut-out and varying resistivity.

[shannone]

The final expression inside the ln simplifies a lot because you can factor the first 3 terms of the denominator into (b-a + a)^2 = b^2. Then the ln just contains (a^2-R^2)/(b^2-R^2).

I made some different u-substitutions along the way to get this answer with less algebra

[dawnlightening]

Prof Michel shines with the brilliance of a master TEACHER, quite apart from his prowness in physics. I really enjoyed his lecture. But to me, his greatest achievement, was the fitting of the complete exposition into the space of one whiteboard. Well judged, Hoogleraar van Biezen!

[NotLegato]

i was close! everything was the same but the log part- that one was just ln(a^2 - b^2) for me. huh. probably made some kind of arithmetic error there.

[liezlhernaez]

I'm confused. We were looking for the resistance R but we denote radius as R as well.

[domoniquemarie]

I'm assuming we need a background in diff equations, because I'm in multivariable calc and I have no idea how to do that integral

[anubose]

is the initial resistivity equation (rho = rho(0) *(X+aL/(b-a)) a separate complication, or is that how resistivity changes in all cases of this system?

[CatsBirds]

That was a boat load of work and thanks for putting all the effort.