Ha,ha.. the typo in the integrand is mine, not from Serway.
And of course, the resistors are in serial (not in parallel). That's what I said...
Instead of this, if we try to do the integration considering parallel strips from face A to face B, it is not possible to do the integration because...
I think when the current is not constant over a differential resistor it is not possible to apply that R = ρ L/S for each resistor.
I mean, when we consider the half ring is made like an ensemble of parallel strips of length πr then the current into one strip is constant (although different to...
Hello Dave:
These are the links in PF related with this problem:
https://www.physicsforums.com/threads/resistance-of-a-semicircular-conductor-with-a-rectangular-cross-section.934323/
https://www.physicsforums.com/threads/the-resistance-of-an-element-shaped-like-a-half-cylinder.996616/
In none...
Thank you for your response.
I don't know if it is reasonable or not, but I'm sure that the result to this problem is :
R = ρπ/[t·ln(b/a)]
And the result obtained considering one ensemble of parallel resistors MUST BE the same when considering one ensemble of serial resistors. That's the question.
Lets suppose a half ring whit internal radius a and external radius b and height t. We can calculate the resistance of the half ring considering that it is made of a number of parallel resistors each one with resistance given by: R = ρ L/S where L = π·r and S = t·dr. The resistance of each...