Resistance of a hollow aluminum cylinder

AI Thread Summary
The discussion centers on calculating the resistance of a hollow aluminum cylinder with specified dimensions. The resistance is determined using the formula R=(ρ/2πL)ln(R/r), where R is the outer radius, r is the inner radius, and L is the length of the cylinder. There is confusion regarding whether the current flows radially through the cylinder and how the ohmmeter connects to the surfaces. The assumption is that the connection is equipotential across the surfaces, which influences the resistance calculation. Clarification on the approach and detailed calculations is needed for accurate results.
digitaleyes
Messages
2
Reaction score
0

Homework Statement



A hollow aluminum cylinder is 2.50m long and has an inner radius of 3.20 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface.

At room temperature, what will an ohmmeter read if it is connected between the inner and outer surfaces?

Homework Equations



R=4.60cm
r=3.20cm

R=\rhoL/A

and possibly

R=(\rho/2piL)*ln(R/r)

The Attempt at a Solution



Well, the first part of the question (not asked here) was to find the resistance from one end of the hollow cylinder to the other (the faces). I found that: 2.00*10-5 \Omegas. The problem does not say that the current is flowing radially through the cylinder though, but is that to be assumed for doing this second part? Or not? I plugged everything into the second equation, but the answer is wrong. Should the resistance be the same as it is from end to end? Is it 0?
*confused*
 
Physics news on Phys.org
It is a curious question. Connected exactly how to the two surfaces? Connection at infinitely small points will lead to infinite resistance, so it seems we must assume the contact is spread, equipotentially, across each entire cylindrical surface.

That should mean your second equation is appropriate. See e.g. https://www.miniphysics.com/uy1-resistance-of-a-cylindrical-resistor.html.
Can't say any more without seeing your working and/or answer.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top