Question

A resistor is made from a hollow cylinder of length, l, inner radius a, and outer radius b. The region a<r<b is filled with material of resistivity ρ. The resistance R of the resistor is ?​

Answer 1

Answer:

the resistance ---of resistor ---

We recall that J=IAJ=IA, E=dVdrE=dVdr. The area, A will be the surface area of the cylinder. Since

JIAI2πrLdV=1ρE=1ρE=1ρdVdr=Iρ2πrLdr

J=1ρEIA=1ρEI2πrL=1ρdVdrdV=Iρ2πrLdr

Since dR=dVIdR=dVI,

dR=ρ2πrLdr

dR=ρ2πrLdr

Integrating from a to b,

R=∫abdR=∫abρ12πrLdr=ρ2πL∫ab1rdr=ρ2πLlnba

R=∫abdR=∫abρ12πrLdr=ρ2πL∫ab1rdr=ρ2πLlnba

thanks

hope it's helpful for you ....

Answer 2

Answer:

the resistance ---of resistor ---

We recall that J=IAJ=IA, E=dVdrE=dVdr. The area, A will be the surface area of the cylinder. Since

JIAI2πrLdV=1ρE=1ρE=1ρdVdr=Iρ2πrLdr

J=1ρEIA=1ρEI2πrL=1ρdVdrdV=Iρ2πrLdr

Since dR=dVIdR=dVI,

dR=ρ2πrLdr

dR=ρ2πrLdr

Integrating from a to b,

R=∫abdR=∫abρ12πrLdr=ρ2πL∫ab1rdr=ρ2πLlnba

R=∫abdR=∫abρ12πrLdr=ρ2πL∫ab1rdr=ρ2πLlnba

thanks

hope it's helpful for you ....