Question

A cylindrical resistor with radius K and length L is made from a material with conductivity ?. The potential difference between the circular ends is V.

What is the current that flows from one end to the other?

What is the resistance?

Show that the resistance you found is R = ?L/A, where ? is the resistivity of the material, and A is the cross-sectional area of the cylinder.

(Hint: The electric field is constant throughout the resistor, but its value is not given.)

Answer 1

a]

Use Ohm's law microscopic regime.

Then, the current density is related to electric field as:

multiplying by cross sectional area on both sides gives:

=>

where k is the radius of the wire.

this is the current which flows from one end to the other.

b]

multiply by the length of the wire on both sides

but we know that electric field is negative gradient of potential.

so, |V| = EL

this gives,

=>

but from Ohm's law, we know that V = IR

so, R = V/I

substituting this above gives:

[since conductivity is reciprocal of resitivity].