Question

Asked Nov 5, 2019

1. A hollow cylinder of length L, inner radius R_{1 , }and radius R_{3 }is filled with two different materials. From R_{1 }to R_{2, }the space is filled with a material of resistivity *p*_{1 }. From R_{2 }to R_{3 }, the space is filled with material of resistivity *p _{2 }. *

*a) Derive an equation for the resistance of this structure as current flows from R _{1 }to R_{3}* (ALONG the radial direction, NOT along the length). Ignore edge effects.

b) If the total voltage across the object is V_{o}, find an expression for the current density along the objects ( i.e. find J(r)).

Take V= V_{o }at R_{1 } and V=0 at R_{3}

Step 1

(a)

Formula for the resistance is:

Step 2

Consider an elemental strip of thickness *dr* and density rho. Here the area will be the area of the surface of the thin cylinder that is 2pi*rl*.

Therefore, from definition of resistance. The expression of the resistance of the elemental strip is:

Step 3

(b)

From ohm&rsqu...

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