A simple resistor can be modeled of a cylinder of metal. Your resistor has initi

Question

A simple resistor can be modeled of a cylinder of metal. Your resistor has initial length 0 and radius 0, and has a resistance of 1.0 . Unfortunately, you need a resistor with a resistance of 16.0 . You decide to carefully melt down and reshape your resistor into a cylinder with a new length and radius and radius to obtain the resistance you need. What is the new length and radius of your wire? Give your answer in terms of the original length 0 and radius 0 (i.e. “final length is =20”). Hint: the amount of material in your resistor, i.e. the volume, will not change when you melt it.

equation to use is R=PL/A

R= resistance

P=density

L=lenght

A= area of resitor pie r ^2

Explanation / Answer

Ro = rho*Lo/Ao = 1 ohms

R = rho*L/A = 16 ohms

so, R = 16*Ro

rho*L/A = 16*rho*Lo/Ao

L/A = 16*Lo/Ao ---(1)

here volume is constant, Ao*Lo = A*L

A = Ao*Lo/L   --(2)

from equations 1 and 2

L/(Ao*Lo/L) = 16*Lo/Ao

L^2 = 16*Lo

L = 4*Lo <<<<<<------Answer

===> A = Ao/4

===> pi*r^2 = pi*ro^2/4

r^2 = ro^2/4

r = ro/2 <<<<<<------Answer

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