Find resistance of aluminum wire of length 25 cm and cross s

Find resistance of aluminum wire of length 25 cm and cross section radius 1 mm. b) Assume a perfectly stretchable resistor with resistance R, length L and cross section area A. Let\'s stretch our resistor to length 4L, what is its resistance now? c) Consider resistor from part a (aluminum wire). If initially it was at temperature 20 C (and resistance that you found in a), what is the resistance of the wire at 80C? For aluminum resistivity rho = 2.65 * 10^-8Ohmm and temperature coefficient alpha = 0.00429/K^-1.

Solution

A.

Resistance = rho*L/A

A = pi*r^2 = 3.14*(1*10^-3)^2 = 3.14*10^-6 m^2

L = 25 cm = 0.25 m

rho of aluminium = 2.65*10^-8

R = 2.65*10^-8*0.25/(3.14*10^-6)

R = 2.10*10^-3 ohm

B.

R = rho*L/A

L\' = 4L

Volume = V = A*L

V\' =A\'*L\' = A*L

A\' = V/L\' = A*L/4L

A\' = A/4

R\' = rho*L\'/A\'

R\' = rho*4L/(A/4)

R\' = 16*rho*L/A

R\' = 16*R

C.

R = R0*( 1 + alpha*(Tf - Ti))

R = 2.1*10^-3*(1 + 0.00429*(80 - 20))

R = 2.64*10^-3 ohm