coefficien Copper has from em 1: The radius of a 22-gauge Nichrome wire is 0.32

Question

coefficien Copper has from em 1: The radius of a 22-gauge Nichrome wire is 0.32 mm Its resistivity is 1.0 x 10 Om and its temperature t is 04x /0-C". (a) Show the resistance per unit length of this wire is 3.11 Dr. (b) If a potential ce of ro v is maintained across a 1.0-m length of the Nichrome wire, calculate the current in the wire. (e) a resistivity of 1.7x10Mr(two orders of magnitude smaller than that for Nichrome) and a temperature coefficient a is 3.9x 10 C-, calculate the resistance per unit length of the copper wire with the same gauge as the ichrome wire. (d) If it was suggested that copper wire should be used in a climate where the temperature changes 20Cto-45" C, which of the two wires should be recommended to your boss in this extreme climate? Back up your answer with calculation(s).

Explanation / Answer

Given,

r = 0.32 mm ; rho = 1 x 10^-6 Ohm-m ; alpha = 0.4 x 10^-3 per deg C ;

a)We know that, resistance per unit length is given by:

R/L = rho/A

R/L = 1 x 10^-6/[3.14 x (0.32 x 10^-3)^2] = 3.11 Ohm/m

Hence, R = 3.11 Ohm/m (Proved)

b)R/L = 3.11 Ohm/m

R = 1 m x 3.11 Ohm/m = 3.11 Ohm

V = 10 V ; from Ohm's law, V = IR => I = V/R

I = 10/3.11 = 3.22 A

Hence, I = 3.22 A

c)for copper, rho = 1.7 x 10^-8 ; same area

R/L = rho/A = 1.7 x 10^-8/[3.14 x (0.32 x 10^-3)^2] = 0.053 Ohm/m

Hence, R/L = 0.053 Ohm/m

d)T1 = 20 deg C ; T2 = -45 deg C

We know that the resistance is related to temp as:

R = R0 (1 + alpha (T2 - T1))

for nichrome, R0 = 3.11 ; alpha = 0.4 x 10^-3 ;

R = 3.11 [1 + 0.4 x 10^-3 (-45 - 20)] = 3.03 Ohm

for copper, Resistance for 1 m = 0.053

R = 0.053 [ 1 + 3.9 x 10^-3 (-45 - 20)] = 0.039 Ohm

As we see that the resistance of Copper is very low for the temp given so we will suggest Copper wire.

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