Question

1) Two wires are identical, except that one is aluminum and one is silver. The aluminum wire has a resistance of 0.17 Ω. What is the resistance of the silver wire?

2) A coil of wire has a resistance of 38.0 Ω at 25° C and 43.7 Ω at 51° C. What is the temperature coefficient of resistivity?

Answer 1

Given,

Ra = 0.17 Ohm

We know that

R = rho L/A

the lenfth and Area for the wire are assumed to be the same but the resistivity is the property of the material of the wire and for Al and Ag it has the value of:

rho(Al) = 2.65 x 10^-8 ; rho(Ag) = 1.59 x 10^-8

rho(Al) l/A = 0.17

rho(Ag) l/A = Rs

Rs/0.17 = rho(Ag)/rho(Al)

Rs = 1.59/2.65 x 0.17 = 0.102 Ohm

Hence, Rs = 0.102 Ohm

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2)R1 = 38 Ohm ; T1 = 25 deg

R2 = 43.7 Ohm ; T2 = 51 deg

We know that

R = R0 (1 + alpha delta T)

delta T = 51 - 25 = 26

43.7 = 38 (1 + alpha x 26)

1 + alpha x 26 = 1.15 - 1 = 0.15

alpha = 0.15/26 = 5.77 x 10^-3 per deg C

alpha = 5.77 x 10^-3 per deg C