The resistivity and temperature coefficient of resistance of Evanohm are 800 CM-Ω/ft and
20 x 10-6 /C, respectively, at 20C. A #40 round wire has a diameter of 0.00314 in. Find the resistance of a 14.79 in long sample of a #40 round Evanohm wire at (a) 20C, and
(b) 520C.
Q170588
The resistivity and temperature coefficient of resistance of Evanohm are 800 CM-Ω/ft and
20 x 10-6 /C, respectively, at 20C. A #40 round wire has a diameter of 0.00314 in. Find the resistance of a 14.79 in long sample of a #40 round Evanohm wire at
(a) 20 0C, and
(b) 52 0C.
Solution:
We are given resistivity, ρ = 800 CM-Ω/ft.
Convert this to Ω.m by using the conversion factor, 1 Ω.m = 60153.49.3 circular mil Ω/ft.
resisitivity in Ω.m =
Temperature coefficient of resistance, α = 20 * 10-6 / 0C.
Answer a:
To find the resistance of the 14.79-inch long sample of a # 40 Evanohm wire at 20 0C.
Resistance R is related to the length and cross-sectional area of the wire by the relation:
Length of the wire, L
diameter of wire = 0.00314 inch
radius of wire, r = 0.00314 inch/2 = 0.00157 inch.
radius of wire in meter, r
cross sectional Area, A
plug A= 5.00 * 10 -9 m2,
resisitivity, ρ 1.33 * 10^{-6} Ω.m
and lenght, L = 0.376 meter in the formula, we have
Answer b :
To find the resistance of the 14.79-inch long sample of a # 40 Evanohm wire at 520 0C.
We will use the formula
R = R ref [ 1 + α (T-Tref )]
resistance at 20 0C will be R ref.
T ref = 20 0C.
T = 520 0C.
Temperature coefficient of resistance, α = 20 * 10-6 / 0C.
R = 100.00 Ω [ 1 + 20 * 10-6 / 0C. (520 0C - 20 0C )]
= 100.00 Ω [ 1 + 20 * 10-6 / 0C. * 500 0C ]
= 100.00 Ω [ 1 + 0.01]
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