(a) A 34.9-m length of copper wire at 20.0°C has a radius of 0.23 mm. If a poten

Question

(a) A 34.9-m length of copper wire at 20.0°C has a radius of 0.23 mm. If a potential difference of 7.0 V is applied across the length of the wire, determine the current in the wire. (Use the values in this table.)
__________ A

(b) If the wire is heated to 40.0°C while the 7.0-V potential difference is maintained, what is the resulting current in the wire?
___________ A

This is the table

Resistivities and Temperature Coefficients of Resistivity for Various Materials (at 20°C) Temperature Coefficient of Resistivity Resistivitv Material rm 1.59 x 10-8 1.7 X 10-8 2.44× 10-8 2.82 x 10-8 5.6 X 10-8 10.0 X 10-8 11 × 10-8 22 x 10-8 150× 10-8 3.5 X 10-5 0.46 640 1010-1014 1013 1015 75 X 1016 3.8 10-3 3.9 x 10-9 3.4× 10-3 3.9 x 10-9 4.5 X 10-3 5.0 X 10-3 3.92 X 10-3 3.9 X 10-3 0.4 x 10-3 0.5 × 10-3 48 X 10-3 75 × 10-3 Silver Copper Gold Aluminum Tungstern ron Platinum Lead Nichromea Carbon Germanium Silicon Glass Hard rubber Sulfur Quartz (fused) A nickel-chromium alloy commonly used in heating elements.

Explanation / Answer

here,

a)

length of wire , l = 34.9 m

radius , r = 0.23 mm = 2.3 * 10^-4 m

resistivity , p = 1.7 * 10^-8 ohm.m

the resistance , R0 = p * l /area

R0 = 1.7 * 10^-8 * 34.9 /( pi * (2.3 * 10^-4)^2) ohm

R0 = 3.57 ohm

current , I0 = V/I = 7/3.57 A = 1.96 A

b)

temprature coefficient , alpha = 3.9 * 10^-3 C^-1

the resistance , R = R0 * ( 1 + alpha * ( 40 - 20))

R = 3.57 * ( 1 + 0.0039 * ( 40 - 20)) ohm

R = 3.85 ohm

the resulting current in the wire , I' = V /R

I' = 7/3.85 A = 1.82 A

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