Question

(a) A 34.7-m length of copper wire at 20.0°C has a radius of 0.29 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 the following table.)

Resistivities and Temperature Coefficients of Resistivity for Various Materials (at 20°C)

Material	Resistivity (Ω · m)	Temperature Coefficient of Resistivity [(°C)−1]
Silver	1.59 ✕ 10−8	3.8 ✕ 10−3
Copper	1.7 ✕ 10−8	3.9 ✕ 10−3
Gold	2.44 ✕ 10−8	3.4 ✕ 10−3
Aluminum	2.82 ✕ 10−8	3.9 ✕ 10−3
Tungsten	5.6 ✕ 10−8	4.5 ✕ 10−3
Iron	10.0 ✕ 10−8	5.0 ✕ 10−3
Platinum	11 ✕ 10−8	3.92 ✕ 10−3
Lead	22 ✕ 10−8	3.9 ✕ 10−3
Nichromea	150 ✕ 10−8	0.4 ✕ 10−3
Carbon	3.5 ✕ 10−5	−0.5 ✕ 10−3
Germanium	0.46	−48 ✕ 10−3
Silicon	640	−75 ✕ 10−3
Glass	1010–1014
Hard rubber	≈1013
Sulfur	1015
Quartz (fused)	75 ✕ 1016

^aA nickel–chromium alloy commonly used in heating elements.

(b) If the wire is heated to 38.0°C while the 7.0-V potential difference is maintained, what is the resulting current in the wire?

Answer 1

here,

a)

the length of wire , l = 34.7 m

radius , r = 0.29 mm = 2.9 * 10^-4 m

resistivity of copper at 20 degree C , p = 1.7 * 10^-8 ohm.m

the resistance , R = p * l /area

R = p * l/(pi * r^2)

R = 1.7 * 10^-8 * 34.7 /(pi *(2.9 * 10^-4)^2) = 2.23 ohm

V = 7 V

the current in the wire , I = V /R

I = 7/2.23 A = 3.13 A

b)

when the temperature , T2 = 38 degree C

the new reistance , Rb = R * ( 1 + alpha * (T - 20))

Rb = 2.23 * ( 1 + 3.9 * 10^-3 * (38 - 20)) = 2.3865 ohm

the new current , Ib = V /Rb = 2.93 A