physicss helpp?

Question

The copper wire used in a house has a cross-sectional area of 2.90 mm2. If 10.5 m of this wire is used to wire a circuit in the house at 20.0°C, find the resistance of the wire at the following temperatures.
(a) 30.0°C

(b) 10.0°C

Answer 1

Resistance is temperature dependent.
For copper we have
resistivity to be copper r = 1.68 e -8 ohms per meter (at 20 deg C)

Temperature coefficient a = .0068 per degree C

Conductivity of copper Cr = 5.95 e+7 per ohms meter


R=rL/A
R - resistance
r - resistivity
L length of wire
A - area of wire


r(T) = r(Tr) x [ 1 + a(T - Tr) ]
Tr = reference temperature (deg Celsius)
T = temperature in question (deg Celsius)
r(Tr) = resistivity at reference temperature (ohm-meters)
r(T) = resistivity at temperature of interest (ohm-meters)
a = temperature coefficient of resistivity (1/deg Celsius)

Now we have all we need

R(T)=r(T)L/A

R(T)=[r(20) x[ 1 + a(T - 20) ] ]L/A

R(30)=[r(20) x[ 1 + a(30 - 20) ] ]L/A
R(30)=[1.68 e -8 x [ 1 + .0068x(30 - 20) ] ]10.5/(2.90 e - 6)
R(30)=0.0608 ohms

R(10)=[r(20) x[ 1 + a(10 - 20) ] ]L/A do the math..

I hope it helped