Temp v. Resistance...help with physics Please?

Question

A copper wire has a resistance = 0.501 ohms at 20 degrees C and has a temp coefficient of resistivity = 3.9e-3. A iron wire has resistance = 0.487 ohms at the same temp with a temp coefficient of resistivity = 5.0e-3. At what temperature do these two wires have the same resistance???? I have been using the equation R=R_ [ 1 + temp coefficient of resistivity ( T - T_)] in trying to find the temp but cannot come up with the right answer...

Answer 1

R(final) = R(initial) [ 1 + alpha (T(final) – T(initial) ], where alpha is the temperature coefficient of resistance of either copper or iron as appropriate.

The final resistance is the same for both copper and iron, so use the equation for copper and set it equal to the equation for iron at the same final temperature. It simplifies the arithmetic if you substitute deltaT = (T(final) – T(initial):

R(final) = 0.501 [1 + (3.9x10^(-3)) (deltaT)] = 0.487 [1 + (5.0x10^(-3)) (deltaT)]


deltaT = [0.501 – 0.487] / [(0.487) (5.0x10^(-3)) – (0.501) (3.9x10^(-3))]

deltaT = 29.099979 = 29.1 to three significant figures

T(final) = deltaT + T(initial) = 29.1 + 20.0 = 49.1 C

R(final) = 0.5578584 = 0.558 ohms to three significant figures.

Notice the temperature coefficient of resistance for both copper and iron is positive. Since the copper initial resistance is higher than the iron initial resistance, the temperature must increase above 20 C to raise the iron resistances to the same equal value as the copper resistance. This only works because the iron resistance is increasing faster than the copper resistance, and the initial resistance of the iron was less than the initial resistance of the copper. If the situation is reversed, so the initial iron resistance is greater than the copper resistance, the wires would have to be cooled until they are the same resistance.

Answer 2

Ó¨ = (0.501- 0.487) / {0.501 * 3.9 - 0.487*5} x 10^ (-3)
Ó¨ = - (0.014)10^ 3/ 0.4811
Ó¨ = - 29. 09 C.
Ó¨ = T - 20 = - 29.1

T = -49.1C.

The resistance of copper at - -49.1C is

0.501 + 0.501*3.9 x 10^ (-3)* (- 29.1) = 0.444 ohm.

The resistance of iron at - -49.1C is

0.487 + 0.487 *5 x10^ (-3)* (- 29.1) = 0.416 ohm.