Answer to Question #147410 in Algebra for Rafay

Question

The electrical resistance R ohm for a pure metal wire is related to its temperature T (in c^0) by the formula R=R_o (1+aT) for positive constant a and R_o.

For what temperature is R=R_o.

Assuming that the resistance is 0 if T=-270 C^o, find a.

Silver wire has a resistance of 1.25 ohms at 0c^o. At what temperature is the resistance 2 ohms?

Answer 1

Consider the function for resistance

$R = R_0(1 + αT)$ ohm

Temperature when $R = R_0$

$R_0 = R_0(1 + αT)$

0= 1 + αT

$T = \frac{-1}{α}$

When R = 0 and T = -273 ºC:

$R_0(1 + α(-273)) = 0$

1 + α(-273) = 0

$α = \frac{-1}{-273} = \frac{1}{273}$

When R = 0 and T = -273 ºC, the constant $α = \frac{1}{273}$

Now when R = 1.25 and T = 0 ºC:

$R_0(1 + α(0)) = 1.25$

$R_0(1 + 0) = 1.25$

$R_0 = 1.25$

Now if R = 2, we get:

(1.25)(1 + αT)) = 2

$(1 + \frac{1}{273}T) = 1.6$

$T = 0.6 \times 273 = 163.8\;ºC$

When R = 2 the temperature is T = 163.8 ºC