# Question dfffa

Jan 19, 2018

The temperature coefficient of resistance is $5.7$x${10}^{- 3}$$/$${.}^{\circ} \text{C}$.

#### Explanation:

The coefficient of resistance is given by the equation below:

$\Rightarrow$$R \left(T\right) = {R}_{o} \left[1 + \alpha \left(T - {T}_{o}\right)\right]$
where $R$ is the resistance at temperature $T$ and ${R}_{o}$ is the resistance at temperature ${T}_{o}$. Also $' \alpha '$ is the coefficient of resistivity.

From above equation we can write
$\Rightarrow$$\alpha = \left[\left(\frac{R}{R} _ o\right) - 1\right] \times \left[\frac{1}{T - {T}_{o}}\right]$
Considering the values as $R = 5 \Omega , T = {50}^{\circ} \text{C}$ and ${R}_{o} = 7 \Omega , {T}_{o} = {100}^{\circ} \text{C}$, and substituting them we get,
$\Rightarrow$$\alpha = \left[\frac{5 \Omega}{7 \Omega} - 1\right] \times \left[\frac{1}{{50}^{\circ} \text{C"-100^@"C}}\right]$
$= \left(0.71428571 - 1\right) \times \left(\frac{1}{- {50}^{\circ} \text{C}}\right)$
=(-0.2857143)xx(1/(-50^@"C"))=0.005714286/(1^@"C")#
Therefore the coefficient of resistance is $\approx \left(5.7 \times {10}^{- 3}\right) / {.}^{\circ} \text{C}$.