Question

A platinum wire has resistance of $10\Omega $ at $0^\circ C$ and $20\Omega $ at $273^\circ C$. Find the value of temperature coefficient of resistance

Answer 1

Hint: Here the coefficient is positive means its resistance is proportional to the temperature. As we know, Resistance proportional to the temperature. So, now by using direct formula
Formula Used:
$R = R'(1 + \alpha (T - T'))$
$R$ and $R'$ are the resistance
$T$ and $T'$ are the temperature
$\alpha $ is the coefficient of resistance

Complete step by step Solution:
Resistance is a measure of the opposition to current flow in an electrical circuit it is measured by ohms.
The resistance-change factor per degree Celsius of temperature change is called the temperature coefficient of resistance.
So as current should be limited in a particular circuit here we use a resistor so it can be made by different materials like carbon metal oxide etc.
So while working with the electronic circuit it's compulsory to check what is the resistance and how resistance affects the circuit.
So by applying the relation between them we get the coefficient
$R = R'(1 + \alpha (T - T')$
Here
$T' = 0^\circ C$
$T = {273^ \circ }C$
$R' = 10\Omega $
$R = 20\Omega $
By substituting the values
$ \Rightarrow 20 = 10(1 + \alpha (273 - 0)$
$ \Rightarrow \alpha = \dfrac{1}{{273}} = 0.003^\circ C$
$0.003^\circ C$ is the temperature coefficient of the resistance.

Additional information:
If a material resistance increases with an increase in temperature, the material has a Positive temperature coefficient. When resistance falls with an increase in temperature, the material has a negative temperature coefficient.

Note:
Check whether the coefficient is positive or negative. Change units of temperature to $^\circ C$ Careful while using the formula and sign. Here in question we get temperature and resistance well both in increased form.