Question

A platinum wire has a resistance of \[2.62\Omega \] at \[15{}^\circ C\] and \[3.29\Omega \] at \[80{}^\circ C\]. Find the temperature coefficient of the resistance platinum wire.
A. $4.18\times {{10}^{(-3)}}{}^\circ {{C}^{-1}}$
B. $9.34\times {{10}^{(-3)}}{}^\circ {{C}^{-1}}$
C. $1.934\times {{10}^{(-3)}}{}^\circ {{C}^{-1}}$
D. $934\times {{10}^{(-3)}}{}^\circ {{C}^{-1}}$

Answer 1

Hint:Resistance is the ability of a material to resist the amount of electric current flowing through the circuit. Temperature and resistance for a metal are directly proportional to each other and if the temperatures of the material increases, then the resistance of the metal object will also increase in a linear way.

Complete step by step answer:
According to Ohm's law, “Under a definite physical condition, the current flowing through the conductor is directly proportional to the applied potential difference at its ends. Thus,
 \[
I\propto V \\
\Rightarrow V=IR \\
\]
And here, R is the proportionality constant, which is called the resistance of the conductor. Resistance of a conductor is the ability of a conductor to resist the flow of electrons in the conductor, which is how much it stops current to get flowing in the conductor.

Now, when the temperature of the wire rises, then the resistance of the wire is also increased, hence they have a directly proportional relationship with each other. The change in resistance with respect to temperature is given as below:
\[\Delta R=R\alpha \Delta (T)\]
Here,\[\Delta R\] is the change in resistance, R is the resistance of the platinum wire,\[\alpha\] is the temperature coefficient and\[\Delta T\] is the change in temperature. Here, in our case,
\[\Delta T=353-288=65K\]
\[\Delta R=3.29-2.62\Omega =0.67\Omega \]
Thus, the temperature coefficient is given by
\[\alpha =\dfrac{0.67}{65\centerdot 2.62}\\
\therefore\alpha =4.18\times {{10}^{(-3)}}{}^\circ {{C}^{-1}}\]

Thus option A is the correct answer.

Note: Here, as the substance used is a metal, with increase in temperature, the resistance also increases, but in the case of semi-metals and insulators, this is not the case. For semimetals, with increase in temperature, resistance increases up to a certain point and then decreases, while for insulators, the resistance decreases.