Question

The resistance of a bulb filament is $100\Omega$ at a temperature of ${100^0}C$. If its temperature coefficient of resistance is $0.005\Omega {/^0}C$ , its resistance will become $200\Omega$ at the temperature of:
(A) ${500^0}C$
(B) ${200^0}C$
(C) ${300^0}C$
(D) ${400^0}C$

Answer 1

We will use the idea of temperature dependence of resistance. Then we will put up the given values. Finally, we will equate and evaluate them.
Formulae Used: ${R_{final}} = {R_{initial}}\left[ {1 + \alpha \left( {{T_{final}} - {T_{initial}}} \right)} \right]$
Where, ${R_{final}}$ is the final resistance of the material, ${R_{initial}}$ is the initial resistance of the material, $\alpha$ is the temperature coefficient of the material, ${T_{final}}$ is the final temperature and ${T_{initial}}$ is the initial temperature.

Step By Step Solution
Given,
${R_{initial}} = 100\Omega$
${R_{final}} = 200\Omega$
$\alpha = 0.005\Omega {/^0}C$
${T_{initial}} = {100^0}C$
Now,
Putting these values in the formula, we get
$200 = 100\left[ {1 + 0.005\left( {{T_{final}} - 100} \right)} \right]$
Then,
After Calculation, we get
${T_{final}} = {300^0}C$

Hence, the correct answer is (c).

Additional Information The basic resistance which a charge flowing in a wire is actually provided by the atoms and molecules of the material of the wire. Broadly speaking, primarily, the charges collide with the atoms of the wire and get deflected at random directions, due to which the wire offers an opposition to the flow of the charge as the collision takes place. Over that, if the flowing charge is negative, then the electrons in the valence shell of the atoms of the wire will repel the charge flowing and provide an extra opposition to the flow.

Note: The resistance depends on the temperature as if let us say the temperature increases. Due to the increase, the atoms of the wire as well as the charge gets excited and the frequency of collision also increases. As a result, the net resistance of the wire also increases.