Question

For a metallic wire, the ratio $\dfrac{V}{i}$ (where, V is equal to applied potential difference and i is current flowing)
A. is independent of temperature
B. increases as the temperature rises
C. decreases as the temperature rises
D. increases or decreases as temperature rises depending upon the metal

Answer 1

Hint: Here a metallic wire is used and we know that metal is a conductor. Also we know that changes occur when the temperature of a conductor increases or decreases. So we need to find out if there is any change in the resistance of the conductor with respect to temperature.

Formula used:
Resistance, $R = \dfrac{V}{I}$
Where, V is the potential difference applied here in case of metallic wire and I is current flowing in the metallic wire.

Complete step by step solution:
Here we need to find that the ratio $\dfrac{V}{i}$ depends on temperature or not. If it depends on temperature, then in what ways they are related. Metallic wire is a conductor, and we know that conductor contains free electrons that help in conduction of electricity.

When the temperature of the conductor rises, atoms start vibrating more frequently which causes an increase in the number of collisions of atoms. Therefore, this increases resistance to the movement of electrons present in the atoms which are colliding. As the resistance is the ratio of V and i. We know that, resistance,
$R = \dfrac{V}{I}$
As $R \uparrow $ that implies $\dfrac{V}{i} \uparrow $ with the increase in temperature of the conductor that is metallic wire here.

Hence, the correct answer is option B.

Note: Here the change in ratio of V/i with respect to temperature is asked and we know that ratio of V and i is resistance. So, ultimately we needed to find the relation between the resistance and temperature of the conductor that is metallic wire here and finally we get the answer.