Question

How does the resistivity change with temperature? (a) Increases linearly (b) Decreases linearly (c) First increases and then decreases (d) None of the above​

Answer 1

The resistivity increases.

• In general, when the standard overall temperature of an element rises, the element's potential resistivity also augments.
• It further changes linearly with effective temperature for minor temperature changes.
• A marked increase in standard temperature in such materials can liberate more charge carriers, naturally resulting in an augmentation in the overall current.

Answer 2

Resistivity increases linearly.

Detailed Discussion:

• Resistivity is defined as a quantity numerically equal to resistance for a a conductor of unit length and unit area.

• It changes with temperature in the following equation:

$\boxed{ \rho_{t} = \rho_{0} \bigg \{1 + \alpha \Delta t \bigg \}}$

$\implies\rho_{t} = \rho_{0} \bigg \{1 + \alpha (t - t_{0})\bigg \}$

$\implies\rho_{t} = \rho_{0} \bigg \{1 + \alpha t - \alpha t_{0}\bigg \}$

$\implies\rho_{t} = \rho_{0} \bigg \{1 - \alpha t_{0}\bigg \} + \rho_{0} \alpha t$

This above equation is in the form of:

$\implies y = mx \: + \: c$

So, resistivity increases linearly !