Temperature Dependence of Resistance

Resistance-

 

Before you go through this article, make sure that you have gone through the previous article on Resistance of Conductor.

 

We have learnt-

• Resistance of a conductor is the property due to which it opposes the motion of charge carriers inside it.
• The collisions of free electrons with the positive metal ions is the basic cause of resistance.

 

In this article, we will discuss the temperature dependence of resistance.

 

Temperature Dependence of Resistance-

 

For Metals (Conductors)-

 

• As temperature increases, the thermal speed of free electrons increases and also the amplitude of vibration of the metal ions increases.
• Consequently, the free electrons collide more frequently with the metal ions.
• As a result, the path of free electrons is obstructed which are responsible for conductivity.

 

Hence,

On increasing the temperature, the resistance of metals (conductors) increases.

 

For most of the metals, resistance increases linearly with the rise in temperature.

In such cases, resistance at any temperature T is given by-

 

 

where-

• R_T = Resistance at temperature T
• R₀ = Resistance at a reference temperature T₀
• α = Temperature coefficient of resistance

 

For Alloys-

 

On increasing the temperature, the resistance of the alloys increases but the increase is not much.

 

It is interesting to note that-

For some metal alloys, the temperature coefficient of resistance is very close to zero meaning that the resistance hardly changes at all with temperature.

 

Why alloys like constantan or manganin are used for making standard resistors?   It is because of the following reasons- They have very high value of resistivity. They have very small temperature coefficient, so their resistance does not change appreciably even for several degrees rise of temperature. They are least affected by atmospheric conditions like air, moisture etc.

 

For Semiconductors and Insulators-

 

Insulators and semiconductors typically have negative temperature coefficient of resistance meaning that-

 

On increasing the temperature, the resistance of insulators & semiconductors decreases.

 

For insulators, on increasing the temperature, resistance decreases because of the increase in number of electrons.

 

For semiconductors, on increasing the temperature, resistance first decreases (up to 400 K) due to generation of more number of holes and electron pairs, then remains constant (400 K to 600 K) but after 600 K, it increases due to increased number of collisions.

 

 

For Electrolytes-

 

As the temperature increases, the inter-ionic attractions (solute-solute, solvent-solute and solvent-solvent types) decreases and also the viscous forces decreases and therefore the ions move more freely.

 

Hence,

As the temperature of electrolytic solution increases, the resistance of electrolyte decreases.

 

Read the next article on-

Ohm’s Law

 

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