Effect of Temperature on Resistance & Resistivity - JEE PDF Download

 Resistance of Pure Metals

(i) We know that

For a given conductor, l, A and n are constant, hence R  is directly proportional to (1/τ)

If λ represents the mean free path (Average distance covered between two successive collisions) of the electron and v_rms, the root-mean-square speed, then

 Hence R is directly proportional to  

Now,

(a) λ decreases with rise in temperature because the amplitude of vibrations of the +ve ions of the metal increases and they create more hindrance in the movement of electrons and,

(b) (i) v_rms increases because v_rms is directly proportional to  under root T. Therefore, Resistance of the metallic wire increases with rise in temperature. As ρ is directly proportional to  R and σ is directly proportional to (1/ρ), hence resistivity increases and conductivity decreases with rise in temperature of the metallic of the metallic wires.

(ii) If R₀ and R_τ represent the resistances of metallic wire at 0°C and t°C respectively then R_t is given by the following formula :

where α is called as the Temperature coefficient of resistance of the material of the wire.

α depends on material and temperature but generally it is taken as a constant for a particular material for small change.

R_t - R₀ = R₀ α t

for very small change in temperature dR = R₀ α dt

(c) Resistance of semiconductors

(i) There are certain substances whose conductivity lies in between that of insulators and conductors, higher than that of insulators but lower than that of conductors. These are called as semiconductors, e.g., silicon, germanium, carbon etc.

(ii) The resistivity of semiconductors decreases with increase in temperature i.e., a for semiconductors is -ve and high.

(iii) Though at ordinary temperature the value of n (no. of free electrons per unit volume) for these materials is very small as compared to metals, but increases very rapidly with rise in temperature (this happens due to breaking of covalent bonds). Though τ decreases but factor of n dominates. Therefore, the resistance

  goes on decreasing with increase in temperature.

Specific Resistance or Resistivity 

• R of a conductor is directly proportional to its length (l).
• R of a conductor is inversely proportional to the area of cross-section (A).

 Resistivity depends only upon the material of which the conductor is made. It is defined as the resistance of the conductor made of a given material having length of 1 meter and area of cross-section 1 m²

If P₁ and P₂ are resistivities of a material at temperatures T1

and T2 respectively, then :