# Resistance

The property of substance by virtue of which it opposes the flow of current through it is known as the resistance.

# Formula of resistance

For a conductor if

*l*= length of a conductor*A*= area of cross-section of conductor,*n*= number of free electrons per unit volume in conductor, τ = relaxation time, then resistance of conductor,where

*ρ*= resistivity of the material of conductor.**Unit and dimension**Its SI unit is V/A or (Ω). Also 1 ohm = 10

^{9}emu of resistance. Its dimension is [

*ML*

^{2}

*T*

^{–3}

*A*

^{–2}].

# Dependence of resistance

The resistance of a conductor depends upon the following factors:

*Length of the conductor:**R*∝*l*and inversely proportional to its area of cross section, i.e.,*R*∝ 1/*A*.*Temperature:*For a conductor, Resistance

If

*R*_{0}= resistance of conductor at 0°C*R*= resistance of conductor at

_{t}*t*°C

and α,

*β*= temperature co-efficient of resistancethen

*R*=_{t}*R*_{0}(1 + α*t*+*βt*^{2}) for*t*> 300°C and*R*=_{t}*R*_{0}(1 + α*t*) for*t*≤ 300°C orIf

*R*_{1}and*R*_{2}are the resistances at*t*_{1}°C and*t*_{2}°C, respectively, then .The value of α is different at different temperature. Temperature coefficient of resistance averaged over the temperature range

*t*_{1}°C to*t*_{2}°C is given by which gives*R*_{2}=*R*_{1}[1 + α (*t*_{2}–*t*_{1})]. This formula gives an approximate value.