# Resistance

## Resistance

Resistance is the opposition to the passage of current within a component. The resistance of a component decides how much voltage will be dropped across it for a particular current.

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

2) Formula of Resistance: For a conductor if $$l=$$length of a conductor, A = Area of cross section of conductor, n = number of free electron per unit volume in conductor, $$\tau$$ = relaxation time then resistance of conductor, $$R=\frac{\rho l}{A}=\frac{m}{n{{e}^{2}}\tau }\times \frac{l}{A}$$; where, $$\rho =$$ resistivity of the material of conductor.

3) Unit and Dimension: its S.I. unit is Volt/Amp (or)$$\Omega$$. Also,

$$1\Omega =1\frac{Volt}{Amp}$$$$=\frac{{{10}^{8}}\,emu\,\,of\,potential}{{{10}^{-1}}\,emu\,\,of\,current}={{10}^{9}}\,emu\,of\,resistance$$ ; Its dimension is $$\left[ M{{L}^{2}}{{T}^{-3}}{{A}^{-2}} \right]$$

4) Dependence of resistance: Resistance of a conductor depends upon the following factors.

i) Length of the conductor: Resistance of a conductor is directly proportional to its length i.e. $$R\propto l$$ and inversely proportional to its area of cross section i.e. $$R\propto \frac{1}{A}$$

ii) Temperature: For a conductor, Resistance $$\propto$$ Temperature

if, $${{R}_{0}}=$$ Resistance of conductor at $${{0}^{0}}C$$

$${{R}_{t}}=$$ Resistance of conductor at $${{t}^{0}}C$$ and $$\alpha ,\beta =$$ Temperature co-efficient of resistance then, $${{R}_{t}}={{R}_{0}}\left( 1+\alpha t+\beta {{t}^{2}} \right)$$ for $$t>{{300}^{0}}C$$ (or) $$\alpha =\frac{{{R}_{t}}-{{R}_{0}}}{{{R}_{0}}\times t}$$

If $${{R}_{1}}$$ and $${{R}_{2}}$$ are the resistances at $${{t}_{1}}^{0}C$$ and $${{t}_{2}}^{0}C$$ respectively then, $$\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1+\alpha {{t}_{1}}}{1+\alpha {{t}_{2}}}$$

The value of $$\alpha$$ is different at different temperature. Temperature coefficient of resistance averaged over the temperature range $${{t}_{1}}^{0}C$$ and $${{t}_{2}}^{0}C$$ is given by, $$\alpha =\frac{{{R}_{2}}-{{R}_{1}}}{{{R}_{1}}\left( {{t}_{2}}-{{t}_{1}} \right)}$$ which gives$${{R}_{2}}={{R}_{1}}\left( 1+\alpha \left( {{t}_{2}}-{{t}_{1}} \right) \right)$$. This formula gives an approximate value.