**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.