JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Resistance

(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, \[n=\] No. of free electrons per unit volume in conductor, \[\tau =\] relaxation time then resistance of conductor \[R=\rho \frac{l}{A}=\frac{m}{n{{e}^{\mathbf{2}}}\tau }.\frac{l}{A}\]; where \[\rho =\] resistivity of the material of conductor

(3) Unit and dimension : It's S.I. unit is Volt/Amp. or Ohm \[(\Omega )\]. Also 1 ohm \[=\frac{1volt}{1Amp}=\frac{{{10}^{8}}emu\,\text{of potential}}{\text{1}{{\text{0}}^{-\text{1}}}emu\,\text{of current }}\]\[={{10}^{9}}\]emu of resistance. It?s dimension is \[[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}]\].

(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 it's length i.e. \[R\propto l\] and inversely proportional to it's 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

\[{{0}^{o}}C\] \[{{R}_{t}}=\] resistance of conductor at \[{{t}^{o}}C\]

and \[\alpha ,\,\,\beta =\] temperature co-efficient of resistance

then \[{{R}_{t}}={{R}_{0}}(1+\alpha \,t+\beta \,{{t}^{2}})\] for \[t>{{300}^{o}}C\] and

\[{{R}_{t}}={{R}_{0}}(1+\alpha t)\] for \[t\le {{300}^{o}}C\] or \[\alpha =\frac{{{R}_{t}}-{{R}_{0}}}{{{R}_{0}}\times t}\]

If \[{{R}_{1}}\] and \[{{R}_{2}}\] are the resistances at \[{{t}_{1}}^{o}C\] and \[{{t}_{2}}^{o}C\] 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 \[{{t}_{1}}{{\,}^{o}}C\] to \[{{t}_{2}}{{\,}^{o}}C\] is given by \[\alpha =\frac{{{R}_{2}}-{{R}_{1}}}{{{R}_{1}}({{t}_{2}}-{{t}_{1}})}\] which gives \[{{R}_{2}}={{R}_{1}}[1+\alpha ({{t}_{2}}-{{t}_{1}})]\]. This formula gives an approximate value.  

Variation of resistance of some electrical material with temperature