JEE Main & Advanced Physics Current Electricity, Charging & Discharging Of Capacitors / वर्तमान बिजली, चार्ज और कैपेसिटर का निर Resistivity (p), Conductivity and Conductance (C)

(1) Resistivity : From \[R=\rho \frac{l}{A};\] If \[l=1m,\,\,A=1\,{{m}^{2}}\] then \[R=\rho \] i.e. resistivity is numerically equal to the resistance of a substance having unit area of cross-section and unit length.

(i) Unit and dimension : It's S.I. unit is ohm \[\times \] m and dimension is \[[M{{L}^{3}}{{T}^{-3}}{{A}^{-2}}]\]

(ii) It's formula : \[\rho =\frac{m}{n{{e}^{2}}\tau }\]

(iii) Resistivity is the intrinsic property of the substance. It is independent of shape and size of the body (i.e. \[l\] and \[A\]).

(iv) For different substances their resistivity is also different e.g. \[{{\rho }_{\text{silver}}}=\] minimum \[=1.6\times {{10}^{-8}}\,\,\Omega -m\] and \[{{\rho }_{\text{fused quartz}}}=\] maximum \[\approx {{10}^{16}}\,\,\Omega -m\]W

\[\underset{\mathbf{(Maximum for fused quartz)}}{\mathop{{{\rho }_{\mathbf{insulator}}}}}\,>{{\rho }_{\mathbf{alloy}}}>{{\rho }_{\mathbf{semi-conductor}}}>\underset{\mathbf{(Minimum for silver})}{\mathop{{{\rho }_{\mathbf{conductor}}}}}\,\]

(v) Resistivity depends on the temperature. For metals \[{{\rho }_{t}}={{\rho }_{0}}(1+\alpha \Delta t)\] i.e. resitivity increases with temperature.

(vi) Resistivity increases with impurity and mechanical stress.

(vii) Magnetic field increases the resistivity of all metals except iron, cobalt and nickel.

(viii) Resistivity of certain substances like selenium, cadmium, sulphides is inversely proportional to intensity of light falling upon them.

(2) Conductivity : Reciprocal of resistivity is called conductivity \[(\sigma )\] i.e. \[\sigma =\frac{1}{\rho }\] with unit mho/m and dimensions \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\].

(3) Conductance : Reciprocal of resistance is known as conductance. \[C=\frac{1}{R}\] It's unit is \[\frac{1}{\Omega }\] or \[{{\Omega }^{-1}}\] or 'Siemen'.