The resistivity of a conductor increases linearly with increases of temperature and if a graph is plotted between resistivity and temperature, it will be a straight line. However at a temperature below 0^o the graph deviates considerably from the straight line.

(a) shows the variation resistivity of copper in low temperature range.
(b) At ok, the semiconductor has an infinite value of resistivity.

The area of cross - section of two wires = 2:1
\(R\alpha \cfrac { \rho l }{ A } oi.eR\alpha \cfrac { 1 }{ R } \)
According to ohm's law
\(I\alpha \cfrac { V }{ R } i.eI\alpha \cfrac { 1 }{ R } \)
The current in the two wires 2 : 1 when the same potential difference is applied across the two wires. When the temperature of a conductor is increased, the amplitude of vibrate of the positive ions in the conductor increases. Consequently, the free electrons collide more frequently with the vibrating ions. This decreases relaxation time \(\tau .\rho \alpha \cfrac { 1 }{ \tau } \). So resistantly increases

The resistors value of carbon resistors changes considerably during storage and use.

V - I graph for an ohmic material is a straight line passing through origin. Metals are ohmic materials.

V - I graph for non-ohmic material is not a straight line thermistor is non - ohmic.

\({ V }_{ d }=\cfrac { eE }{ m } \tau =\cfrac { eV }{ ml } .\tau \left[ E=\cfrac { V }{ l } \right] \)
Keeping V constant, if 1 is doubled, v_d is halved. Again keeping area constant if length is doubled, if R will be doubled [R \(\alpha\) 1,if a is constant].