Electric power:
(i) The electric power P is the rate at which the electrical potential energy is delivered.
(ii) The electric power P is the rate at which the work is done.
\( P= \frac{d U}{d t} (or)= \frac{d W}{d t} (or)=VI(or)\frac{V^2}{R}\)
Unit: watt (W)
Electric energy:
(i) The electric energy is the product of power (P) and duration of the time (t) when electric energy is delivered.
(ii) E = Pt
Unit: watt-hour (Wh)

Temperature coefficient of resistance is defined as the ratio of increase in resistivity per degree rise in temperature to its resistivity at T_o.
\(\alpha=\frac{\rho_{T}-\rho_{0}}{\rho_{0}\left(T-T_{0}\right)}\)

Devices that follow Ohm's law are called Ohmic conductor. Devices that do not follow Ohm's law are called non - Ohmic conductors.

Microscopic form of ohm's law is 
\(\vec{J}=\sigma\vec {E}\) 
\(J=\frac{ne^2\tau}{m}\vec{E}\)
\(\frac{e \tau}{m} \rightarrow Drift \ velocity \ v_d\)
where \(\vec{J} \) - current density
\(\sigma \)  - conductivity
\(\vec{E} \) - Electric field

Current is defined as the ratio of the net (i.e. amount of) charge (Q) passing through any cross section of a conductor to time.
\(I=\frac{Q}{t}\)
Since current is the ratio of two scalar quantities, it is a scalar. In addition current I is defined as the scalar product of the current density and area vector at which the charges cross.
I = \(\vec{J}.\vec{A}\)