when we consider the close surface essentially encloses a junction of an electrical circuit.

The above equation is the Kirchhoff’s current law of circuit theory, which states that algebraic sum of all the currents flowing out of a junction in an electric circuit, is zero.

Power Dissipation and Joule’s Law

We have mentioned that in practical conductors, under the action of an applied electric field, the electrons travel with drift velocity and the collision of electrons with the atomic lattice transfers energy acquired by the electrons from the field to the lattice in form of vibration and subsequent dissipation of energy as heat.

Under the action of applied electric field , the power delivered to the charge carriers in a volume is given by,

......................(3.24)

where N is the density of carriers, q represent charge of a carrier and v_d is the drift velocity.

Therefore,

 ......................(3.25)