Question

Using theory of drift velocity express ohms law

Answer 1

I is current and V is drift velocity

Answer 2

Let us consider a conductor of length l.The area of cross section of the conductor is A

Let n number of electrons are present per each area of cross section.

The current flowing through this conductor will be -

                                                $i=\ eAnv_{d}$

$v_{d}$  is the drift velocity of the electron.

The drift velocity of the electron is defined as -

                            $v_{d} =\ \frac{eV}{ml} t'$

Here, m is the mas of electron and V is the potential difference across the two ends of the conductor.

t' is called as the relaxation time.

Putting the value of drift velocity in current equation we get-

                                  $i=\ eAn*\frac{ev}{ml} t'$

                                         $=ne^{2} A*\frac{t'}{ml} V$

                                         $=\ [\frac{ne^2A}{ml}] t'.V$

                               ⇒  $V = i.\frac{ml}{ne^2At'}$

                               ⇒  $V=\ Ri$          

Here R is the proportionality constant called resistance.

The value of $R=\ \frac{ml}{ne^2At'}$

                         ⇒  $V\ \alpha\ i$      

This expression is called Ohm's law i.e the current flowing through a conductor is directly proportional to the potential difference maintained across the two ends of conductor at constant temperature and pressure.