# Derivation of Ohm’s Law class 12 (using drift velocity equations)

Last updated on June 26th, 2022 at 05:12 pm

Derivation of Ohm’s Law class 12 – Here, in this post, we will derive Ohm’s Law using drift velocity equations following the class 12 syllabus. Know more about the fundamentals of Ohm’s law, graph, etc. here.

## Derivation of Ohm’s Law class 12

Here, we will take the help of 2 equations or formulas of drift velocity and derive Ohm’s Law.

Let L be the length and A be the area of cross-section of a metallic wire. When a potential difference V is applied across the ends of the wire, the acceleration experienced by an electron of mass is expressed as:

a = F/m = Ee/m … (1)

As, E = V/L,

Hence, a = (eV)/(Lm)……….. (2)

The drift velocity of the electron: v_{d }= a τ ………….. (3)

Further, in terms of current, the drift velocity is expressed as: v_{d} = I / (n e A) ……….. (4)

From (3) and (4),

a τ = I / (n e A)

=>[(eV)/(Lm)].τ = I / (n e A)

=>V = [(mL)/(ne^{2}τA)] I ……………….. (5)

In equation 5, the parameters m and e are universal constants. Further, if the physical conditions of the conductor, such as temperature, pressure, etc., remain constant then parameters L, A, and n remain constant, as well.

Thus, from equation (5) we can write,

V α I

**That is, the potential difference (PD) across the ends of a conductor is directly proportional to the current – which is Ohm’s law.**

Expressing equation 5 in terms of Ohm’s law, we can write,

V = R I, where R = [(mL)/(ne

^{2}τA)]

Thus, using drift velocity equations we can derive Ohm’s Law. (following class 12 syllabus – ISC, CBSE, etc.)

Rearranging equation of R we get, R = [(m)/(ne^{2}τ)] [L/A]

=> R = ρ (L/A),

here ρ =resistivity or specific resistance = (m)/(ne^{2}τ)

Also, read more about resistivity here.

And, here you can read on j = sigma e derivation using Ohm’s law formula