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)/(ne²τA)] 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)/(ne²τA)]

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)/(ne²τ)] [L/A]

=> R = ρ (L/A),
here ρ =resistivity or specific resistance = (m)/(ne²τ)

Also, read more about resistivity here.

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

(Vector form of Ohm’s Law)