Derive ohms law using concept of drift velocity
Answers
Answer:
➡Derivation : ➡Consider a current of length l and cross sectional area A. When a potential difference V is applied across its ends, the current produced is I. If n is the number of electrons per unit volume in the conductor and vd the drift velocity of electrons, then the relation between current and drift velocity is.
Answer:
To find the relationship between current and drift velocity, consider a conductor of length l and area of cross-section A. If V is the potential difference across the ends of the conductor, then the strength of the electric field is image
The acceleration acquired by each electron due to the electric field is
image
where image
is the coulomb’s force experienced by each electron and m is the mass of the electron.
The drift velocity of the electrons is given by image
where t, the relaxation time, is the average time that an electron spends between two collisions. It is of the order of 10-14 s.
image
Now the volume of the conductor is equal to Al and if n is the number of free electrons per unit volume, then, the total number of free electrons in the conductor will be equal to n Al.
Hence, the total charge q = - n Ale
The time taken by free electrons to cross the conductor is
image
image
where we have substituted for t and q.
image
For a given conductor, I a Vd
A small value of drift velocity 10-5m/sec produces a large amount of current, as there are a large number of free electrons in a conductor.
The drift velocity of the electrons Vd is (using E = V / l)
image
Also I = - neAVd
On substituting for Vd in the above expression we get,
image
image
or
image
Which shows that current is directly proportional to the applied voltage(Ohm’s law).From this, the resistance R can be identified as
image