Question

Obtain the macroscopic form of Ohm’s law from its microscopic form and discuss its limitation.

Answer 1

1. Consider a segment of wire of length l and area of cross-section A
2. Electric field is created when a potential difference V is applied
3. If ‘E’ is uniform, then, V = El
4. Current density, J = σ E = σ`"V"/l`

Since J = `"I"/"A"`

`"I"/"A" = sigma "V"/l`

Rearranging the above equation, Current through the conductor

Current through the conductor

V = `"I"(l/(sigma"A"))`

Where `(l/(sigma"A"))` → resistance of conductor (R)

∴ R `alpha (l/(sigma"A"))`

∴ The macroscopic form of Ohm's law is

V = IR  ...[V α I]

Limitations:

There are certain materials and devices where the proportionality of V and I does not hold good.