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Question
Obtain the macroscopic form of Ohm’s law from its microscopic form and discuss its limitation.
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Solution
- Consider a segment of wire of length l and area of cross-section A
- Electric field is created when a potential difference V is applied
- If ‘E’ is uniform, then, V = El
- 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.
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