Explain the validity of ohms law from the relation between current and drift velocity

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Solution

We know that
$v_{d} = \frac{e E}{m} τ (v_{d} = d r i f t s p e e d, τ = R e l a x a t i o n t i m e) B u t E = V / l t h e r e f o r e, v_{d} = \frac{e V}{m l} τ A l s o, I = A n e v_{d} (A = a r e a o f c r o s s - s e c t i o n o f w i r e) I = A n e (\frac{e V}{m l} τ) = (\frac{A n e^{2} τ}{m l}) V o r \frac{V}{I} = \frac{m l}{A n e^{2} τ} = R = a c o n s \tan t f o r a g i v e n c o n d u c t o r . I t i s k n o w n a s t h e r e s i s \tan c e o f t h e c o n d u c t o r . T h u s V = R I T h i s i s o h m' s l a w .$

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