Let I = current through a conductor, R = its resistance and V = p… - Vidyadip

Question

Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are $\text{ML}^2\text{I}^{-2}\text{T}^{-3}$ and $\text{ML}^2\text{T}^{-3}\text{I}^{-1}$ respectively.

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Answer

Dimensional formulae of $\text{R}=[\text{ML}^2\text{T}^{-3}\text{I}^{-2}]$ Dimensional formulae of $\text{V}=[\text{ML}^{2}\text{T}^3\text{I}^{-1}]$ Dimensional formulae of $\text{I}=[\text{I}]$$\therefore[\text{ML}^2\text{T}^3\text{I}^{-1}]=[\text{ML}^2\text{T}^{-3}\text{I}^{-2}][\text{I}]$
$\Rightarrow\text{V = IR}$

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