Answer:
Let
\[\text{V}={{\text{I}}^{\text{a}}}{{\text{R}}^{\text{b}}}\]
...(i)
\[\left[
\text{M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-\text{3}}}{{\text{A}}^{-\text{1}}}
\right]\text{ }={{\text{A}}^{\text{a}}}{{\left[
\text{M}{{\text{L}}^{\text{2}}}{{\text{T}}^{-\text{3}}}{{\text{A}}^{-\text{2}}}
\right]}^{\text{6}}}=\text{
}{{\text{M}}^{\text{b}}}{{\text{L}}^{\text{2b}}}{{\text{T}}^{-\text{3b}}}{{\text{A}}^{\text{a}-\text{2b}}}\]
Applying the principle of homogeneity of dimensions, we gel
\[\text{b}=\text{1},\text{
2b}=\text{2},-\text{3b}=-\text{3a}-\text{2b}=-\text{1},\text{
a}=-\text{1}+\text{2b}=-\text{1}+\text{2}=\text{1}\]
.
Putting these values in (i), we get
\[\text{V
}=\text{ }{{\text{I}}^{\text{1}}}{{\text{R}}^{\text{1}}}\]
.
This is Ohm's law.
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