Ohm ($\rm \Omega$) is the unit of electric resistance. We define electric resistance as the ratio of Voltage to Current, i.e., $\rm R = \frac{V}{I}$.

We know that Voltage (or potential difference) is Work done and Charge, i.e., $\rm V = \frac{W}{q}$.

When we combine the above two equations, we get,

$\rm R = \frac{W}{q \cdot I}$

Expressing charge in the form of electric current, we get,

$\rm R = \frac{W}{ \frac{q}{T} \cdot {T} \cdot I}$

$\rm R = \frac{W}{ I \cdot T \cdot I}$

$\rm R = \frac{W}{ I^{2} \cdot T}$

Replacing the symbols with their corresponding units, we get,

$\rm \Omega = \frac{ kg m^{2} s^{-2} }{ A^{2} \cdot s}$

$\rm or, \Omega= kg m^{2} s^{-2 -1} A^{-2}$

$\rm \therefore \Omega = kg m^{2}s^{-3} A^{-2}$

Hence, the unit of electric resistance ($\Omega$) is $\rm kg m^{2}s^{-3} A^{-2}$.