Which of the following quantities can be written in SI units in kgm²A⁻² s⁻³?

The correct option is Resistance.

To determine which physical quantity has the SI unit $\mathrm{kg}{m}^2{A}^{-2}{s}^{-3}$, we can derive the units of Resistance step-by-step from fundamental physical relationships.

1. According to Ohm's law, electrical resistance ($R$) is the ratio of potential difference ($V$) to electric current ($I$):
$R=\frac{V}{I}$

2. Potential difference ($V$) is defined as the work done ($W$) per unit charge ($q$):
$V=\frac{W}{q}$

3. The SI unit of work done ($W$) is the Joule ($J$). In base SI units, work is force times distance:
$J=\mathrm{kg}{m}^2{s}^{-2}$

4. The SI unit of electric charge ($q$) is the Coulomb ($C$), which is equivalent to current ($I$) multiplied by time ($t$):
$C=As$

5. Substituting the base units of work and charge back into the formula for potential difference ($V$):
$\mathrm{Unit\; of\; V}=\frac{\mathrm{kg}{m}^2{s}^{-2}}{As}=\mathrm{kg}{m}^2{s}^{-3}{A}^{-1}$

6. Finally, substituting this back into the formula for resistance ($R=\frac{V}{I}$) by dividing the unit of potential difference by the unit of current (Ampere, $A$):
$\mathrm{Unit\; of\; R}=\frac{\mathrm{kg}{m}^2{s}^{-3}{A}^{-1}}{A}=\mathrm{kg}{m}^2{A}^{-2}{s}^{-3}$

Thus, the quantity that corresponds to the given SI units is Resistance.