Which physical quantity is represented by $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1} ?$ (a) Stress (b) Resistance (c) Electric field (d) potential Difference

Let's analyze the dimensions of each given physical quantity: (a) Stress: Stress is equal to force per unit area. We have dimensions of force as \([MLT^{-2}]\) and area as \([L^2]\). Therefore, the dimensions of stress are: \(\frac{[MLT^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]\) (b) Resistance: We can find the dimensions of resistance using Ohm's law, which states that \(V = R x I\), where \(V\) is the potential difference, \(R\) is the resistance, and \(I\) is the current. The dimensions of potential difference are \([ML^2T^{-3}A^{-1}]\), and the dimensions of current are \([A]\). Therefore, the dimensions of resistance are: \(\frac{[ML^2T^{-3}A^{-1}]}{[A]} = [M^1 L^2 T^{-3} A^{-2}]\) (c) Electric field: Electric field is equal to force per unit charge. The dimensions of force are \([MLT^{-2}]\), and the dimensions of charge are \([AT]\). Therefore, the dimensions of the electric field are: \(\frac{[MLT^{-2}]}{[AT]} = [M^1 L^1 T^{-3} A^{-1}]\) (d) Potential difference: The potential difference has dimensions of \([ML^2T^{-3}A^{-1}]\).

Now we will compare the given dimensional formula \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\) to the dimensional formulas of our four choices: (a) Stress: \([M^1 L^{-1} T^{-2}]\) - Not equal (b) Resistance: \([M^1 L^2 T^{-3} A^{-2}]\) - Not equal (c) Electric field: \([M^1 L^1 T^{-3} A^{-1}]\) - Equal (d) Potential difference: \([ML^2T^{-3}A^{-1}]\) - Not equal Based on the comparison, the given dimensional formula matches the electric field's dimensional formula.

The physical quantity represented by the dimensional formula \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\) is the Electric field (c).