A physical quantity is given by X = ₀ L V^2 t , where ₀ is the permittivity of free space, L is length, V is electric potential difference, and t is time. The dimensions of X are the same as those of :

Step-by-step solution

Instead of calculating the base dimensions of each term, we can group the terms to recognize standard physical quantities. The capacitance of a parallel plate capacitor is given by C = ₀ A d . Here, area A has dimensions of [ L ^2] and distance d has dimensions of [ L ] . Thus, the term ₀ L has the dimensions of capacitance C . The expression can be rewritten dimensionally as: [X] = [C][V^2] [t] We know that the energy stored in a capacitor is U = 1 2 CV^2 . Therefore, the term CV^2 has the dimensions of energy. Su