To determine the dimensional formula of capacitance ($C$), we use the relation between charge ($Q$), potential ($V$), and capacitance: $C = Q/V$ .

1. Dimensions of Charge ($Q$): Since current $I = Q/t$, the dimensions of charge are $[A T]$ .
2. Dimensions of Potential ($V$): Potential is work done per unit charge ($V = W/Q$). Work ($W$) has dimensions $[M L^2 T^{-2}]$ . Therefore, $[V] = \frac{[M L^2 T^{-2}]}{[A T]} = [M L^2 T^{-3} A^{-1}]$ .
3. Dimensions of Capacitance ($C$):

• Substituting these into the formula for $C$: $[C] = \frac{[Q]}{[V]} = \frac{[A T]}{[M L^2 T^{-3} A^{-1}]}$ $[C] = [M^{-1} L^{-2} T^{1 - (-3)} A^{1 - (-1)}]$ $[C] = [M^{-1} L^{-2} T^4 A^2]$

This derived formula matches the value given in the NCERT Appendices .