Capacitance is the ability of a system (like a capacitor) to store an electric charge. Finding its dimensional formula requires combining several fundamental concepts like Work, Charge, and Potential Difference.
The SI unit of capacitance is the Farad (F), named after the English scientist Michael Faraday.
Because 1 Farad is an incredibly massive amount of capacitance, practical capacitors are usually measured in microfarads ($\mu F$) or picofarads (pF).
The basic formula for Capacitance ($C$) is: Capacitance ($C$) = $\frac{\text{Charge (Q)}}{\text{Voltage (V)}}$
Voltage ($V$) is defined as Work Done ($W$) per unit Charge ($Q$).
Now, substitute the dimensions of Charge and Voltage back into the main Capacitance formula ($C = Q/V$):
$C = \frac{[A^1 T^1]}{[M^1 L^2 T^{-3} A^{-1}]}$
Bring all the terms from the denominator to the numerator (change the signs): $C = [A^1 T^1] \times [M^{-1} L^{-2} T^3 A^1]$
Combine the similar terms ($A^{1+1}$ and $T^{1+3}$): Final Dimensional Formula = $[M^{-1} L^{-2} T^4 A^2]$
It depends purely on the physical geometry: the surface area of the plates, the distance between them, and the dielectric material placed inside them.
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