The dimensional formula for capacitance (C) can be derived using the fundamental units of the International System of Units (SI). The formula is as follows:
[C] = [Q] / [V]
Where:
- [C] represents the dimensional formula for capacitance (Farads, F)
- [Q] represents the dimensional formula for charge (Coulombs, C)
- [V] represents the dimensional formula for voltage (Volts, V)
The dimensional formula for charge is: [Q] = [I] x [T]
Where:
- [I] represents the dimensional formula for electric current (Amperes, A)
- [T] represents the dimensional formula for time (Seconds, s)
The dimensional formula for voltage is: [V] = [W] / [Q]
Where:
- [W] represents the dimensional formula for energy (Joules, J)
Combining these formulas, we can derive the dimensional formula for capacitance:
[C] = [Q] / [V] = ([I] x [T]) / ([W] / [Q]) = [I] x [T] x [Q] / [W] = [I] x [T] x [Q] / ([M] x [L]^2 / [T]^2) = [I] x [T]^3 x [Q] / ([M] x [L]^2)
Simplifying further, we can represent the dimensional formula for capacitance (C) as:
[C] = [I] x [T]^3 x [Q] / ([M] x [L]^2)
Where:
- [M] represents the dimensional formula for mass (Kilograms, kg)
- [L] represents the dimensional formula for length (Meters, m)
Note: The dimensional formula for capacitance (C) includes dimensions of current (I), time (T), charge (Q), mass (M), and length (L).