# Dimensional Formula of Capacitance

The dimensional formula of Capacitance is

[ M-1  L-2  T2 A2 ]

where [M], [L], [T], and [A] are the fundamental quantities: Mass, Length, Time, and Ampere.

From the above formula, the dimensions of capacitance are (-1, -2, 2, 2).

## How to calculate the dimensional formula of capacitance?

In physics, we can determine the amount of charge by the capacitance and the voltage difference across the capacitors. Mathematically, it means

``````
Charge (Q) = Capacitance (C) * Voltage (V)

Capacitance = Charge / Voltage
``````

We know that,

• Charge = Current * time
• Voltage = Work / Charge

Now, let’s drive this formula in terms of fundamental quantities:

``````
Voltage = Work / Charge
``````

Work = Force * displacement, so the formula becomes

``````
Voltage = (Force * displacement) / Charge
``````

Replacing the value of Force by mass * acceleration, we get

``````
Voltage = (mass * acceleration * displacement) / Charge
``````

Also,

• acceleration = speed / time
• speed = distance / time
• acceleration = distance / time2
``````
Voltage = (mass * distance / time2 * displacement) / Charge

= (mass * distance * displacement) / (Charge * time2)

= (mass * distance * displacement) / (Current * time * time2)

= (mass * distance * displacement ) / (Current * time3)

= (mass * distance * displacement * Current-1 * time-3)
``````

Now, the formula of capacitance becomes

``````
Capacitance = (Current * time) / (mass * distance * displacement * Current-1 * time-3)

= (Current * time * Current * time3) / (mass * distance * displacement)

=  ( Current2 * time4 ) / (mass * distance * displacement)

=  (Current2 * time4 * mass-1 * distance-1 * displacement-1)
``````

Dimensionally, we use

• [M] for mass
• [L] to represent both distance and displacement
• [T] for time
• and [A] for current

Now, the formula becomes

``````
Capacitance = [A2] * [T4] * [M-1] * [L-2]

= [M-1] * [L-2] * [T4] * [A2]
``````

Hence, the dimensional equation of Capacitance is C = [ M-1 L-2 T4 A2 ].

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