# Capacitance

The capacitance of a system (represented by $$C$$) is a measure of how efficient and quickly that system accumulates an amount of charge $$Q$$ and is defined as

$$C≡\frac{Q}{ΔV_{ab}}.\tag{1}$$

If we're charging a capacitor by an amount $$Q$$, the voltage $$ΔV_{ab}=\frac{ΔU}{q}$$ measures how much potential energy is transferred to the capacitor every time an amount of charge $$q$$ is transferred from one conductor in the capacitor to another. In Equation (1), $$Q$$ is the total amount of charge that gets stored in the capacitor.

(Let's, for arguments sake, just assume for the moment that the capacitor is charged to the amount $$Q=q$$.) Now, the important thing to know is that the capacitance $$C$$ is a number that we measure which only depends on the type of material comprising the conductors and the insulator of the capacitor. The value of $$C$$ does not depend on $$Q$$ or $$ΔV_{ab}$$. So, if $$C$$ has say a small value ($$C=\text{'small value'}$$) then if we charged the capacitor by an amount $$Q+q$$, then the amount of energy (or, to be more precise, the amount of electric potential energy) $$ΔV_{ab}=\frac{ΔU}{q}=ΔU=\frac{q}{C}=\frac{q}{text{'small value'}}$$ stored in the capacitor is large. If the capacitor is, however, made out of material for which $$C=\text{'big value'}$$, then if we charged the capacitor to an amount $$Q=q$$ the total energy $$ΔV_{ab}=\frac{q}{\text{'big value'}}=ΔU$$ stored in the capacitor would be small. So, in a certain sense, the capacitance of a capacitor can be viewed as how efficiently energy is transferred to the capacitor as you charge it. Capacitors for which the capacitance is lower accumulates energy faster and morre efficiently as you charge it up, whereas capacitors with a higher capacitance assumulates energy much slower and less efficiently as you charge it.