1.06 Area of the Capacitor Plates

In the previous section we described how a battery has an accumulation of charge at its terminals, which causes a voltage between them. When the battery isn't connected to a circuit and there is no current flowing through it, this voltage is equal to the e.m.f. voltage of the battery (see d.c. theory - internal resistance of power supplies).


Consider now connecting two electrically neutral copper plates to these terminals. The repulsion between the electrons at the negative terminal of the battery, would tend to push the electrons as far apart from each other as possible. So when the copper plate is connected, the electrons can disperse onto it and the concentration of charge at the negative terminal is therefore reduced. Similarly at the positive terminal, electrons from the copper plate will be attracted to the positive terminal until the positive charge is evenly distributed. This reduces the concentration of charge at that terminal. As the concentration of charge at the terminals has now been reduced, the chemical reaction in the battery is able to transfer electrons between the terminals again.

capacitor plates

As charge begins to accumulate on the copper plates, it creates a voltage between them and reduces the current flow, causing the charge to build up more slowly. After a short period of time, the concentration of charge on the copper plates, will reach the initial level of the battery terminals and the voltage between the plates will be equal to the e.m.f. voltage of the battery. At this point the current flow will stop completely. As the concentration of charge extends beyond the battery terminals and over the copper plates, more charge has now been accumulated at the same voltage level and hence the capacitance of the circuit has significantly increased.

capacitor plates

(Note, In practice the inherent capacitance due to the area of the battery terminals and conducting wires, will often be negligible and we would just focus on the capacitance that exists, due to the area of the copper plates alone. (However this does highlight the point, that some level of capacitance will always be present in an electrical circuit, even if the circuit does not include capacitors. This is an important aspect for some areas of electrical circuit design, especially high frequency a.c. circuits.))

In summary, when the copper plates are connected there is an initial flow of current, which immediately begins to reduce, stopping completely when the concentration of charge on the plates reaches a certain level, at which point the voltage between the capacitor plates, is equal to the voltage between the battery terminals. The larger the area of the plates, the more charge will be transferred before this point is reached. i.e. The capacitance of a capacitor is proportional to the area of the plates.
C is proportional to A.

Note: If we were now to disconnect the battery, this displaced charged would be “trapped” on the plates of the capacitor. i.e. The capacitor can “store” electrical charge.