One method used to increase the overall capacitance of a capacitor while keeping its size small is to “interleave” more plates together within a single capacitor body. Instead of just one set of parallel plates, a capacitor can have many individual plates connected together thereby increasing the surface area, A of the plates.
A capacitor is formed of two square plates, each of dimensions a × a a × a, separation d d, connected to a battery. There is a dielectric medium of permittivity ϵ ϵ between the plates. I pull the dielectric medium out at speed x˙ x ˙. Calculate the current in the circuit as the battery is recharged. Solution.
The capacitors ability to store this electrical charge ( Q ) between its plates is proportional to the applied voltage, V for a capacitor of known capacitance in Farads. Note that capacitance C is ALWAYS positive and never negative. The greater the applied voltage the greater will be the charge stored on the plates of the capacitor.
By applying a voltage to a capacitor and measuring the charge on the plates, the ratio of the charge Q to the voltage V will give the capacitance value of the capacitor and is therefore given as: C = Q/V this equation can also be re-arranged to give the familiar formula for the quantity of charge on the plates as: Q = C x V
This is because the top plate of capacitor, C1 is connected to the top plate of C2 which is connected to the top plate of C3 and so on. The same is also true of the capacitors bottom plates.
A capacitor can be charged by connecting the plates to the terminals of a battery, which are maintained at a potential difference ∆ V called the terminal voltage. Figure 5.3.1 Charging a capacitor. The connection results in sharing the charges between the terminals and the plates.