Capacitance and Dielectrics

We learned about charge in our first physics lesson. A capacitor is a device that stores charge. Capacitors are formed by a pair of conductors. The type of capacitor we are most interested in will have a charge, Q, on each conductor. There will also be a resultant voltage, V, between the two conductors. This voltage is linearly dependent on the charge. If we triple the charge, we triple the voltage. Because of this relationship, the ratio of Q/V is a constant for that capacitor. The value of Q/V for a given capacitor is known as its capacitance.

The unit of capacitance is the farad. It is equivalent to one coulomb per volt. One farad is an extremely large capacitance; most capacitors come in units of micro-, nano-, or pico-farads.

The capacitance of a capacitor is determined by two factors. The geometry of the capacitor, and the material between the conductors. This material is known as a dielectric. In a parallel plate capacitor, capacitance can be calculated from the equation:

Where C is capacitance, k is the dielectric constant, e is the permittivity of free space, A is the area of a plate, and d is the distance between the plates.

When one has several capacitors in a circuit, they can be combined in many ways. For example, two circuits could be connected in series:


or in parallel:


The equations show how to calculate the equivalent capacitance, Ceq for that type of combination. For example, to find the equivalent capacitance of two capacitors in series, you would add the inverse of their values and then take the inverse of their sum. To find the equivalent capacitance of 5 capacitors in parallel, you would add their capacitances.