Capacitors are electrical components that are capable of storing small amounts energy in an electric field.
Simple capacitors generally consist of two opposing plates of conductive material of area A, separated by a distance d. An applied potential difference across the capacitor will cause net charges of opposite signs to be induced on each plate. When this potential difference is removed, the charge stored on each plate is rapidly discharged, thus inducing a current on each side of the capacitor. Due to this property, capacitors can be used as frequency filters in AC systems, leading to their use in systems such as high pass signal filters and signal coupler/decoupler systems 1. Capacitor capacitance, C, is a measure of the amount of charge (in Farads, F) that can be induced on each plate for a given potential difference. The capacitance of a capacitor with no dielectric is given by C = ?_0A/d (1)where ?_0 is the permittivity of free space (8.
854x?10?^(-12) Fm-1) 2.By inserting an insulating material known as a dielectric between the two plates, the capacitance of a capacitor can be increased. The atoms inside a dielectric will change their orientation depending on the charges present on the two plates, and as a negative charge builds on one plate, positive atomic nuclei inside the material are attracted to the plate, and their electron clouds are repelled in a process known as electric polarization. This mechanism has the effect of reducing the net electric field across the two plates, allowing a greater quantity of charge to be stored on each plate per volt. The increase in capacitance is measured by the relative permittivity of the dielectric, ?_r (Fm-1), which is simply a ratio of the capacitance with constant charge with and without the dielectric present 3 (hence we can see ?_r = 1 for a simple capacitor). Therefore, the capacitance of a capacitor with a dielectric is therefore given by C = ??_0 ??_rA/d (2)In this experiment, variances in the relative permittivity of a dielectric due to temperature will be examined, as well as the processes that cause these changes.
It is worth noting that a “stray capacitance” can unintentionally occur between two wires in a circuit, due to conductors in the circuit acting as capacitor plates. The consequences of this effect will be considered further on in experiment.In this experiment, a concept known as equivalent circuits will be used to model the non-ideal capacitors used in this experiment as ideal capacitors. Ideal capacitors have no resistive properties, meaning no current can pass through them. In practice however, capacitors will allow small amounts of current to pass through. This leads to the modelling of non-ideal capacitors in equivalent circuits, whereby the capacitor can be modelled as an ideal capacitor of capacitance C_s (series capacitance) in series with a resistor R_s, or as an ideal capacitor of capacitance C_p in parallel with a resistor R_p.
Non-ideal capacitors also experience a power loss due to their resistive properties. In an AC circuit, this dissipation can be expressed as a ratio, D, of the resistive power loss of the resistor, in relation to the power in the capacitor 4. Conversion between C_p or C_s can be done using the equivalent circuit relation