Capacitors

• A capacitor is a device that stores charge and energy when a potential difference (PD) is applied across it
• When the PD across a capacitor is doubled, the charge (Q) doubles as well, showing that they are proportional
• The gradient of a graph of charge against voltage is the capacitance of the capacitor, which indicates how much charge is stored per volt
• The unit of capacitance is the farad (F)
• The equation for energy stored in a capacitor is E = 1/2 QV
• To calculate charge, it can be expressed as the product of current and time (Q = It)
• When discharging a capacitor through a resistor, the PD decreases exponentially with time, following the equation V/V0 = e^(-t/RC)
• To find an unknown capacitance, one can measure the PD as it changes with time during discharge and use the equation log(V/V0) = -t/RC
• The time constant (RC) is the time it takes for the PD across the capacitor to decrease to 37% of its initial value
• The capacitance of a capacitor is proportional to the area of the plates and inversely proportional to their separation
• The constant that relates capacitance to the physical dimensions of the capacitor is the permittivity (ε)
• The permittivity of a material is the product of the permittivity of free space (ε0) and the relative permittivity of the material (εr)
• Inserting a dielectric between the plates of a capacitor increases the capacitance by reducing the electric field between the plates
• Changing aspects of a capacitor, such as the area, distance between plates, or relative permittivity, will have knock-on effects on voltage (V), charge (Q), and energy stored
• When disconnecting a capacitor from a battery, the charge remains constant while the voltage changes
• The energy stored in a capacitor can be explained in terms of electrostatic potential energy, where work is done to separate the charged edges of the dielectric from the plates
• Energy put into removing the dielectric goes into the capacitor