Capacitance

• Capacitance is the charge stored by a capacitor per unit potential difference and has the equation C= Q/V.
• A capacitor is made of two conducting parallel plates with a gap between them and often separated by an insulating material known as a dielectric.
• When a capacitor is connected to a power source, opposite charges build up on the plates causing a uniform electric field to be formed.
• Permittivity is a measure of the ability to store an electric field.
• The relative permittivity of a material is its permittivity divided by the permittivity of free space.
• The capacitance of a capacitor can be calculated using the properties of its components and is the area of the plates multiplied by the permittivity of the dielectric all divided by distance between the plates.
• A dielectric is formed of polar molecules which align themselves with the field, with their negative end at the plates positive end and vice versa. Each molecule has its own electric field, the strength of which depends on the dielectrics permittivity and will oppose the field formed by the capacitor.
• The energy stored by a capacitor can be found by the area under a graph of charge against potential distance.
• The equations for energy stored by a capacitor are E= QV/2 = CV^2/2 = Q^2/2C.
• When charging a capacitor, current flows and negative charge builds up on the plate connected to the negative terminal. On the opposite plate, electrons are repelled by this charge and so they move to the positive terminal but travel through the power supply and are repelled onto the original plate by the negative terminal. As charge across the plates increases, potential difference increases but the electron flow rate decreases until the potential difference across the capacitor equals the potential difference across the power supply.
• The time constant is the time taken to discharge a capacitor to 1/e (0.37) of its original value of charge, current or potential difference, or to charge a capacitor to 1-1/e (0.63) of its original value of potential difference or charge.
• The equation for time constant is t=RC.
• The equations for current, potential difference and charge for capacitor discharging all follow the same structure: the equation for current is I= I0 e^(-t/RC), the equation for pd is V= V0 e^(-t/RC) and the equation for charge is Q= Q0 e^(-t/RC).
• The current equation for capacitor charging and discharging is the same and is I= I0 e^(-t/RC).
• The equation for charging for pd and charge is different than for discharging and is V= V0(1-e^(-t/RC)) and Q= Q0(1-e^(-t/RC)).