Section 7.4: Capacitance Flashcards
Define capacitance
The charge stored by a capacitor per unit potential difference, symbol C and measured in Farads (F).
What is a capacitor?
An electrical component which stores charge.
Describe the structure of a capacitor
It consists of two conducting parallel plates with a gap between them that may contain an insulating material known as a dielectric.
What is permittivity?
A property of a dielectric, which is the ability to store an electric field in the material, symbol ε. It can be used to find the relative permittivity (dielectric constant), symbol εr, by dividing it by the permittivity of free space, symbol ε0. The relative permittivity can then be used to find the capacitance of a capacitor.
How does a dielectric work?
A dielectric consists of many polar molecules, meaning they have a positive and negative end. These polar molecules are normally randomly arranged, however when an electric field is present the molecules align themselves with the field. The negative ends of the molecules rotate towards the positive plate and vice versa. Each molecule will have its own electric field, the strength of which depends on the permittivity, which will oppose the field formed by the capacitor, reducing it. Due to this the potential difference required to charge the capacitor decreases as electric field strength decreases, and so the capacitance will increase.
How do you find energy stored by a capacitor graphically?
Find the area underneath a graph of charge over potential difference.
What are the shapes of the graphs of current, voltage and charge against time when charging a capacitor?
Current against time will be a negative exponential, while both voltage and current will start at the origin and curve with decreasing gradient up to an asymptote parallel to the x-axis.
What are the shapes of the graphs of current, voltage and charge against time when discharging a capacitor?
They will all be negative exponentials
How does a capacitor charge?
When the circuit is switched on, the plate connected to the negative terminal of the supply will build up a negative charge. This negative charge repels the electrons in the plate connected to the positive terminal of the supply, making that plate positive. Since there is now an equal but opposite charge on the plates there is a potential difference between the plates, but charge cannot flow since the plates are separated by an insulator.
What is the time constant?
The product of circuit resistance and capacitance, and is the time taken to:
- Discharge a capacitor to 1/e of its original value of current, voltage or charge.
- Charge a capacitor to 1 - 1/e of its final value of charge or voltage.
What are the two ways to find time constant graphically?
Find the time at which the y value is either 1/e or 1 - 1/e of the maximum, depending on whether the graph is of discharging or charging.
or
Take natural logs of both sides of the discharging equation for charge and plot lnQ against t. The gradient is -1/RC, so the time constant is -1/gradient.
What is the time to halve?
The time taken for the current, charge or voltage of a capacitor to discharge to half of the initial value.
