TODO: Re-organize this note to be more like the Resistor note

Capacitors are "mini" rechargeable batteries that can discharge very quickly. They are usually constructed with parallel plates wrapped in a circle.

The quantity of charge a capacitor can store is described by the capacitance of the capacitor.

Capacitor are represented in circuit diagrams as two lines with equal lengths.

Example circuit diagram of an capacitor

Charging a Capacitor

The charge that a capacitor holds () can be calculated as follows

Where is the voltage into the capacitor (usually a battery).

Graph

The graph of in a capacitor with respect to time forms an logarithmic graph with a horizontal asymptote at the of whatever is charging the capacitor.

Time Constants

As a capacitor charges up the current in the circuit decreases. As the voltage in the capacitor approaches its maximum the current in the circuit approaches 0.

This time constant can be used to model the graph using the equation

Where is the current time and is the "time constant".

The time constant is calculated as

Where is the resistance of the circuit where the capacitor is placed.

Formally it takes forever () for a capacitor to charge. However for convenience most people say it's "charged" after .

Discharging a Capacitor

The graph of discharging a capacitor is a reversed graph of it being charged and takes the form of an exponential decay.

Formally it takes forever () for a capacitor to discharge. However for convenience most people say it's "discharged" after .

Voltage from a Capacitor

The first charge that leaves the capacitor has full voltage and then it decreases as more Q's are removed from the capacitor. Voltage is a pre-calculation of energy so each subsequent charge leaving has less energy.

Capacitors in Parallel

As more capacitors are wired in parallel the total capacitance of the circuit increases.

Capacitors in Series

As more capacitors are wired in series.md) the total capacitance of the circuit decreases. This is because the "gap" between the positive and negative sides can be said to increase.

Ratios of Voltages when Charged

Parallel

Two capacitors one with a capacitance of and another with are wired in parallel. These capacitors are then wired in series with a battery.

When both capacitors are charged both capacitors have a difference over the capacitors.

Even though they have the same voltage they still have different values.

Series

Two capacitors one with a capacitance of and another with are wired in series to a battery.

Both the capacitors must have the same value when they're full charged

Capacitors in Steady and Transient States

TODO: make separate notes for these

Steady States

Steady states are when circuits have been sitting unchanged for a <u>long</u> time (usually ).

• There is 0 current through capacitors
• Capacitors can be treated like volt meters (super high resistance)

Transient States

Transient states describe right after a change to a circuit (ie. a switch is closed)

• Big current flow
• Capacitors can be treated like ammeters (very low resistance)