Purpose

Limits the flow of current in a circuit.

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Resistors work by absorbing electrical energy and then releasing it again as heat. The amount of energy absorbed depends on the rating (in ohms) of the resistor and the voltage of the circuit it is placed in.

Depending on where resistors are placed in a circuit they can perform many tasks such as protecting other components, pulling up/down logic levels, volume control, limiting capacitor charge/discharge rate, or creating low-pass filters when combined with a capacitor.

Protecting components

Ohm's Law shows that as the resistance in a circuit approaches zero ohms the current flow tends towards infinity. We need to be careful when connecting components with very little internal resistance (like LEDs) to a power source to avoid exceeding their current ratings.

To bring the current flow down to levels that the component is rated for (around 20mA for a standard LED) we need to add a resistor in series in the circuit.

The correct value of resistor is calculated based on the voltage of the circuit, the resistance of the circuit without the resistor, and the desired current flow. These numbers can be plugged into Ohm's Law to determine the correct resistor value.

Let's take an LED rated for 20mA that has a forward voltage of 1.7 volts and connect it to a 5 volt power supply:

( 5V - 1.7V ) / 0.02A = 165Ω

The ideal resistor value is 165 ohms but we'll need to round that value up to the nearest standard resistor value which is 180 ohms.

Pull up/down

In logic based circuits it's important to set the voltage level of pins on an integrated circuit (inputs or outputs) so that they aren't left "floating" leading to undefined behaviour.

High value resistors, often 10,000 (10K) ohm or more, are used to connect the pins directly to ground (pull-down) or to a voltage source (pull-up) ensuring that the voltage levels are well defined when the circuit isn't actively driving them.

Volume control

Capacitor (dis)charge rate

Because a resistor limits the flow of current in a circuit, it can be used to alter the time it takes a given capacitor to charge or discharge. This is fundamentally how timing circuits work, and the charge/discharge rate of a capacitor is what defines the behavior of a 555 Timer.

Low-pass filter

That's all folks!

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