Resistors

We use resistors in the circuits to limit the flow of current through the LEDs.
They are very important as an LED has, effectively, no resistance of its own.
If we attach an LED direct to a power source without a resistor, an unlimited amount of current is allowed to flow, burning out the LED instantly.

If the power source was the water tank in the loft and the current was the diameter of the hosepipe you've got rigged from the tank to the garden, then the resistor is your hand squeezing the pipe. The harder you squeeze (the higher the resistance) the slower the flow (of the current).

Resistors can be joined together to make combined resistances with combined power handling capacities. This is very useful if you only have a few different values of resistor, or if you want to use them in a more powerful circuit than usual.

Resistors in Series

In series the resistances add up so Total Resistance is R1 + R2 + R3

If each resistor had a resistance of 22Ω, the total resistance would be 66Ω.

The total power capacity is the capacity of each resistor added together.

If each resistor had a 1 watt power capacity the total capacity would be 3 watts.

Resistors in Parallel

In parallel the total resistance is the resistance of a single resistor divided by the number of resistors.

If each resistor had a resistance of 39Ω, the total resistance would be 13Ω.

The power capacity is still the total of the individual power handling capacities, so if each resistor was rated at 1 watt, the total power capacity would be 3 watts.

This only works if all the resistors have the same resistance and power rating.

Resistor Arrays

In an array, as long as the rows and columns are the same size (3 x 3, 5 x 5 etc.), the total resistance is the same as any of the individual resistances. What use is this? The power handling capacity of the above array is nine times the individual capacity. In a 5 x 5 array it would be 25 times...

If each resistor in the digram was a 100Ω 2 watt resistor, the whole array would still be 100Ω but the power handling capacity would be 18 watts.

This only works if all the resistors have the same resistance and power rating.

You can use any of the above resistor combinations in combination with each other.
The more resistors you use the greater the power capacity of the effective resistor.
And the nearer you can get to your actual desired resistance.

You will probably need to know how to calculate resistance values for LED circuits.