The answer is really simple when you understand how it works. Most switches are called SPST (Single-Pole, Single-Throw), that is they are either on or off. There are no other options. But a "Three-way" switch has three terminals - a "common" or "Arm", and it switches to one of the two other terminals. It's called a SPDT or Single-Pole, Double-Throw). When you throw this switch, it disconnects from one terminal and connects to the other terminal. The other three-way switch is exactly the same, with an "arm" and two other terminals. Connect a pair of wires just to the two other terminals - these wires are called "carriers", and apply power to the arm on one switch, and connect the arm on the other switch to the light bulb or other load. So switching either switch will change the carrier wire that the power is going to, and the position of the other switch determines of the power will be allowed to go to the load. This can be illustrated another way: If switch #1 and switch #2 are both in position A or if both are in position B then the light will light, but if one switch is in position A and the other switch is in position B, the light will not light. Only one switch moves when it is thrown, the other switch just carries or doesn't carry the current and doesn't do anything else.
When the circuit is "Off", it would look something like this. (Dots are for spacing only).
__/................ _____> To load
When it's on the circuit would look like this:
__/...............\_____> To load
I hope this makes it clear.
If you want to add more switches, any one of which can turn the load on or off, that's easy too! It can be done with DPDT, (Double-Pole, Double-Throw) switches. Doing this you can add as many as you want, just add another DPDT to reverse the carrier wires!
By the way, all this can also be done with mechanical switches, relays or all solid-state electronics, but they all work basically the same.
Good luck and God Bless.
Over 60 years training and experience in electronics.
· 7 years ago