You have two tasks. You must design a 3-switch lamp and a 4-switch lamp. It is recommended that you try the 3-switch lamp first. Your design will include a lightbulb, wires, switches and power sources. The design must follow these rules:

1. You may only use 1 lightbulb for each lamp. The 3-switch lamp can only have one power source, and the 4-switch lamp must have exactly two. You may use any number of wires.
2. Every flip of a switch, no matter the previous positions, must turn the lamp from on to off or off to on.
3. Each wire may connect to any number of switches, power sources, and other wires, and to the lightbulb.
4. Each switch has two separate positions to which wires can connect. If the switch is up, then all the wires connected to position 1 are considered connected to each other. If the switch is down, all the wires connected to position 2 are considered connected to each other.
5. The lightbulb turns on if and only if there exists a complete circuit that includes both the lightbulb and at least one power source.
6. A circuit is a sequence of wires, power sources, and the lightbulb where each is connected to the next item in the sequence (the last is connected to the first). No such sequence may list the same wire, power source, or the lightbulb twice.

I recommend that you denote the different wires with letters like A, B, C, etc.

Will a circuit still get the light bulb to light even if the power supply is short circuited?

For instance, consider in the three switch case (notation PS=Powersupply, SN+/- = up/down side of switch N, LB=LightBulb), with wires:

A from PS to S1+
B from S1+ to LB
C from LB to S1+
D from S1+ to PS

Then with S1 in the + position, we have a "circuit" following the path PS -> A -> S1+ -> B -> LB -> C -> S1+ -> D -> back to PS, and follows rule 6 in that it does not list any wire, power source, or lightbulb twice, (it does list S1+ twice, but that is not excluded) however in reality the power supply is short circuited using the path PS -> A -> S1+ -> D -> back to PS.

I think in reality a small amount of current would still flow through the light bulb, but not enough to really notice.

Edit: Also, how does the power supply work exactly? Does current behave like in reality, where it will only flow in one direction depending on the orientation of the positive and negative ends of the power source? If so, is it necessary to distinguish between wires connected to the positive end of the power source and wires connected to the negative end of the power source? If not, could we design a circuit such that current will flow through a wire connected to the power supply in one direction under a certain configuration of switches, and the other way under a different configuration?

Edited on May 10, 2005, 4:41 pm

Edited on May 10, 2005, 4:42 pm

Posted by Avin on 2005-05-10 16:28:30