#2             72. SHORT CIRCUIT                       

Bill has always been rather good with electrical circuits, so I was surprised the other day when he came to me for advice. He showed me his sketch of a couple of simple circuits. Each had a battery represented on the left, and a lamp at the top. Switches a and b were included at the bottom of each circuit.

“In this first case,” said Bill, “the switches are in series. If we close both switches, then the current flows around the circuit and the lamp lights up.

“In the second diagram, the switches are in parallel. Here the lamp lights up if either switch a or switch b or both are closed.

“Now, my problem is this. Is there a simple circuit which has two switches, and such that the lamp lights up if switch a or switch b is closed, but not when both switches are closed?”

My intuition tells me that the answer is “Yes”, but I do wish that someone would show me how it is done!







Hints and strategies
HINT 1

The problem really asks us to do something involving switches which are open. Can we add to the design of the switch to make something actively happen when the switch is open?
HINT 2

What about adding an extra wire so that the open switch makes current flow to a different circuit?
SOLUTION

The diagram at right shows the solution. When a is closed and b open, or vice versa, the circuit is completed and the current flows. When a and b are both closed, there is a break in the circuit, and the lamp doed not light up.
EXTENSIONS

1. Make up some similar problems of this type.

2. You will notice that this problem sets up a correspondence between logical statements involvinh ‘or’ and ‘and’ with simple circuits. Explore this further by looking up on the web the terms ‘Boolean logic’ and ‘logic gates’.