Staircase lighting

Curricula: KS3, Sek I, cycle 4

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Aim

Find out how two two-way switches let one lamp be switched on and off from either of two places, like the light on a staircase or in a long corridor.

Theory

An ordinary switch has two terminals: it closes or opens the circuit at one point (see the lab "AND" and "OR" switches). A two-way switch (in North America, a three-way switch) has three: a common terminal, which has no number, and the terminals "1" and "2". Its lever joins the common terminal to "1" or to "2", never to both; halfway between them, in the position Open, it touches neither.

In the staircase circuit the source \(U\) is connected to the common terminal of \(S_1\), and the lamp \(L\) to the common terminal of \(S_2\). The numbered terminals of the two switches are joined by two wires, which electricians call travellers. The current reaches the lamp only when both levers are on the same traveller. When they are on different travellers, or one of the levers is in the middle, the circuit is open.

To control a lamp from three places or more, intermediate switches are put into the travellers between the two two-way switches. An intermediate switch has four terminals: in one position it passes the travellers straight through, in the other it crosses them over.

The bench

The diagram in Theory keeps the order of the bench from left to right; the source is drawn below the row. A 4.5 V source \(U\), two two-way switches \(S_1\) and \(S_2\) and a 4.5 V / 1 W lamp \(L\). The "+" of the source goes to the common terminal of \(S_1\), and the common terminal of \(S_2\) to the lamp. \(S_2\) is turned over, so its terminal "1" is at the top, level with "2" of \(S_1\): the two yellow wires, the travellers, run straight across but join terminals with different numbers, "1" of \(S_1\) to "2" of \(S_2\) and "2" of \(S_1\) to "1" of \(S_2\). Both switches are in position "1", and the lamp is off. A tap on a lever moves it one step, from "1" to Open and on to "2": to flip a switch, drag its lever all the way across or tap it twice.

Procedure

1. Draw a table with the columns \(S_1\), \(S_2\) and lamp. With both switches in position "1", write down whether the lamp is lit.
2. Flip \(S_1\) to position "2" and write down whether the lamp is lit.
3. Flip \(S_2\) to position "2" and write it down.
4. Flip \(S_1\) back to position "1" and write it down.
5. Tap the lever of \(S_1\) once: it stops in the middle, in the position Open. Flip \(S_2\) to "1" and back to "2", and write down whether the lamp lights.
6. On the diagram, trace the path of the current for each row of your table in which the lamp is lit.

Expected result

The lamp is lit when the switches are in positions with different numbers, and goes out when the numbers are the same: each flip of either switch changes the state of the lamp. With \(S_1\) in Open the lamp stays off whatever \(S_2\) shows: the common terminal of \(S_1\) touches neither traveller.

\(S_1\)	\(S_2\)	Lamp
1	1	off
2	1	on
2	2	off
1	2	on
Open	1	off
Open	2	off

Questions

1. Imagine two ordinary switches in place of the two-way ones, first in series, then in parallel. For each case, find a position of one switch in which the other can no longer change the lamp.
2. Both switches start in position "1", yet the lamp is off. Use the diagram to explain why.
3. What happens if, on \(S_2\), the two travellers are swapped, each to the other numbered terminal?
4. Compare your table with the tables of the lab "AND" and "OR" switches. Say in words when the lamp is lit.

Answers

1. In series the lamp is lit only when both switches are closed: while one of them is open, the other cannot turn the lamp on. In parallel the lamp is lit when either of them is closed: while one of them is closed, the other cannot turn it off. A two-way switch moves the current from one traveller to the other, so each switch can always both turn the lamp on and turn it off.
2. In position "1" the lever of \(S_1\) is on the lower traveller, which goes to "2" of \(S_2\), while the lever of \(S_2\) is on its terminal "1", on the upper traveller. The levers are on different travellers, so the circuit is open.
3. The travellers then join terminals with the same numbers, "1" to "1" and "2" to "2". The table turns over: the lamp is lit when the numbers are the same and off when they differ, and each flip still switches it on or off.
4. The lamp is lit when exactly one of the switches is in position "2", that is, when the numbers differ. This is neither "AND" nor "OR": logic calls it "exclusive OR", and changing either input changes the output.