The term refers to the fact that there are three different ways the switch toggles can be arranged. An intermediate switch is a three way light switch.
Three Way Lights How Three Way Switches Work Howstuffworks
Intermediate light switch meaning. An intermediate switch is a hugely versatile switch that can be used for most situations however this does mean that it becomes more expensive and is only used where necessary. Intermediate switches are used for when there are three switches or more controlling one light. It is used when you have three or more switches controlling one light the middle switch needs to be an intermediate light switch. Turning the actuator does not initially cause any motion of the contacts which in fact continue to be positively held open by the force of the spring. The switch actuator does not control the contacts directly but through an intermediate arrangement of springs and levers. A characteristic feature of a single pole toggle switch is that it has on and off markings on the toggle.
Turning the actuator gradually stretches the spring. When both toggles are up or both are down the circuit is complete and the light fixture will be illuminated. This is something you will not find on three way or four way switches. The typical example of this is on a landing in a house when perhaps there is a switch at the bottom of the stairs one at the top of the stairs and one at the end of the landing. Intermediate switch is mostly used in a hall big rooms or godown where different lamps are needed to onoff from different places. On a staircase a light switch at the bottom and at the top of the stairs controlling the landing light circuit would be a 2 way circuit.
An intermediate light switch is where 3 lighting points control the same circuit. The single pole switch is the general purpose workhorse of switches. Both toggle levers up both toggle levers down or the toggle levers in opposite positions. It is used to control a light receptacle or other device from a single location. One light switch in a bedroom controlling say a central light would be a 1 gang 1 way light switch. If you need to control the lights from three places say you have 3 entrances to a large room and need a light switch next to each one you will need an intermediate switch.
Moreover in a multistory building the lamp at ground floor or in car parking shade can be controlled or on off from any floor by using intermediate switch circuit. These are often used on a stair case large room with switches by each door.