Switches

Switches: ON/OFF operation, resistance R_on and loss P_on = I2 R_on. Theory, formulas, worked examples and applications.

Conceptual context

A switch is a device that opens or closes an electrical circuit mechanically or electronically. In a domestic installation, wall switches control lights; appliance switches control motors and heating elements; thermostats are temperature-controlled switches. In all these cases, the physical function is the same: to allow or cut the flow of current $I$ between the supply voltage $V$ and the load of power $P$.

The ideal switch does not exist in practice. A real switch presents in ON state (closed) a non-zero resistance $R_{on}$ that generates a loss $P_{on}$ by the Joule effect. That heat is dissipated in the metallic contacts of the switch. If $P_{on}$ is large enough or the conduction time $t_{on}$ is long enough, the accumulated energy $E_{on}$ can degrade the contacts, reduce the switch service life, and in extreme cases create a fire risk.

🟢 Essential level

A switch has two states: OFF (open, no current flows) and ON (closed, with current $I$ flowing). The current demanded by the load depends on its power and on the installation's voltage.

When the switch contact is worn or oxidized, it presents a non-zero resistance that generates heat through the Joule effect. That heat accumulates in the metallic contacts. If the conducted current is high or the usage time is long, the heating can degrade the contact and reduce the switch's service life.

A new, quality switch barely heats up because its contact resistance is very small. An aged switch can heat up noticeably even with moderate loads — a sign that it needs replacing.

An everyday example helps tell the two cases apart: the living-room lamp switch, with a low-consumption bulb, practically never heats up in its whole service life. A powerful electric heater's switch, by contrast, can feel noticeably warm to the touch after a while of continuous use, precisely because it carries a much larger current through the same contacts.

🔵 Formal level

Basic formulas

The complete causal chain starts from circuit data. The voltage $V$ and load power $P$ determine the switching current $I$ of the switch:

Switching current

With that $I$ and the contact $R_{on}$ of the switch, the resistive loss is:

Resistive loss in ON state

If the switch operates for a time $t_{on}$, the energy dissipated in its contacts is:

Energy dissipated during conduction

Real student questions

Why does the heater switch heat up but not the light switch? Because the heater current is 30–50 times larger than the bulb current, and $P_{on}$ ∝ $I$². The same $R_{on}$ produces 900–2,500 times more heat with the heater.

Does a switch with high $R_{on}$ protect against overloads? No. High $R_{on}$ generates heat in the switch itself but does not significantly limit the load current. For current limitation, a fuse or MCB is needed, not a degraded switch.

Can $R_{on}$ be measured at home? Yes, with a milliohm-resolution multimeter (low resistance measurement function, typically marked "Low Ω" or "mΩ"). With a basic multimeter it is difficult because the resolution is insufficient to distinguish between 0.01 and 0.1 Ω.

Final synthesis

The ideal switch has $R_{on}$ = 0 and dissipates no energy. The real switch has $R_{on}$ > 0 and generates $P_{on}$ = $I$² · $R_{on}$ when conducting. The loss grows with the square of $I$: high-power switches have the greatest contact thermal risk. The accumulated energy $E_{on}$ = $P_{on}$ · $t_{on}$ determines whether heating is significant over the usage period. A switch with heating symptoms (surface temperature > 40 °C, smell, discolouration) must be inspected or replaced regardless of whether the current is within the nominal range, because the problem is elevated $R_{on}$, not circuit overload.