Problem — the trip switch that trips

Problem

A person switches on the stereo, two lamps and the hairdryer, all plugged into different sockets in the same room. Suddenly the trip switch trips. Explain what happened in terms of total current and protection of the wiring.

Solution

All the sockets in a room are fed by the same line at the mains voltage $V \approx 230\ \text{V}$: the appliances are therefore effectively connected in parallel, all subjected to the same voltage.

In a parallel connection the currents add up: the line carries the sum of the currents drawn by the individual appliances. Each draws $i = P/V$, so the total current is $i_\text{tot} = \frac{P_\text{stereo} + P_\text{lamp} + P_\text{lamp} + P_\text{dryer}}{V}$

The hairdryer dominates: with $P_\text{dryer} \approx 2000\ \text{W}$ it alone draws $i \approx 2000/230 \approx 8{,}7\ \text{A}$. Adding the stereo ($\sim 50\ \text{W}$) and two lamps ($\sim 60\ \text{W}$ each) exceeds the threshold of the circuit breaker protecting the line (typically $10\text{–}16\ \text{A}$).

When the total current exceeds that threshold value, the protection trips, opening the circuit: this prevents the wiring, carrying excessive current, from overheating through Joule heating ($P = R\,i^2$) until the insulation melts and starts a fire.

In short: switching on several appliances in parallel does not divide the current but adds it up; once the capacity of the wiring is exceeded, the protection intervenes. The practical solution is to spread high-power loads across different lines or not to use them simultaneously.

$\ev{\text{the total current in parallel exceeds the capacity: the protection opens the line}}$

Links

Topics: Circuiti elettrici Concepts: Potenza