Household Electrical Network

The household network is a nearly constant AC voltage source; each load connected in parallel draws the current it needs.

Conceptual context

The domestic electrical network is the system that distributes electrical energy from the utility company to all receptors in a dwelling. Unlike a constant current source, the European network is designed to maintain a practically constant voltage of 230 V at a $f$ of 50 Hz, regardless of how many appliances are connected.

This constant voltage source behavior has fundamental physical implications. When we connect a receptor (a lamp, a refrigerator, a computer), it draws from the network the current it needs to operate, proportional to its power. The voltage does not decrease, but the total current flowing through the line increases. This is the central principle that explains why domestic circuits have power limits and why miniature circuit breakers (MCBs) exist as protection.

Understanding this model is essential for sizing installations, avoiding overloads, and comprehending the practical limitations of electricity in the home.

🟢 Essential level

The dominant physical idea is surprisingly simple: the electrical network always maintains 230 V, and each appliance you connect "requests" the current it needs. The network does not "send" current; rather, receptors extract it according to their power.

Imagine the network as a water tank at constant pressure (the voltage). When you open a tap, water flows out at a certain rate (the current). If you open more taps, the total flow rate increases, but the pressure remains constant as long as the system can supply the water. Only when you exceed the capacity of the pipes does the pressure begin to drop or a safety valve activates.

In electricity, the same thing happens. A 2000 W oven draws approximately 8.7 A from the network. If you also connect a 1500 W hair dryer, it draws another 6.5 A. The total current adds both: 15.2 A. The voltage remains 230 V, but the wiring and the MCB must withstand those 15.2 A without overheating.

The MCB (magnetotermico) is the guardian of the circuit. It is calibrated to withstand a maximum current (typically 16 A, 20 A, or 25 A in domestic installations). If the total current exceeds that limit, the device automatically cuts the supply to prevent fires from overheating of the wiring.

[!IMPORTANT] The network voltage does not decrease when you connect more appliances. The network is designed as a constant voltage source. What increases is the total current, not the voltage.

🔵 Formal level

Basic formulas

The resistive model operates within the context of the European network with its characteristic parameters:

Network frequency (context)

The mathematical relationship between power, voltage, and current is expressed through the fundamental formula of the resistive model:

Total line current

This equation establishes that the total current $I_{\mathrm{tot}}$ demanded by the installation is directly proportional to the total connected power $P_{\mathrm{tot}}$ and inversely proportional to the network voltage $V$, which remains constant at 230 V in the European standard.

The formula has a natural rearrangement that allows calculating power if we know the current:

Total supplied power

This pair of equations constitutes the mathematical core of the model. Both are valid exclusively for resistive loads with unity power factor, where active power coincides with apparent power.

Real student questions

Q: Why doesn't the voltage drop when I connect more appliances? A: Because the network is designed as a constant voltage source. Distribution transformers actively regulate the voltage. What increases is the total current, not the voltage.

Q: Can I change the 16 A MCB for a 25 A one to get more power? A: Only if the wiring is sized to safely carry 25 A without overheating. A 1.5 mm² cable cannot safely carry 25 A. Consult an electrician before changing ratings.

Q: Why does the refrigerator sometimes make the breaker trip when it starts? A: Motors have a starting current much higher than the nominal current (can be 6 times higher) for a few seconds. If the circuit is already loaded, that peak can momentarily exceed $I_{\max}$.

Q: Does the model fail with LEDs? A: LEDs have internal electronics (driver) that make them not behave as pure resistances. However, their consumption is so low that the model error is insignificant in practice.

Q: How do I know if I'm near the limit without doing calculations? A: Sum mentally: every 1000 W is approximately 4.3 A at 230 V. A 16 A circuit can support about 3600 W of continuous load. If you have an oven (2000 W) and a hair dryer (1500 W), you are already near the limit.

Final synthesis

The domestic electrical network operates as a constant voltage source of 230 V. Each receptor connected in parallel draws the current it needs according to its power, and the total current is the sum of all those individual currents. The MCB protects the installation by cutting the supply when the total current exceeds the safety limit of the wiring.

The resistive model, based on the relationship between $I_{\mathrm{tot}}$, $P_{\mathrm{tot}}$ and $V$, allows calculating the expected current and evaluating the usage margin of the circuit. However, this model has limitations: it fails with inductive loads, long lines, or when the wiring impedance is not negligible. Understanding these validity boundaries is as important as mastering the equations of the basic model.