The domestic electrical grid: 230 V - 50 Hz

Characteristics of the mains supply in France

In French electrical outlets, the voltage follows the law:

u(t) = 325 * sin(2pi50*t)

This means an amplitude Umax = 325 V, a frequency f = 50 Hz, and therefore an RMS value Ueff = 325/sqrt(2) = 230 V. It is this last value that is indicated on household appliances.

Standards vary by country

Country / region	RMS voltage	Frequency
France, Europe	230 V	50 Hz
United States	120 V	60 Hz
Japan (East zone)	100 V	50 Hz
Japan (West zone)	100 V	60 Hz

This is why some electronic devices require a voltage adapter when traveling.

Electrical safety

Alternating mains current is dangerous starting at 50 V in dry conditions and at 25 V in wet conditions. The live and neutral wires, together with the earth, protect users via residual-current circuit breakers that cut the circuit in case of a current leak.

Common pitfall

Be careful: when we say the mains supply is "230 V", it should not be assumed that the instantaneous voltage stays at 230 V at all times. It continuously oscillates between -325 V and +325 V, fifty times per second; 230 V is only the RMS value, a quadratic mean.