It is designed to measure kWh, and to do so it measures
Voltage (Across Incoming Line)
Current (probably only in one leg, as the other would be symmetric with it)
Phase (offset between voltage sine wave and current sine wave)
Cable suitable for measuring current has to physically pass through a part of the equipment - usually a current transformer is placed around the current-carrying conductor. The most convenient designs have four large connection terminals - two in and two out (some more in 3-phase meters, of course) to make wiring operations easier. One can think of the meter as a black box in series with the supply, if that helps.
The instrument starts by continuously measuring the instantaneous power, using the calculations:
Power = Voltage × Current × Cosine (θ)
where is the phase offset measured between the two waves.
To convert this to kWh (which we pay for) the instantaneous power is integrated over time - for a static load that simplifies to kW x time, of course.
The resulting kWh is then stored in a non-resettable totalizer for display to the meter reader (or, in the case of smart meters, transmission to the supplier).
Mechanical meters used a pair of wound coils to drive a rotating wheel, one for voltage, one to drive a rotating wheel whose speed was the product of the two measurements, and one to measure actual power. Automatically ignored the reactive component. That wheel moved to a gear train that completed the revolutions.
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