When estimating power consumption with a current sensor, what is the usual precision that can be achieved for home appliances? I'd like to make a simple circuit using such a sensor and a microcontroller to collect the measurements and estimate consumed power.
For an ideal resistor, we can compute power as I²R. But for an ideal capacitor or inductor, this would be very different. For example, an ideal inductor/capacitor connected to an AC would have 0 average power regardless of current, so I²R over-estimates the actual value.
How much can the above ideal resistor estimate be off for devices that contain inductors, such as motors? And can it ever under-estimate?