If power is current times meter shouldn't the overall resistances and inductances and capacitances of my house appliances be known so the power meter could calculate the power. I look at my house as a closed circuit. some people say the amp meter measures the current that is used by the appliances but according to ohm's law I need to know the impedances to measure the current.The voltage is standard 120 rms volts.
The impedance is just the voltage phasor divided by the current phasor. If you measure both (as energy meters do) then the impedance could be known (it's a complex number in general). The impedance of a pure inductance or pure capacitance load will be imaginary (no real part).
However there is no need to calculate the impedance. The energy (what you pay for) is just the time integral of the instantaneous product of current and voltage. Since the meter measures both current and voltage, that is all that is needed.
In the case of old-school energy meters, it's done cleverly with a motor-like arrangement using eddy currents. Modern electronic energy meters do the calculations digitally after digitizing the current measurement (from a shunt, current transformer or Rogowski coil) and the voltage measurement (from a voltage divider or potential transformer).
The power meter measures voltage and current to the appliance. Those two values are multiplied by means of physic phenomena on rotating disc that is spinning with the rate of u * i * cos(phi). If you measure both current and voltage, then the impedance doesn't to be known, because the meter indirectly "senses" the change of impedance.