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simulate this circuit – Schematic created using CircuitLab I'm trying to understand if the average of instantaneous power is equal to real power. My reasoning is that the reactive components average out to zero and from there the average of that signal will give you just the power dissipated by the resistor. Is this true or do we always have to use P=IVpf.
Thanks
Instantaneous power is v x i from the perspective of the power source. So, you average that to produce average power.
Is the average of instanteous power equal to real power?
It sure is - that is what generates the heat in your resistor and that ultimately is what you get billed for.
I'm trying to understand if the average of instantaneous power is equal to real power.
Yes.
My reasoning is that the reactive components average out to zero ...
This is true only if their impedances match and cancel. In your example $$ Z_C = \frac {1}{2 \pi fC} = \frac {1}{2 \pi \cdot 60 \ 1 \mu} = 2653 \; \Omega $$ and $$ Z_L = 2 \pi f L = 2 \pi \cdot 60 \cdot 1 = 377 \; \Omega $$ so they don't balance. There will be a reactive component in your supply load.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Since the reactive and inductive vectors don't cancel out the result is the kVA vector and it is inductive.
... and from there the average of that signal will give you just the power dissipated by the resistor. Is this true or do we always have to use P=IVpf.
If you are measuring V and I at the supply then you need to use the power factor in your calculations. (If you measure V and I at the resistor then the power factor there will be unity.)
If you measure the instantaneous voltage and current at the power supply, the real power is the average of the instantaneous V X I. The reactive components average to zero. Internally to the load circuit, some or all of the reactive components may cancel out. Any reactive power that does not average to zero inside the load must average to zero between the load and the supply. The real and reactive power can be completely calculated from instantaneous measurements anywhere in the circuit. As long as you are careful about the +/- signs of the instantaneous values, you can calculate the real and reactive values for each circuit component and see that the real power furnished by the supply is equal to the real power dissipated by the resistor and that the reactive VA of the supply, capacitor and inductor sum to zero. The same results would be found using RMS values and power factors.
