Power in pure inductive circuits:
The voltage leads the current by 90° in a pure inductive circuit. Let the voltage and current at any instant be respectively represented by
V=Vm sin(wt+90°) and i = Im sin wt
The instantaneous power is given by
p = vi
=(1/2) Vm lm Sin (wt+90°) sin wt
=(1/2) Vm lm (2cos wt sin wt)
= (1/2)Vm Im Sin 2wt
Active Power or Avg Power:
Therefore, in a pure inductive circuit, the active supplied over a complete cycle average out to zero.
The power supplied to a reactance (inductive or capacitive) is termed reactive power. Unlike active power denoted by symbol P, the reactive power is denoted by symbol Q and given the name volt-amp-reactive (var). Let us now see how the reactive power is calculated.
The peak value of instantaneous power is given by
For a Pure Inductive circuit
Here Q is the rate of change of reactive energy between the load and the source. By convention, Q is taken as positive and is called the lagging reactive power.