Electrical Engineering ⇒ Topic : Power Determination Using Complex Notation
Power Determination Using Complex Notation
If the voltage and current in an a.c. circuit are expressed in complex form, we can easily determine the true power or active power consumed in the circuit. Let the circuit voltage and circuit current be expressed as
Fig. (a) shows the phasors V and I resolved into rectangular components. The component V1 of voltage and component I1 of current are in phase and contribute to true power given by
P1 = V1 I1
The component V2 of voltage and component I2 of current are 180° out of phase and, therefore,contribute to negative true power given by
P2 = -V2 I2
The components V2 and I1 as well as V1 and I2 are 90° out of phase and contribute to no power.Therefore, total power P consumed in the circuit is the algebraic sum of P1 and P2 because power is a scalar quantity.
Total power consumed, P = P1+ P2 = (V1I1) + (-V2I2)
P = V1I1 - V2I2
Hence the total power consumed in an a.c. circuit is the algebraic sum of product of in-phase components of V and I and the product of quadrature components of V and I. Note that operator j is not to be included in the multiplication.
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