Electrical Engineering ⇒ Topic : Power Determination Using Complex Notation

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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
figure (a)
Fig. (a) shows the phasors V and I resolved into rectangular components. The component V_{1} of voltage and component I_{1} of current are in phase and contribute to true power given by P_{1} = V_{1} I_{1} The component V_{2} of voltage and component I_{2} of current are 180° out of phase and, therefore,contribute to negative true power given by P_{2} = V_{2} I_{2} The components V_{2 }and I_{1} as well as V_{1} and I_{2} are 90° out of phase and contribute to no power.Therefore, total power P consumed in the circuit is the algebraic sum of P_{1 }and P_{2} because power is a scalar quantity. Total power consumed, P = P_{1}+ P_{2} = (V_{1}I_{1}) + (V_{2}I_{2}) P = V_{1}I_{1}  V_{2}I_{2} Hence the total power consumed in an a.c. circuit is the algebraic sum of product of inphase 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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