Final answer:
The formula for three-phase real power (P) is the sum of the power dissipation in each phase, which should equal the power output of the source due to energy conservation. Power can also be expressed using Ohm's Law in the forms P = V^2/R or P = I^2R, based on known quantities.
Step-by-step explanation:
The formula for real power (P) in a three-phase electrical system can be found by considering the power dissipation in each phase and the conservation of energy principle. The total real power in a three-phase system is the sum of the power in each phase. If we have three resistors with power dissipation labeled as P₁, P₂, and P₃, respectively, the total power can be found by summing each of these individual powers. According to conservation of energy, the power output of the electrical source must be equal to the total power dissipated by resistors in the system.
To express real power in terms of voltage and current, we can use Ohm's Law (V = IR) along with the basic power formula P = IV. Through substitution, we obtain multiple expressions for electric power: P = V2/R, P = I2R, and P = IV. The specific formula to be used depends on the known quantities.
For example, if we have three resistors with power dissipations of 0.360 W, 2.16 W, and 4.68 W, the total power P is the sum of these, which is 7.20 W. This demonstrates that the power supplied by the source is equal to the power dissipated by the resistors, illustrating the conservation of energy within the system.