Problem 84-4    Source:   Problem elaborated by the author of the site.

Using the data from the previous problems, compare the results of power in the load with the power supplied by the source.

Solution of the Problem 84-4

From the previous problem (84-2) we calculated the line currents. So, there are the following data to solve this problem:

V_AN = 100 ∠30°,  V_BN = 150 ∠-60°   V_CN = 120 ∠180°  and

I_A = 19.26 ∠19.6°  ,   I_B = 18.83 ∠-59.7°,     I_C = 29.32 ∠160.4°

With this data it is possible to calculate the power supplied by the source. So:

Let's write these power in Cartesian form. Like this:

Adding real part with real and imaginary part with imaginary, we will get the total active power and the total reactive power. Like this:

Therefore, the total apparent power will be:

By comparing these values with those found in problem 84-3, we clearly perceive the conservation of energy. The small discrepancies in the values occur due to the rounding done during the solution of the problems.