Problem 83-1    Source:   Problem elaborated by the author of the site.

In the balanced circuit of the Figure 83-1.1, assuming a direct sequence, we have:

V_C = 220 ∠30°  , and   Z_A = Z_B = Z_C = 10∠45° . Calculate:

a) The line and phase voltages.

b) The phase and line currents.

c) The total real, total reactive and apparent total power in the load.

Solution of the Problem 83-1

Item a

How line voltage is known V_CA, then V_BC should be advanced by 120° in relation to V_CA and V_AB delay of 120°, because the sequence is direct. Soon:

In order to calculate the phase voltages, just apply the eq. 83-03 below. Remember that the tensions corresponding line and phase are those that begin with the same index letter. So:

Item b

Since the circuit is in a star configuration, the current of phase and the current of line are the same. Soon:

Item c

In the calculation of the apparent power modulus, we use the eq. 82-01 below:

Making the substitution by the numerical values and taking the calculation:

As the circuit is balanced the angle of the apparent power is the same as the impedance, that is, 45°. Then:

And in Cartesian form:

We know that the real part of the apparent power is active power and the imaginary a reactive power, then: