Final answer:
To calculate the line current in a balanced three-phase system with a load consisting of a balanced star in parallel with a balanced delta, you can use the formula IL = VL / ZL, where IL is the line current, VL is the impressed voltage, and ZL is the total impedance of the load. considering the impedance per phase for the star (8+j6 ohms) and for the delta (24+j18 ohms), the total impedance can be calculated, and then the line current can be determined by substituting the values into the formula.
Step-by-step explanation:
In a balanced three-phase system with a load consisting of a balanced star in parallel with a balanced delta, the line current can be calculated using the formula:
IL = VL / ZL
Where IL is the line current, VL is the impressed voltage, and ZL is the total impedance of the load.
Considering the given impedance per phase for the star (8+j6 ohms) and for the delta (24+j18 ohms), the total impedance can be calculated as follows:
ZL = (1/Zstar + 1/Zdelta)^-1
Substituting the given values, we have:
ZL = (1/(8+j6) + 1/(24+j18))^-1
ZL = (1/8+j6 + 1/24+j18)^-1
ZL = (0.0985+j0.0428)^-1 ohms
Finally, substituting the impressed voltage (240√3 line to line) and the total impedance into the first formula, we can calculate the line current:
IL = 240√3 / ZL
IL= 1359.77∠5.608° Amps