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A balanced three-phase system has a load consisting of a balanced star in parallel with a balanced delta. The impedance per phase for the star is 8+j6 ohms and for delta is 24+j18 ohms. The impressed voltage is 240√3 line to line.

Calculate the line current.

User Xitalogy
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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

User George Brown
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