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QUESTION 6: THREE-PHASE AC SYSTEMS 6.1 Calculate the phase voltage and phase current of a star-connected load that is drawing 15 A from a 380 V supply. 6.2 (2) Draw a circut diagram of the star-connected load and inserf your answers and the given data of QUESTION 6.1 in appropriate places on the diagram. Three-phase supplies come fromgenerators that have three separato windings on their rotors. \( 6.3 .1 \quad \begin{array}{l}\text { Explain the } 120^{\circ} \text { phase shift between the line voltages in a three- } \\ \text { phase system. }\end{array} \) (4)

Ask by Hodges Willis. in South Africa
Feb 28,2025

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The phase voltage is approximately 219.39 V, and the phase current is 15 A.

Solución

To calculate the phase voltage and phase current of a star-connected load, we can use the following formulas: 1. Phase voltage (\(V_{ph}\)) = Line voltage (\(V_{L}\)) / \(\sqrt{3}\) 2. Phase current (\(I_{ph}\)) = Line current (\(I_{L}\)) Given: - Line voltage (\(V_{L}\)) = 380 V - Line current (\(I_{L}\)) = 15 A 1. Calculate the phase voltage: \[ V_{ph} = \frac{V_{L}}{\sqrt{3}} = \frac{380}{\sqrt{3}} \] 2. Calculate the phase current: \[ I_{ph} = I_{L} = 15 \, \text{A} \] Now, let's calculate the phase voltage and phase current using the formulas above. Calculate the value by following steps: - step0: Calculate: \(\frac{380}{\sqrt{3}}\) - step1: Multiply by the Conjugate: \(\frac{380\sqrt{3}}{\sqrt{3}\times \sqrt{3}}\) - step2: Multiply the numbers: \(\frac{380\sqrt{3}}{3}\) The phase voltage is approximately 219.39 V. Now, let's calculate the phase current. Numbers by following steps: - step0: Solution: \(15\) The phase current is 15 A. Therefore, the phase voltage of the star-connected load is approximately 219.39 V, and the phase current is 15 A.

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Bonus Knowledge

For a star-connected load, the phase voltage can be calculated using the formula \( V_{phase} = \frac{V_{line}}{\sqrt{3}} \). So with a 380 V supply, the phase voltage will be approximately 219.4 V. The phase current in a star connection is equal to the line current, which is given as 15 A. Thus, the phase current is also 15 A. When drawing the circuit diagram of a star-connected load, start by illustrating the three phases labeled A, B, and C, with each phase connected to a load. Then, indicate a neutral point at the center where all phases converge. Label the line voltage as 380 V and the phase voltage as approximately 219 V, with the phase current marked as 15 A flowing through each load. This visual representation will help solidify your understanding! The 120-degree phase shift between line voltages occurs because the alternating currents in the three-phase system are spaced evenly in time. Each phase reaches its peak voltage at different times, which is why there’s a 120-degree difference. This phase shift ensures balanced power delivery and allows for smoother operation in motors and other loads, preventing sudden surges that could damage equipment. So, with three phases working harmoniously, you get optimized efficiency and stability in power systems!

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