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1. A 380 / 220 V r.m.s. 3-phase 4-wire circuit carries loads of 8 + j8.1 ohm; 4 + j4.1 ohm; and 2 +j2.1 ohmin the three phases respectively. The length of the circuit is 100 m, and the resistivity of the phase conductors is 0.0005 Ω/m. The neutral conductor is of the same size as the phase conductors. a) Select a reference angle 0for the first phase. Then write down the three phase voltages in both polar format and complex number format. b) Make appropriate assumptions, and take temperature effects on resistance is insignificant. Calculate the currents in the three phases. (Note: Determine conductor resistance, and apply Kirchhoff’s Voltage Law) Based on the result, suggest a main switch rating for the circuit. c) Show your preferred direction of neutral current in a diagram, and then determine its value. (Note: Apply superposition principle, and Kirchhoff’s Current Law) Use its magnitude to show that in this circuit, the unbalanced load may increase the voltage drop in some of the phases. (Note: Also observe the common volt drip in neutral) State your assumptions, if there are any. d) Suddenly the neutral wire of the circuit is broken. Estimate the new currents in the first phase, i.e. Phase L1. State your assumptions, if there are any.
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