Explain the advantages of three-phase supply for distribution purposes. (b) Assuming the relationship between the line and phase values of currents and voltages, show that the active power input to a three-phase balanced load is √3VI cos φ, where V and I are line quantities. (c) Three similar inductors, each of resistance 10 Ω and inductance 0.019 H, are delta-connected to a three-phase, 400 V, 50 Hz sinusoidal supply. Calcu late: the value of the line current; the power factor and the active power input to the circuit. ANS:  59.5 A, 0.858 lag, 35.5 kW

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A three-phase, 400 V, star-connected motor has an output of 50 kW, with an efficiency of 90 per cent and a power factor of 0.85. Calculate the line current. Sketch a phasor diagram showing the voltages and currents. If the motor windings were connected in mesh, what would be the correct voltage of a three phase supply suitable for the motor? ANS:  90.8 A, 240 V

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Show with the aid of a phasor diagram that for both star- and delta-connected balanced loads, the total active power is given by √3VI cos φ, where V and I are the line values of voltage and current respectively and φ is the angle between phase values of voltage and current. A balanced three-phase load consists of three coils, each of resistance 4 Ω and inductance 0.02 H. Determine the total active power when the coils are (a) star-connected, (b) delta-connected to a 400 V, three phase, 50 Hz supply.  ANS:11.56 kW, 34.7 kW

The load connected to a three-phase supply comprises three similar coils connected in star. The line currents are 25 A and the apparent and active power inputs are 20 kVA and 11 kW respectively. Find the line and phase voltages, reactive power input and the resistance and reactance of each coil. If the coils are now con nected in delta to the same three-phase supply, calculate the line currents and the active power taken.  ANS :  462 V, 267 V, 16.7 kvar, 5.87 Ω, 8.92 Ω; 75 A, 33 kW

A three-phase delta-connected load, each phase of which has an inductive reactance of 40 Ω and a resistance of 25 Ω, is fed from the secondary of a three-phase star-connected transformer which has a phase voltage of 230 V. Draw the circuit diagram of the system and calculate: (a) the current in each phase of the load; (b) the p.d. across each phase of the load; (c) the current in the transformer secondary windings; the total active power taken from the supply and its power factor.

Derive the numerical relationship between the line and phase currents for a balanced three-phase delta connected load. Three coils are connected in delta to a three-phase, three-wire, 400 V, 50 Hz supply and take a line current of 5 A 0.8 power factor lagging. Calculate the resistance and inductance of the coils. If the coils are star-connected to the same supply, calculate the line current and the total power. Calculate the line cur rents if one coil becomes open-circuited when the coils are connected in star.  Ans: 110.7 Ω, 0.264 H; 1.67 A, 926 W; 1.445 A, 1.445 A, 0

Derive, for both star- and delta-connected systems, an expression for the total power input for a balanced three-phase load in terms of line voltage, line current and power factor. The star-connected secondary of a transformer supplies a delta-connected motor taking a power of 90 kW at a lagging power factor of 0.9. If the volt age between lines is 600 V, calculate the current in the transformer winding and in the motor winding. Draw circuit and phasor diagrams, properly labelled, showing all voltages and currents in the transformer secondary and the motor. ANS:  . 96.2 A, 55.6 A