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Q3. (a) Three identical coils of impedance Z are to be connected to a balanced three-phase a.c. power supply of line voltage . When the coils are star connected, the line currents are one third of the line currents when delta connected.

Using relationships for balanced three-phase circuits, show that this ratio is correct. (4)

(b) Three identical coils connected in delta across a three-phase, 415 V, 50 Hz power supply have a total power demand of 12 kW with line current of 25 A.

(i) Calculate the supply power factor. (2)

(ii) Determine the resistance and inductance of each coil. (6)

(c) The supply frequency is now raised to 60 Hz while the voltage remains constant.

Calculate the new line current and the total power supplied. (4)