Answer to Question #124163 in Electricity and Magnetism for victoria

Question

A three–phase transformer has its primary winding delta-connected and its secondary winding starconnected. The number of turns per phase on the primary is four times that on a secondary, and the secondary line voltage is 400V. A balanced load of 20kW, at power factor 0.8, is connected across the secondary terminals. Assuming an ideal transformer, calculate the primary voltage and the phase and line currents on the secondary and primary sides. Sketch a circuit diagram and indicate the values of the voltages and currents on the diagram.

Answer 1

As per the given question,

Let the number of turns in the primary winding =4N

Hence number of turns in the secondary winding=N

Voltage of the secondary voltage line=400V

Balance load (P)=20kW

Power factor =0.8

$\Rightarrow \frac{N_{ph1}}{N_{ph2}}=\frac{V_{ph1}}{V_{ph2}}$

$\Rightarrow V_{ph1}=\frac{N_{ph1}}{N_{ph2}}V_{ph2}$

$\Rightarrow V_{ph1}=\frac{4N}{N}\times 400V=1600V$

Primary voltage=$\sqrt{3}V=1600\sqrt{3}Volt$

Apparent power $=\frac{20kW}{0.8}=25kW$

$\Rightarrow I=\frac{A}{V}=\frac{25000W}{400V}=62.5A$