2.1 Name the instrument that is used to measure electrical energy - NSC Electrical Technology Electronics - Question 2 - 2016 - Paper 1

1. Higher Efficiency: Three-phase systems can transmit more power over the same conductor size compared to single-phase systems, minimizing power losses.

2. Smoother Power Delivery: Three-phase systems provide a more constant voltage and power supply, which reduces vibrations in motors and improves overall performance.

The sketch should illustrate three sinusoidal waveforms, each 120 degrees apart. The y-axis represents voltage, and the x-axis represents time. Each waveform should be labeled as Phase A, Phase B, and Phase C, with their respective peaks and troughs clearly marked.

To calculate the line voltage in a star-connected system, we use the formula:

V_L = rac{S}{rac{ ext{sqrt}(3)}{I_L}}

Substituting in the values:

V_L = rac{20,000 ext{ VA}}{rac{ ext{sqrt}(3)}{25 ext{ A}}}

Calculating gives:

$V_L = 267.67 ext{ V}$

Phase voltage in a star-connected system is given by:

V_P = rac{V_L}{ ext{sqrt}(3)}

Substituting in the previously calculated line voltage:

V_P = rac{267.67 ext{ V}}{ ext{sqrt}(3)}

This results in:

$V_P = 154.78 ext{ V}$

The total input power in a two-wattmeter system is calculated as:

$P_T = P_1 + P_2$

Substituting the given values:

$P_T = 8 ext{ kW} + 4 ext{ kW} = 12 ext{ kW}$

The line output power can be calculated using the formula:

$P_{out} = P_T imes ext{pf}$

With the power factor of 0.8, we find:

$P_{out} = 12 ext{ kW} imes 0.8 = 9.6 ext{ kW}$