Mumbai University > FE > Sem 1 > Basic Electrical and Electronics Engineering

Marks: 6 M

Year: May 2014, May 2015

1.Assumption:-

The 3-ø system considered here is a load, which is star connected.

The phase sequence is R→Y→B.

It is a balanced load.

The pf of each phase is logging.

2.Connection:-It is as shown in Fig (a)

3.Proof

Reading of wattmeter W1

$W_1=V_{AB}I_{RL}\cos(\angle between V_{AB})\& I_{RL} \\=V_LI_L \cos(3\theta^0-\emptyset_{ph})$

Reading of wattmeter W2

$W_2=V_{AB}I_{YL}\cos(\angle between V_{YB} \& I_{YL}) \\ =V_LI_L \cos (3\theta^0+\emptyset_{ph}) \\ \therefore (w_1+w_2)=V_LI_L\{\cos(3\theta^0-\emptyset_{ph})+\cos(3\theta^0+\emptyset_{ph})\} \\=\bigg\{2\cos\bigg(\dfrac{60^0}{2}\bigg)\cos\bigg(-\dfrac{2\emptyset_{ph}}{2}\bigg)\bigg\}V_LI_L \\ =V_LI_L\{2\cos3\theta^0 \cos \emptyset_{ph} \} \\ =V_LI_L\bigg\{7\times\dfrac{\sqrt3}{2},\cos \emptyset_{ph} \bigg\} \\ =\sqrt3 V_LI_L\cos \emptyset \\ =\text{Total powervconsumede by the 3} -\emptyset \text{load and hence the proof}$

Pharos Diagram