5.4 Balanced three-phase systems 113

1 The voltage across each resistor is the phase voltage, and from Equation
(5.1)
VpH = VL/X/3 : 440/X/3 : 254 V

2 The phase current is

IpH = VpH/ZPH = 254/10 = 25.4 a

Since this is a star connection the line current is IL = IpH = 25.4 A.

3 Let the resistor in the B phase become open circuited. The circuit now
consists of the other two resistors connected in series across 440 V. The
current in line B is IL = 0. The current in line A equals that in line C:
IB -- Ic- 440/(10 + 10) = 22 A

Example 5.2

Three identical coils having a resistance of 3 1) and an inductive reactance of
4 D are connected in star to a three-phase supply whose line voltage is 240 V.
Determine (1) the voltage across each coil, (2) the current drawn from the
supply, (3) the power factor.

Solution

Fig. 5.11 shows the circuit.

Figure 5.11

V L : 240V

4D

vPHT

1 VpH- VL/X/3- 240/X/3- 139 V.

2 le = IpH VpH/ZPH = 139/X/(32 + 42) -- 139/5 = 27.8 A.

3 The power factor is cos 4, - R/Z - 3/5 = 0.6 lagging.