Three non-inductive resistances, each of 100 ohms, are connected in st

1.	Three non-inductive resistances, each of 100 ohms, are connected in star to a three-phase, 440-V supply. Three inductive coils, each of reactance 100 ohms connected in delta are also connected to the supply. Calculate: (i) Line-currents, and (ii) power factor of the system.
Answer» (a) Three resistances are connected in star. Each resistance is of 100 ohms and 254 – V appears across it. Hence, a current of 2.54 A flows through the resistors and the concerned power-factor is unity. Due to star-connection, Line-current = Phase-current = 2.54A (b) Three inductive reactance are delta connected. Line-Voltage = Phase – Voltage = 440 V Phase Current = 440/100 = 4.4 A Line current = 1.732 × 4.4 = 7.62 A The current has a zero lagging power-factor. Total Line Current = 2.54 - j 7.62 A = 8.032 A, in each of the lines. Power factor = 2.54/8.032 = 0.32 Lag.

Three non-inductive resistances, each of 100 ohms, are connected in star to a three-phase, 440-V supply. Three inductive coils, each of reactance 100 ohms connected in delta are also connected to the supply. Calculate: (i) Line-currents, and (ii) power factor of the system.

Answer»

(a) Three resistances are connected in star. Each resistance is of 100 ohms and 254 – V appears across it. Hence, a current of 2.54 A flows through the resistors and the concerned power-factor is unity. Due to star-connection,

Line-current = Phase-current = 2.54A

(b) Three inductive reactance are delta connected.

Line-Voltage = Phase – Voltage = 440 V

Phase Current = 440/100 = 4.4 A

Line current = 1.732 × 4.4 = 7.62 A

The current has a zero lagging power-factor.

Total Line Current = 2.54 - j 7.62 A

= 8.032 A, in each of the lines.

Power factor = 2.54/8.032 = 0.32 Lag.

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