Question

A balanced delta-connected load (16 + j12)Ω/phase is connected to a 3-phase 230 V balanced supply. The line current and the real power drawn respectively are
1. 19.9 A and 3.17 kW
2. 11.5 A and 6.34 kW
3. 19.9 A and 6.34 kW
4. 11.5 A and 3.17 kW

Answer 1

Correct Answer - Option 3 : 19.9 A and 6.34 kW

Concept:

In a three-phase balanced system,

Real power (P) = √3 V_L­I_L cos ϕ

Reactive power (Q) = √3 V_L­I_L sin ϕ

In a star-connected three-phase system,

VL = √3 × Vph

And IL = Iph

\({I_{ph}} = \frac{{{V_L}}}{{\surd 3Z}}\)

In a delta connected three-phase system,

VL = Vph

IL = √3 × Iph

\({I_{ph}} = \;\frac{{{V_L}}}{Z}\)

Where,

VL is line voltage

Vph is phase voltage

IL is line current

Iph is the phase current

Calculation:

The given load is a delta connected load.

VL = 230 V

Inductive reactance = X = 12 Ω

R = 16 Ω

Impedance Zph = (16 + j12) Ω = 20∠ 36.86

ϕ = 36.86°

Power factor = cos ϕ = 0.8

Phase current \({I_{ph}} = \frac{{230}}{{20}} = 11.5\;A\)

Line current, I_L = √3I_ph = √3 × 11.5 = 19.9 A

Real power = √3 × 230 × 19.9 × 0.8 = 6.34 kW