Step-by-step explanation:
Line current: To find the line current, we can use the formula:
I = P / (√3 * V * cos(Φ))
where:
I = line current (A)
P = power per phase (W)
V = line-to-line voltage (V)
cos(Φ) = power factor (lagging, so cos(Φ) = 0.8)
Plugging in the values:
I = 6 kW / (√3 * 240 V * 0.8) = 20.5 A
Phase current: To find the phase current, we divide the line current by √3:
I_phase = I / √3 = 20.5 A / √3 = 11.7 A
Total power: To find the total power, we multiply the power per phase by 3:
P_total = 3 * 6 kW = 18 kW
Apparent power: The apparent power, S, can be found using the formula:
S = √(P^2 + Q^2)
where:
P = real power (W)
Q = reactive power (VAR)
To find the reactive power, Q, we can use the formula:
Q = P / tan(Φ) = P / tan(arccos(cos(Φ)))
Plugging in the values:
Q = 6 kW / tan(arccos(0.8)) = 7.5 kVAR
S = √(6 kW^2 + 7.5 kVAR^2) = √(36 + 56.25) kVA = 9 kVA
The results show that the balanced delta-connected load is supplied by a 60-Hz three-phase source with a line voltage of 240V and draws a total of 18 kW of real power at a lagging power factor of 0.8. The line current is 20.5 A and the phase current is 11.7 A. The apparent power is 9 kVA.