# 3 Phase Machine Line Current problem

Hi guys,

I would really appreciate some help with this problem(probably quite easy for anybody with Electrical Engineering experience).

## Homework Statement

A 415V, 50Hz, 3-phase supply is connected to a 3 phase load of 10kw with a power factor of 0.8 lagging. Find the magnitude of the line currents.

## Homework Equations

P = VICos(power factor)

Total Power = 3 V(p)I(p)cos(power factor)

## The Attempt at a Solution

Attempted the question using the equations above, except I obtained the wrong answer.

Assuming the 415V is line to line rms and that the 10kW is the total wattage for all three phases:

$$V_{\phi}=\frac{V_{LL}}{\sqrt{3}}$$
with $$V_{\phi}$$ being a per phase voltage and $$V_{LL}$$ being the line-to-line voltage.

Next, we know that:
$$P_{3\phi} = 3V_{\phi}I_{\phi}PF$$
with PF = powerfactor. And if this is star connected...
$$I_{\phi}=I_{LL}$$

so
$$P_{3\phi}=3\frac{V_{LL}}{\sqrt{3}}I_{LL}PF=\sqrt{3}V_{LL}I_{LL}PF$$
or
$$I_{LL}=\frac{P_{3\phi}}{V_{LL}\sqrt{3}PF}$$

You seem to be confusing something. cos(angle) = PF. You don't say cos(PF). As far as I know, cos(PF) means nothing of importance.

Assuming the 415V is line to line rms and that the 10kW is the total wattage for all three phases:

$$V_{\phi}=\frac{V_{LL}}{\sqrt{3}}$$
with $$V_{\phi}$$ being a per phase voltage and $$V_{LL}$$ being the line-to-line voltage.

Next, we know that:
$$P_{3\phi} = 3V_{\phi}I_{\phi}PF$$
with PF = powerfactor. And if this is star connected...
$$I_{\phi}=I_{LL}$$

so
$$P_{3\phi}=3\frac{V_{LL}}{\sqrt{3}}I_{LL}PF=\sqrt{3}V_{LL}I_{LL}PF$$
or
$$I_{LL}=\frac{P_{3\phi}}{V_{LL}\sqrt{3}PF}$$

You seem to be confusing something. cos(angle) = PF. You don't say cos(PF). As far as I know, cos(PF) means nothing of importance.

Thanks very much!