# Homework Help: Supplied complex power from source vs consumed by load

1. Oct 27, 2016

### eehelp150

1. The problem statement, all variables and given/known data

2. Relevant equations
S= 3VaIa*

3. The attempt at a solution
After transformation:

Ia = 120<0 / (6+8j) = 12<-53.13 A
Total complex power = 3 * Va * Ia* = 3*120<0 * 12<53.13 = 2592W + j3456 VAR
This is the power supplied from source. What would be the power consumed by load?

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2. Oct 27, 2016

### cnh1995

You know the load impedance and load current. How will you determine the active and reactive power associated with the load?

3. Oct 27, 2016

### eehelp150

Load impedance = 5 + j6
I*I*Z
?

4. Oct 27, 2016

### cnh1995

Yes. Take magnitudes only.
S=I2Z.

Last edited: Oct 27, 2016
5. Oct 27, 2016

### eehelp150

So 144 * (5+j6)
?

power of (1+j2)= 144 * (1+2j)
and
combined become 864W + j1152VAR

but the total complex power is 2592W + j3456VAR

Is it right for these values to not match?

Last edited: Oct 27, 2016
6. Oct 27, 2016

### cnh1995

Yes.
Yes. Can you say why?

7. Oct 27, 2016

### eehelp150

Is it because it's 1/3 of the "actual" circuit?
Do I need to multiply by 3 to get the total complex power consumed by load?

If no, does this look correct?
720W + j864VAR

S = sqrt(Q^2+P^2) = 1124VA
PF = P/S = 720/1124 = 0.64 lagging (Q>0)
correct?

8. Oct 27, 2016

### cnh1995

Well, you calculated the total power for three phases. So, you should multiply the load power by 3. But they are not equal because out of total input power, some power is associated with the line impedance 1+j2 ohm. Remaining power is fed to the load.

9. Oct 27, 2016

### eehelp150

If the prompt is:
Calculate the total complex power consumed by the load and determine the load's power factor

Do I use what I calculated (720W + j864VAR) or do I need to multiply that by 3?

10. Oct 27, 2016

### cnh1995

You should multiply by 3. You have transformed the circuit into its per phase equivalent. Total power will be thrice the per phase power.
Here, while applying S=I2Z, you should consider the magnitude only. If you want to use the phasor form, you should take the conjugate of the current i.e. (IZ)(I*).

11. Oct 27, 2016

### eehelp150

If the prompt is:
Calculate the total complex power consumed by the load and determine the load's power factor

Do I use what I calculated or do I need to multiply that by 3?
So magnitude of (5+j6) = sqrt(61)?

12. Oct 27, 2016

### cnh1995

For load power factor, you can use the single phase equivalent network since it is a balanced network.
Yes.

13. Oct 27, 2016

### eehelp150

so load would be 3 * 144*sqrt(61)?
How do i get power factor from this?

Last edited: Oct 27, 2016
14. Oct 27, 2016

### cnh1995

If the load impedance is R+jX, what would its power factor?