Finding Total Power, Current & PF in a Circuit

In summary: You're welcome! Just remember, VA is the total apparent power, which is made up of both real (watts) and reactive (VAR) power components. So, VA = W + jVAR. But for calculating power factor, you only need to consider the real power (watts) and the total apparent power (VA).
  • #1
freshbox
290
0
(i)Find the total W, VAR, VA consumed and the power factor (Fp) in the circuit
(ii)Find the r.m.s value of the supply current I

For part I, power factor, I would like to ask for the explanation of the working:
1-0.65=0.35
Fp= Cosθ
=Cos0.35
=0.99 (Ans)

Why do you need to minus both Fp (1-0.65=0.35) to get the θ and how do you know it is not the other way round like 0.65-1 = -0.35?

And for part II, my working:
P=VICosθ
1250=(230)(Cos0.35)(I)
I=5.427A (Ans)

Book Answer is 6A, I would like to ask where I gone wrong, thank you.
 

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  • #2
What's the cos(0.35)? What's the cos(-0.35)?
 
  • #3
Hi SteamKing, I am trying to find the power factor..
 
  • #4
Oh Cos 0.35 = Cos-0.35. Then can you explain how come I need to deduct the Fp from load 1 and 2 to get the θ? Is it because θ=θv-θi ?Thanks.
 
  • #5
freshbox said:
(i)Find the total W, VAR, VA consumed and the power factor (Fp) in the circuit
(ii)Find the r.m.s value of the supply current I

For part I, power factor, I would like to ask for the explanation of the working:
1-0.65=0.35
Fp= Cosθ
=Cos0.35
=0.99 (Ans)

Why do you need to minus both Fp (1-0.65=0.35) to get the θ and how do you know it is not the other way round like 0.65-1 = -0.35?
I'm not sure of the context of this 'working' so I might be off target, but it looks a bit odd to me since the power factor 0.65 is already the cosine of an angle. So the operation cos(1 - 0.65) doesn't make a whole lot of sense to me. Also, 0.99 as the overall power factor doesn't look right to me. I'd expect it to be closer to 0.9.
And for part II, my working:
P=VICosθ
1250=(230)(Cos0.35)(I)
I=5.427A (Ans)

Book Answer is 6A, I would like to ask where I gone wrong, thank you.
If the angle is not 0.35, then that would explain the discrepancy.

Why not start by finding the VA and VAR for both loads (independently). The second load is simple because it has a power factor of 1; what does that tell you about its reactive power (VAR)?
 
  • #6
With reference to the attached picture below, I know how to solve this question. Because I can make use of the information given from the question to get Zt<θ where θ can be plug into the formula to find S,P,Q and pf.

However honestly speaking, I don't understand post#1 question at all. I cannot make use of the information to get Zt. I believe both question are the same, just different way of asking.

Would you be kind enough to explain it to me? Thanks.
 

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  • #7
freshbox said:
With reference to the attached picture below, I know how to solve this question. Because I can make use of the information given from the question to get Zt<θ where θ can be plug into the formula to find S,P,Q and pf.

However honestly speaking, I don't understand post#1 question at all. I cannot make use of the information to get Zt. I believe both question are the same, just different way of asking.

Would you be kind enough to explain it to me?


Thanks.

This new question involves a single load consisting of a resistor and inductor in series. Given the component values and the frequency of operation you can work out the net load (W, VA, VAR, Fp). The question in post #1 involves two separate loads with different power factors. The idea is to find the net load (W, VA, VAR, Fp) that the voltage supply sees, but since the components comprising the loads are not specified you need to use a slightly different approach than the other question.
 
  • #8
Load 1 VA:769.22
Load 2 VA: 750

769.22+750=1519.22 VA.

Book answer is 1379.7VA

And how do I go about solving the Fp? Do I add both Fp from Load 1,2 or...?
 
Last edited:
  • #9
Hi, can I also ask for the 2 question below, I am trying to find the power delivered to the circuit. Formula used is P=i2R.

For the 2nd question (right pic) my R is 16Ω because that is the only resistor.

For the 1st question (left pic) how do I determine my R since there is 2 resistor.
 

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  • #10
freshbox said:
Load 1 VA:769.22
Load 2 VA: 750

769.22+750=1519.22 VA.

Book answer is 1379.7VA

And how do I go about solving the Fp? Do I add both Fp from Load 1,2 or...?

VA's don't add that way. Think of the VA's as vectors with W and VAR components (look at your power triangle). Add the like components to find the sum of the VA's . Determine the new power factor from the new VA's components.
 
  • #11
freshbox said:
Hi, can I also ask for the 2 question below, I am trying to find the power delivered to the circuit. Formula used is P=i2R.

For the 2nd question (right pic) my R is 16Ω because that is the only resistor.
How did you arrive at 16Ω? The resistor is said to be 10Ω and everything else is in parallel with it, so how can the resistance be greater than that?
For the 1st question (left pic) how do I determine my R since there is 2 resistor.

You'll have to determine the impedance of the circuit. I'd suggest using complex arithmetic.
 
  • #12
Sorry it's 10 type wrong hehe. Can i say for a single resistor, i would use P=i2R
and for 2 or more resistor i use P=VICos(θv-θi)?
Thanks.
 
  • #13
freshbox said:
Sorry it's 10 type wrong hehe. Can i say for a single resistor, i would use P=i2R
and for 2 or more resistor i use P=VICos(θv-θi)?
I'm not sure that I understand the question.

In all cases you should find the equivalent impedance. The impedance will have real and imaginary (reactive) components. The real part of that impedance will be the resistance that dissipates energy.
 
  • #14
Va=var+watts?
 
  • #15
freshbox said:
Va=var+watts?

Look at the power triangle (the first post in this thread).
 
  • #16
I got it, thanks for your help.
 

1. What is total power in a circuit?

Total power in a circuit refers to the overall amount of power being delivered or consumed by all the components in the circuit. It is measured in watts (W) and can be calculated by multiplying the voltage (V) and current (I) in the circuit.

2. How do you calculate total current in a circuit?

Total current in a circuit is the sum of all individual currents flowing through each component. To calculate it, you can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R). Alternatively, if the circuit has multiple branches, you can use Kirchhoff's Current Law, which states that the total current entering a junction is equal to the total current leaving the junction.

3. What is power factor (PF) and why is it important?

Power factor (PF) is a measure of how efficiently a circuit is using the power it receives. It is the ratio of real power (watts) to apparent power (volt-amperes). A PF of 1 means all the power is being used effectively, while a PF less than 1 means there is some power being wasted. It is important to maintain a high PF to avoid wasting energy and to ensure the circuit is functioning properly.

4. How do you find the total power in a circuit with multiple components?

To find the total power in a circuit with multiple components, you can use the formula P = I^2 * R, where P is the power in watts, I is the current in amperes, and R is the resistance in ohms. Alternatively, if you know the voltage (V) and current (I) in the circuit, you can use the formula P = V * I.

5. How can you improve power factor in a circuit?

There are several ways to improve power factor in a circuit, including using power factor correction devices, adding capacitors to the circuit, and reducing the amount of reactive power (power that is not used effectively). It is important to regularly monitor and maintain the power factor in a circuit to ensure efficient energy usage and prevent potential issues such as overload or voltage drops.

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