What is the power factor in a series circuit?

In summary, the conversation discusses calculating for PR / Pavg using the formula Irms^2 * R / Irms^2*Z = 15 /33.36 = 0.45, with a discrepancy between using 33.36 and 33.33 as the value for Z. The conversation also mentions a detailed calculation and confirms that the power factor is given by ##\cos\phi=\frac{R}{Z}##.
  • #1
hidemi
208
36
Homework Statement
A series circuit consists of a 15-Ω resistor, a 25-mH inductor, and a 35-μF capacitor. If the frequency is 100 Hz the power factor is:

The answer is 0.45
Relevant Equations
PR / Pavg = Irms^2 * R / Irms^2*Z
I calculated in the following and got the correct answer. However, I wonder whether this way is correct or not. Thanks!

PR / Pavg = Irms^2 * R / Irms^2*Z = 15 /33.36 = 0.45
 
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  • #2
Hi,

hidemi said:
and got the correct answer
So how did you get the 33.36 ? From 15/0.45 ? Then the answer is per se correct, but 'the way' is not :wink:

And you have me wondering why you type 33.36 and not 33.33 :cool:

##\ ##
 
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  • #3
BvU said:
Hi,

So how did you get the 33.36 ? From 15/0.45 ? Then the answer is per se correct, but 'the way' is not :wink:(15^2

And you have me wondering why you type 33.36 and not 33.33 :cool:

##\ ##
z=√[15^2 + (100*2π*25*10^-3 - 1/(100*2π*35*10^-6))^2]
BvU said:
Hi,

So how did you get the 33.36 ? From 15/0.45 ? Then the answer is per se correct, but 'the way' is not :wink:

And you have me wondering why you type 33.36 and not 33.33 :cool:

##\ ##
My detailed calculation is as attached.
 

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  • #4
Yes the power factor is ##\cos\phi=\frac{R}{Z}##.
 
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  • #5
Delta2 said:
Yes the power factor is ##\cos\phi=\frac{R}{Z}##.
Ok Thank you, I understand.
 

What is the power factor in a series circuit?

The power factor in a series circuit is a measure of how efficiently the circuit is using electrical power. It is the ratio of the circuit's true power (Watts) to its apparent power (Volt-Amperes).

How is power factor calculated?

Power factor is calculated by dividing the circuit's true power by its apparent power. This can be represented by the formula: PF = P/VA, where PF is the power factor, P is the true power, and VA is the apparent power.

What is a good power factor?

A good power factor is typically considered to be above 0.9. This means that the circuit is using power efficiently and there is minimal loss of energy. A lower power factor indicates that the circuit is less efficient and may be wasting energy.

What causes a low power factor in a series circuit?

A low power factor in a series circuit can be caused by inductive loads, such as motors or transformers, which create a lag between the voltage and current in the circuit. This lag results in a lower power factor as the circuit is not using power efficiently.

How can a low power factor be improved?

A low power factor can be improved by adding power factor correction devices, such as capacitors, to the circuit. These devices help to offset the effects of inductive loads and improve the power factor. Proper maintenance and regular inspection of equipment can also help to maintain a good power factor.

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