# What power factor differences can be observed when changing the frequency?

#### Dane T

Joined Feb 19, 2020
3
Hello there, I'm struggling on a question that I had received I was wondering if someone could give me the correct answer and explain it to me
Thank you.

Frequency: 503.29Hz
Current: 55.96A
Total Resistance: 4.11Ohms
Voltage Supply: 230V
Inductive Reactance: 31.62H
Capacitive Reactance: 31.62F
Power factor: 55.69^2 x 4.11
= 12.7kW

Frequency: 60Hz

Current: 0.88A
Total Resistance: 4.11Ohms
Voltage Supply: 230V
Inductive Reactance Value: 3.77Ohms
Capacative Reactance: 265.25ohms
Power Factor: 0.88^2 x 4.11
= 3.18W

This isn't really my strong hold, so I was wondering if anyone could help me answer the question by observing the values I've given above for two different frequencies

Thank you.

Last edited:

#### WBahn

Joined Mar 31, 2012
25,290
We don't provide answers to homework problems -- that defeats the purpose of homework.

You need to show your best attempt to work/answer the problem and then we can help you move from their toward where you need to go.

First, review what power factor is? Hint: It is NOT a power (it does not have units of watts).

#### Dane T

Joined Feb 19, 2020
3
Apologies, I didn't know but I had already written up something just didn't know if it was correct.#

The relationship between power and frequency is inversely proportional to each other. At 503.29Hz XL = XC this is called resonance condition. In this condition the inductive reactance gets cancelled by the capacitive reactance. Therefore, the entire RLC circuit acts as a resistive circuit, and the power factor is Unity.

#### Dane T

Joined Feb 19, 2020
3
We don't provide answers to homework problems -- that defeats the purpose of homework.

You need to show your best attempt to work/answer the problem and then we can help you move from their toward where you need to go.

First, review what power factor is? Hint: It is NOT a power (it does not have units of watts).
I just went over everything, and reviewed Power factor. Turns out I was using the wrong formula to calculate it apologies. Therefore the above value is incorrect.

New Value for power factor @ 503.29Hz
$Cos\theta (4.11/4.11) =0.99$

New Value for power factor @ 60Hz
Impedance: 261.51Ohm
$Cos\theta (4.11/261.51) =0.9999$
$Power factor Formula:Cos\theta (R/Z)$