Finding Impedance Values in a Series Circuit at Different Frequencies

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In summary, the conversation discusses a series circuit connected to a power supply set to 300Hz with R=30 ohms, Xc=20 ohms, XL=40 ohms. The question is to work out the values of R, Xc, XL at a range of frequencies from 100-600Hz. The capacitor and inductor cancel each other out at some frequency, and the closest to resonance was found at 200 Hz with a reactance of 26.6 ohms and 30 ohms. The broad resonance is due to the large series resistance compared to the low reactance values of the L and C at this frequency.
  • #1
pj83
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Homework Statement


My question is a series circuit is connected to a power supply set to 300Hz. At this frequency R=30 ohms, Xc=20 ohms, XL=40 ohms. I've then to work out values of R,Xc, XL at a range of frequencys from 100-600Hz.


Homework Equations


Xc=2x3.14xFxC, XL=2 x 3.14 x F x L


The Attempt at a Solution


I have worked out the values of XL, Xc which I'm fairly sure are correct, just wondering does R stay at the same value despite the change in frequency ? Any help greatly appreciated !
 
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  • #2
Yes, R stays the same.

You would have worked out the actual values for the capacitor and the inductor and then worked out the reactances at other frequencies. Can you see that the coil and capacitor cancel each other out at some frequency?

So, what were your conclusions? Where is this circuit resonant?
Why is the resonance so broad?
 
  • #3
I worked the capacitor out to be 26.5 microfarads, inductor 21.2mH by re-arranging the reactance equations, then I made a table for the reactance values at frequencies between 100-600Hz. The closest I got to reasonace was 200 Hz with a inductive reactance of 26.6ohms and capacitive reactance of 30 ohms, nearly cancelling out. I don't know why the reasonace is so broad ?
Thanks for your help.
 
  • #4
Yes, those values seem close to what I got (so they must be right! ... :) ...)

I got resonance at about 212 Hz by calculating it directly. So this agrees with what you got when you took 100 Hz steps.

The resonance is very broad because of the large series resistance compared with the quite low values of reactance of the L and C at this frequency.
 
  • #5
Thanks for your help it was very useful.

Thanks :)
 

1. What is frequency and how is it related to resonance?

Frequency refers to the number of times a wave oscillates per second. Resonance occurs when an object is exposed to a frequency that matches its natural frequency, causing it to vibrate at a larger amplitude.

2. How do we measure frequency and resonance?

Frequency is typically measured in Hertz (Hz) using specialized instruments such as an oscilloscope. Resonance can be measured using a resonance frequency meter or by observing the amplitude of vibrations.

3. What are some real-life examples of frequency and resonance?

Examples of frequency and resonance can be found in musical instruments, where the strings or air inside the instrument vibrate at specific frequencies to produce different notes. Another example is the Tacoma Narrows Bridge, which famously collapsed due to resonance caused by strong winds matching its natural frequency.

4. How does frequency and resonance affect the human body?

The human body has its own natural resonant frequency, and exposure to external frequencies that match or are close to this frequency can potentially cause harm. This is why precautions are taken with certain equipment, such as MRI machines, to avoid exposure to strong magnetic fields that could disrupt the body's natural frequency.

5. How is frequency and resonance used in technology?

Frequency and resonance are essential in the design and functioning of many technological devices. For example, in radios and televisions, frequency is used to tune into specific channels, and resonance is used to amplify signals. In medical imaging technology, resonance is used in MRI machines to create detailed images of the body's tissues and structures.

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