How Do You Calculate Impedance in an RLC Circuit at 3000 Hz?

AI Thread Summary
To calculate the impedance in a series RLC circuit at 3000 Hz, the correct formula is Z=sqrt[R^2+(Xl-Xc)^2], where Xl and Xc are the inductive and capacitive reactances, respectively. The user initially miscalculated Xc due to incorrect unit conversion from nanofarads to farads, leading to an incorrect impedance value of 73.5765 Ω. After correcting the calculations, the user faced issues with impedance at 5000 Hz, suspecting a possible calculator error. The discussion highlights the importance of careful unit conversion and proper sign usage in the impedance formula. Accurate calculations are crucial for determining the circuit's behavior at different frequencies.
ReidMerrill
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Homework Statement


A series RLC circuit consists of a 60.0 Ω resistor, a 2.30 mH inductor, and a 690 nF capacitor. It is connected to an oscillator with a peak voltage of5.80 V .

Part A
Determine the impedance at frequency 3000 Hz.
Part B
Determine the peak current at frequency 3000 Hz.
Part C
Determine phase angle at frequency 3000 Hz

Homework Equations


Z=sqrt[R2+(Xl-Xc)2]
Xc1/wC
Xl=wL[/B]

The Attempt at a Solution



I found Xc=1/(2pi*3000Hz) =0.76886
and XL2pi*3000=43.354

so Z=73.5765

As you might have guessed, this is not the correct answer.

What am I doing wrong? I suspect it has something to do with how I converted Hz to Rad/s

How would I go about parts B and C too?
 
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There should be only one "-" sign in your expression for Z.

Did you involve the value of C in your calculation for XC?
 
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NascentOxygen said:
There should be only one "-" sign in your expression for Z.
That was a typo on my part. I used the correct equation when I worked it out.
 
You have the decimal incorrectly placed in your answer for XC.
 
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NascentOxygen said:
You have the decimal incorrectly placed in your answer for XC.
I converted nF to F wrong... Thanks you!
 
Now I'm working on a later part that involves finding impedance at 5000Hz
Xc=1/(2pi*5000z) =46.13
and XL=2pi*5000*L=72.26

so Z=54.013 but this is somehow wrong even though the exact same process worked for 3000 and 4000 Hz
 
ReidMerrill said:
Now I'm working on a later part that involves finding impedance at 5000Hz
Xc=1/(2pi*5000z) =46.13
and XL=2pi*5000*L=72.26
so Z=54.013 but this is somehow wrong even though the exact same process worked for 3000 and 4000 Hz
Your individual reactance values look fine. Must be a calculator/finger interface issue :smile:

Can you try again? If it still doesn't look right, give us a breakdown of the calculation step by step.
 
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gneill said:
Your individual reactance values look fine. Must be a calculator/finger interface issue :smile:

Can you try again? If it still doesn't look right, give us a breakdown of the calculation step by step.
XL=2pi(5000)(0.0023)=72.2566
XC=1/(2pi5000*(6.9*10^-7))=46.1318

Z=sqrt[(60^2)-(72.2566-46.1318)^2]=54.0138
 
Ah. Why have you used a minus sign between the two terms within the square root?
 
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gneill said:
Ah. Why have you used a minus sign between the two terms within the square root?
I keep doing that. I don't know why I keep doing that
 
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