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

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Homework Help Overview

The discussion revolves around calculating impedance in a series RLC circuit at a frequency of 3000 Hz, involving a resistor, inductor, and capacitor. The original poster presents a problem statement with specific values and seeks assistance in determining impedance, peak current, and phase angle.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the impedance using the formula Z=sqrt[R²+(Xl-Xc)²] but questions their conversion of frequency to radians per second and the placement of decimals in their calculations. Other participants raise concerns about the signs used in the impedance formula and the accuracy of the reactance calculations.

Discussion Status

Participants are actively engaging in clarifying the calculations and addressing potential errors in the original poster's approach. There is a focus on ensuring the correct application of formulas and identifying any mistakes in the arithmetic process. Multiple interpretations of the calculations are being explored, particularly regarding the use of signs and the conversion of units.

Contextual Notes

There are indications of confusion regarding unit conversions, particularly with capacitance, and the implications of using incorrect signs in the impedance formula. The discussion also touches on the need for clarity in the calculation steps to avoid errors.

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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  • #10
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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