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

In summary: It's just what comes to mind when I do the math. In summary, the homework statement is that 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. Z=73.5765. XC=1/(2pi*5000*(6.9*10^-7))=46.1318 and XL=2pi*5000*L=72.26.
  • #1
ReidMerrill
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2

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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  • #2
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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  • #3
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.
 
  • #4
You have the decimal incorrectly placed in your answer for XC.
 
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  • #5
NascentOxygen said:
You have the decimal incorrectly placed in your answer for XC.
I converted nF to F wrong... Thanks you!
 
  • #6
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
 
  • #7
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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  • #8
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
 
  • #9
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
 

1. What is the definition of RLC circuit impedance?

The impedance of an RLC (resistor-inductor-capacitor) circuit is a measure of its opposition to the flow of current. It is represented by the symbol Z and is a complex quantity consisting of a real part (resistance) and an imaginary part (reactance).

2. How is RLC circuit impedance calculated?

The formula for calculating RLC circuit impedance is Z = √(R² + (XL - XC)²), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

3. What factors affect RLC circuit impedance?

The primary factors that affect RLC circuit impedance are the values of resistance, inductance, and capacitance. Other factors that can impact impedance include frequency, temperature, and the type of materials used in the circuit components.

4. How does RLC circuit impedance impact the behavior of a circuit?

The impedance of an RLC circuit can impact the flow of current through the circuit. When the impedance is high, it restricts the flow of current and can result in lower power output. On the other hand, a lower impedance allows for more current to flow and can lead to higher power output.

5. What is the relationship between RLC circuit impedance and resonance?

Resonance occurs in an RLC circuit when the impedance is at its minimum value. This is because at resonance, the reactive components (inductance and capacitance) cancel each other out, leaving only the resistance. This allows for maximum current to flow and can lead to efficient power transfer in the circuit.

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