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

[ReidMerrill]

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+(X_l-X_c)²]
X_c1/wC
X_l=wL[/B]

The Attempt at a Solution

I found X_c=1/(2pi*3000Hz) =0.76886
and X_L2pi*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?

 

[NascentOxygen]

There should be only one "-" sign in your expression for Z.

Did you involve the value of C in your calculation for X_C?

 

[ReidMerrill]

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.

 

[NascentOxygen]

You have the decimal incorrectly placed in your answer for X_C.

 

[ReidMerrill]

You have the decimal incorrectly placed in your answer for X_C.

I converted nF to F wrong... Thanks you!

 

[ReidMerrill]

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

 

[gneill]

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

Can you try again? If it still doesn't look right, give us a breakdown of the calculation step by step.

 

[ReidMerrill]

Your individual reactance values look fine. Must be a calculator/finger interface issue

Can you try again? If it still doesn't look right, give us a breakdown of the calculation step by step.

X_L=2pi(5000)(0.0023)=72.2566
X_C=1/(2pi5000*(6.9*10^-7))=46.1318

Z=sqrt[(60^2)-(72.2566-46.1318)^2]=54.0138

 

[gneill]

Ah. Why have you used a minus sign between the two terms within the square root?

 

[ReidMerrill]

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