Calculate Resonant Frequency & Capacitive Reactance

[aurao2003]

Homework Statement

Now demonstrate how to calculate resonant frequency. Calculate the capacitive reactance for a 300uF capacitor in series with a 800mH inductor.

Homework Equations

f = 1/2pi(LC)^1/2
Xc = -1/2pifC

Hi
I urgently need this solution checked out for my BTech deadline. The question reads thus:

The Attempt at a Solution

where L = 800mH, C = 300uF

so,
f = 1/2pi(800 x 10^-3 x 300 x 10^-6)
So, f = 10.3 Hz

so, Xc =-1/2pi (10.27 x 300 x 10^-6)

Will my final answer be expressed as a negative?
Any suggestions will be appreciated.
Thanks a lot in advance.

 

[gneill]

Homework Statement

Now demonstrate how to calculate resonant frequency. Calculate the capacitive reactance for a 300uF capacitor in series with a 800mH inductor.

Homework Equations

f = 1/2pi(LC)^1/2
Xc = -1/2pifC

Hi
I urgently need this solution checked out for my BTech deadline. The question reads thus:

The Attempt at a Solution

where L = 800mH, C = 300uF

so,
f = 1/2pi(800 x 10^-3 x 300 x 10^-6)
So, f = 10.3 Hz

so, Xc =-1/2pi (10.27 x 300 x 10^-6)

Will my final answer be expressed as a negative?
Any suggestions will be appreciated.
Thanks a lot in advance.

Technically capacitive reactance is a negative reactance, so best to express it so. Also be sure to assign it the appropriate units! Everything should have units

 

[aurao2003]

Technically capacitive reactance is a negative reactance, so best to express it so. Also be sure to assign it the appropriate units! Everything should have units

So, my final answer is in ohms and negative. Aside from that, is my working okay? I feel its fine but its the determinant for a distinction or a merit.

Thanks.

 

[aurao2003]

be sure to assign it the appropriate unitshttp://www.infoocean.info/avatar2.jpg

Thanks everyone. I take that as a yes! My sincere appreciation and gratitude.

 

[asteriatic]

Hi there,

Thank you for your question. It looks like you have the correct equations and have plugged in the values correctly. However, your final answer for Xc should not be expressed as a negative. The negative sign in the equation is just to indicate that Xc is an "opposing" reactance, meaning that it is in the opposite direction of the current flow. But the actual value of Xc should be positive.

So, your final answer for Xc should be:

Xc = 1/2pi(10.27 x 300 x 10^-6)

I hope this helps! Good luck with your BTech deadline.