How to isolate Xc in this equation?

Thread Starter

Flupps

Joined Nov 14, 2013
8
I'm stuck on a homework problem I have.



Q1: For the circuit in question1above: R=(5.80x10^2) (Ω) and C=(4.5000x10^-7) (F). At what frequency the lagging angle of the impedance θ=(3.400x10^1)°. Enter the answer in (Hz)

I believe I first need to isolate Xc in the below equation
θ = tan-1(Xc/R)

Once I figure out Xc I can use f = 1/(2*pi*Xc*C) to calculate the frequency

Could anyone please tell me how to isolate Xc in the first equation?

Thanks!
 

shteii01

Joined Feb 19, 2010
4,644
Ah. You are so close!

Ok. The key formula here is:
theta=tan^-1(-Xc/R)

Here is the thing, you are not interested in Xc, you are interested in one of the components that make up the Xc! Very important this point.

What is Xc? It is:
Xc= 1/(2*pi*f*C)
You want the f!

So. The earlier formula becomes:
theta=tan^-1[(-1/(2*pi*f*C))/R]
theta is given.
C is given.
R is given.
Solve for f.
 

Thread Starter

Flupps

Joined Nov 14, 2013
8
ah I see, but I am not sure how to isolate f in that equation? I have always been confused about rearranging equations like this
 
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