When the circuit shown in the figure is at steady state, the mesh current is
i(t) = 0.3255 cos(10t + 133.3°) A
Determine the values of L and R.
Zc is the impedance of the Capacitor
ZL is the impedance of the Inductor
I1 is the current in the top loop
I2 is the current in the bottom loop
A∠θ = a+bi
KCL and/or KVL
ZL = iωL
Zc = -i(1/ωC)
The Attempt at a Solution
I'm attaching the image to the problem.
It seemed to be hinting that I should use mesh analysis. Which I did, and here is what I got.
For the top loop (I1):
Vs1 + [(I1 -i(t))*Zc]=0
33∠-20° + [(I1 -i(t))*(-25i)]=0
Solving for I1 gives me... I1 = -.675 - i
For the bottom loop (I2):
Vs2 + 22(I2-i(t))
-7∠208° + 22(I2 - i(t))=0
Solving for I2 gives me... I2 = -.0504 + .088i
Well. As I went to solve the middle loop to find R and L, I realized that I would end up with one equation with 2 variables. As so:
22(i(t) - I2) + (i(t)*ZL) + (i(t) - I1)(Zc) + R*i(t) = 0
In it's full form:
Where x is L and y is R.
This is where I get stumped. What am I supposed to do?
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