Finding inductance from inductive reactance of 4π

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jafferrox
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Homework Statement



q3.png


Homework Equations


XL = wL
XC = 1/wC


The Attempt at a Solution


XL = 4pi


Thanks in advance.
 

Discussion

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The first step is to determine the resultant impedance of the two parallel branches. There should be an imaginary operator, j, included in your impedance term for the L and C elements.
 
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and then what's the next step?
 
Step 2 is to equate the impedance to be a pure resistance, because at resonance a circuit appears purely resistive to any applied voltage.
 
doesn't this mean XL=XC, i already found XL and XC is the same and then solve for c?
 
jafferrox said:
doesn't this mean XL=XC,
It does, where XL and Xc are the only impedances present. But there is an R here, and that makes things more interesting.

i already found XL and XC is the same and then solve for c?
That gives a rough approximation, and will usually get you near the right answer, but can be wrong by up to about 15%.
 
I think you need to find impedance in the form: Z= f(R) + j*f(R, XL, XC).
Then solve f(R, XL, XC) = 0 for C with R, XL and W given.
 
I don't know what you mean, can you please make it clearer?

Thanks
 
Can you get the impedance of two parallel branches?
Using ZL = jXL and ZC = -jXC
The first branch: Z1= ZC = -jXC
The second branch: Z2 = R + jXL
Then total impedance:
1/Z = 1/Z1 + 1/Z2
You need to solve for Z and then force imaginary part of Z equals zero. You will find C.
 
I couldn't do it, can someone please do it and attach a picture or a screenshot of the working out.

Thanks