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solve 2 equations in terms of other variables

asked 2015-03-06 19:19:31 -0500

lefti gravatar image

updated 2015-03-07 05:01:39 -0500

Hi,

I have

RL,Rs,C,L,Q,wo=var('RL Rs C L Q wo')

then I say

eq1=wo==Q*(C*RL*Rs+L)/(C*L*RL)
eq2=wo==sqrt((RL+Rs)/(C*L*RL))
solve([eq1,eq2,C,L)

I would like to solve the above system in terms of C and L. How do I do this?

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answered 2015-03-07 07:14:51 -0500

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This post is a wiki. Anyone with karma >750 is welcome to improve it.

Hint: please avoid 'sqrt' within equations.

eq1=wo==Q*(C*RL*Rs+L)/(C*L*RL)
eq2=wo^2==(RL+Rs)/(C*L*RL)
sol=solve([eq1,eq2],C,L)
print sol 

[
[C == -2*(Q*RL + Q*Rs)/(sqrt(-4*Q^2*Rs + RL + Rs)*sqrt(RL + Rs)*RL*wo - RL^2*wo - RL*Rs*wo), 
L == 1/2*(RL + Rs -   sqrt(-4*Q^2*Rs^2 - 2*(2*Q^2*Rs - Rs)*RL + RL^2 + Rs^2))/(Q*wo)],
[C == 2*(Q*RL + Q*Rs)/(sqrt(-4*Q^2*Rs + RL + Rs)*sqrt(RL + Rs)*RL*wo + RL^2*wo + RL*Rs*wo), 
L == 1/2*(RL + Rs + sqrt(-4*Q^2*Rs^2 - 2*(2*Q^2*Rs - Rs)*RL + RL^2 + Rs^2))/(Q*wo)]
]
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Asked: 2015-03-06 19:19:31 -0500

Seen: 91 times

Last updated: Mar 07 '15