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mmh37
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Hi, this is a very nice but (at least for me) quite confusing problem on electric circuits:
Before you read this, it will be helpful to have had a look at the attached picture (sorry - the quality is quite nasty)
_______
By considering each half of the circuit on the left below as a potential divider, one can show that
Z1/Z2 = Z3/Z4
The bridge circuit on the right of the picture is said to be balanced when the detector D registers no voltage difference between its terminals. Use the above equation to find formulae for R and L in terms of the other components when the circuit is balanced.
OK, so this is what I tried:
Z1= R + XL
Z2 = R2
Z3 = R3
[tex]Z4 = (\frac {1} {R4} + iwC4)^{-1} [/tex]
Equation 1
as derived from Z1/Z2 = Z3/Z4
therefore
[tex] R + iwL = R2*R3*(\frac {1} {R4} + iwC4) [/tex]
Equation 2
Now, regard the series connection on the respective sides of the potential divider.
given: U(Z2) = U(Z4) (A)
left hand side:
[tex] U(left) = ( Z1 + Z2)*I = \frac {U(0)} {2} [/tex]
solve for I to calculate
[tex] U (Z2) = \frac {Z(2)*U(0)} {2* (Z3 + Z4)} [/tex]
right hand side:
like lhs
[tex] U(Z4) = \frac {Z(4)*U(i)} {2(Z(1)*Z(2)}[/tex]
So now we put that in eq. (A)
to get:
[tex] R + iwL = R3/R2*(\frac {1} {R4} + iwC4)^{-2} [/tex]
Cool,
But now I don't know how to solve for L and R as w is not given and I don't know how to deal with those complex numbers to find L and R.
Can anyone help?? That would be absoluetly awesome!
Before you read this, it will be helpful to have had a look at the attached picture (sorry - the quality is quite nasty)
_______
By considering each half of the circuit on the left below as a potential divider, one can show that
Z1/Z2 = Z3/Z4
The bridge circuit on the right of the picture is said to be balanced when the detector D registers no voltage difference between its terminals. Use the above equation to find formulae for R and L in terms of the other components when the circuit is balanced.
OK, so this is what I tried:
Z1= R + XL
Z2 = R2
Z3 = R3
[tex]Z4 = (\frac {1} {R4} + iwC4)^{-1} [/tex]
Equation 1
as derived from Z1/Z2 = Z3/Z4
therefore
[tex] R + iwL = R2*R3*(\frac {1} {R4} + iwC4) [/tex]
Equation 2
Now, regard the series connection on the respective sides of the potential divider.
given: U(Z2) = U(Z4) (A)
left hand side:
[tex] U(left) = ( Z1 + Z2)*I = \frac {U(0)} {2} [/tex]
solve for I to calculate
[tex] U (Z2) = \frac {Z(2)*U(0)} {2* (Z3 + Z4)} [/tex]
right hand side:
like lhs
[tex] U(Z4) = \frac {Z(4)*U(i)} {2(Z(1)*Z(2)}[/tex]
So now we put that in eq. (A)
to get:
[tex] R + iwL = R3/R2*(\frac {1} {R4} + iwC4)^{-2} [/tex]
Cool,
But now I don't know how to solve for L and R as w is not given and I don't know how to deal with those complex numbers to find L and R.
Can anyone help?? That would be absoluetly awesome!
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