# Nice and tricky question on electric circuits

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

$$Z4 = (\frac {1} {R4} + iwC4)^{-1}$$

Equation 1

as derived from Z1/Z2 = Z3/Z4

therefore

$$R + iwL = R2*R3*(\frac {1} {R4} + iwC4)$$

Equation 2

Now, regard the series connection on the respective sides of the potential divider.

given: U(Z2) = U(Z4) (A)

left hand side:

$$U(left) = ( Z1 + Z2)*I = \frac {U(0)} {2}$$

solve for I to calculate

$$U (Z2) = \frac {Z(2)*U(0)} {2* (Z3 + Z4)}$$

right hand side:

like lhs

$$U(Z4) = \frac {Z(4)*U(i)} {2(Z(1)*Z(2)}$$

So now we put that in eq. (A)

to get:

$$R + iwL = R3/R2*(\frac {1} {R4} + iwC4)^{-2}$$

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!!! #### Attachments

• Physics Circuit Lent term.jpg
25.2 KB · Views: 498
Last edited: