Wien bridge

Often an unknown component would be put in one arm of a bridge, and then the bridge would be nulled by adjusting the other arms or changing the frequency of the voltage source.

[2] Wien's bridge is used for precision measurement of capacitance in terms of resistance and frequency.

The Wien bridge does not require equal values of R or C. At some frequency, the reactance of the series R2–C2 arm will be an exact multiple of the shunt Rx–Cx arm.

The bridge is balanced when:[4] The equations simplify if one chooses R2 = Rx and C2 = Cx; the result is R4 = 2R3.

In practice, the values of R and C will never be exactly equal, but the equations above show that for fixed values in the 2 and x arms, the bridge will balance at some ω and some ratio of R4/R3.