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13.9: AC Bridges

Last updated

Mar 5, 2022
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- 13.8: The RLC Parallel Rejector Circuit
- 13.9A: The Owen Bridge

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Likewise in a AC (alternating current) bridge, in which the power supply is an AC generator, and there are impedances (combinations of $R$ , $L$ and $C$ ) in each arm (Figure $\text{XIII.8}$ ),

13.8.png
FIGURE $\text{XIII.8}$

balance is achieved when

$\label{13.9.1}\frac{Z_1}{Z_2}=\frac{Z_3}{Z_4}$

$\frac{Z_1}{Z_3}=\frac{Z_2}{Z_4}$ . This means not only that the RMS potentials on both sides of the detector must be equal, but they must be in phase, so that the potentials are the same at all times. (I have drawn the "detector" as though it were a galvanometer, simply because that is easiest for me to draw. In practice, it might be a pair of earphones or an oscilloscope.) Each side of Equation $\ref{13.9.1}$ is a complex number, and two complex numbers are equal if and only if their real and imaginary parts are separately equal. Thus Equation $\ref{13.9.1}$ really represents two equations – which are necessary in order to satisfy the two conditions that the potentials on either side of the detector are equal in magnitude and in phase.

We shall look at three examples of AC bridges. It is not recommended that these be committed to memory. They are described only as examples of how to do the calculation.

Topic hierarchy

13.9A: The Owen Bridge
The Owen bridge can be used for measuring inductance.
13.9B: The Schering Bridge
The Schering Bridge can be used for measuring capacitance.
13.9C: The Wien Bridge
The Wien Bridge can be used for measuring frequency.
13.9D: Bridge Solution by Delta-Star Transform
What if the bridge is not balanced? Can we calculate the impedance of the circuit? Can we calculate the currents in each branch, or the potentials at any points? This is evidently a little harder. We should be able to do it. Kirchhoff’s rules and the delta-star transform still apply for alternating currents, the complication being that all impedances, currents and potentials are complex numbers.

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