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Physics LibreTexts

13.9: AC Bridges

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We have already met, Section 4.11, the Wheatstone bridge, which is a DC (direct current) bridge for comparing resistances, or for "measuring" an unknown resistance if it is compared with a known resistance. In the Wheatstone bridge (Figure IV.9), balance is achieved when R1R2=R3R4. 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 XIII.8),

13.8.png
FIGURE XIII.8

balance is achieved when

Z1Z2=Z3Z4

or, of course, Z1Z3=Z2Z4. 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 ??? is a complex number, and two complex numbers are equal if and only if their real and imaginary parts are separately equal. Thus Equation ??? 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.

  • 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.


This page titled 13.9: AC Bridges is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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