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Homework Help: Measuring inductance with Anderson's bridge

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data

    This is more to do with an experiment I'm failing terribly at rather than a direct homework question. I could not find the right section to ask this in.

    Investigate the inductance of inductors with cores of Perspex and Copper using an Anderson's bridge. For Perspex, compare the experimental value with the theoretical value.

    2. Relevant equations

    Equation for inductance when zero output is achieved across the detector ('balance');

    L = [itex] \frac {C R_2}{R_4}(R_3 R_4 + r R_3 + r R_ 4) [/itex]

    [itex] C, R_2, R_4 [/itex] were kept constant at [itex] 1nF, 30Ω, 10 kΩ [/itex] respectively while [itex] R_3, r [/itex] were varied to achieve balance.

    Theoretical inductance of toroid from dimensions;

    [itex] L = \frac {μ_0 N^2 A}{2 \pi r_t} [/itex]

    In this case I was given that N, the number of turns, was 500. [itex] r_t [/itex], the radius of the toroid to centreline was 1.1cm, and the radius of the coil (used to find A) was 0.25mm.

    Relative permeability;

    [itex] μ = \frac {L_{material}}{L_{vacuum}} [/itex]

    3. The attempt at a solution

    If anyone doesn't know what Anderson's bridge is, it's an a.c. equivalent of a Wheatstone bridge. Inductance is found by varying the resistance of two resistors until balance (zero output) is achieved on the detector and using equations invoked from Kirchoff's laws (put in the relevant equations section) - while keeping two other resistors and a capacitor constant. The inductors are coils bent in to a toroid surrounding the cores. I've been given the dimensions of the inductors (the toroid) so that I can calculate a theoretical value of the inductance of the Perspex core (by assuming the relative permeability is 1)

    The thing is, the difference between my theoretical value and experimental value is two orders of magnitude! I've checked and checked and checked and I am not wrong when plugging these numbers in to the appropriate formulae. The theoretical inductance I get for Perspex is roughly 1x10^-6 (you can check this out yourselves), whereas my experimental gives me 1.4x10^-4.

    Another problem is that I'm measuring the relative permeability of copper using the equation above. It returns to me a value of roughly 100, when I know that the actual value for the permeability of copper should be just less than one (since it's diamagnetic).

    Does anyone have any suggestions as to what the right problem may be? I have a feeling it's because my theoretical value for the inductance of the toroid is too low, but I would have no idea why.
    Last edited: Apr 19, 2012
  2. jcsd
  3. Apr 21, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    I think we need a diagram of the anderson bridge so we know what R1, R2 etc. are & where L and C are located.
  4. Apr 21, 2012 #3
    I've realised my mistake. I thought the radius of the coil was 0.25mm due to a misread of the laboratory script. However I realised this was a ridiculous size and I've now found out that this was actually the radius of the wire - a dimension I'm fairly sure I don't use for this experiment. The actual coil radius is close to 0.45mm, giving me a much more suitable value for the theoretical inductance.
    Last edited: Apr 21, 2012
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