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    Varley bridge/ Wheatstone bridge problem

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    The Varley loop test is a method of fault location in telecom and pilot wire circuits where fairly high circuit resistances are encountered. This solution determines the distance to the fault.

    3. A Varley Bridge is connected to a faulty three-core copper cable by two identical copper leads of resistance R1.
    (a) Show that for the initial reading (connection to earth);
    2Rx = 2R, — Ri (1)
    where R, is the resistance of the cable core
    Ri is the initial reading of the bridge
    Rx is the cable resistance to the fault from the bridge
    and for the final reading:
    2R, = R f — 2R1 (2)
    where R1 is a lead resistance
    Rf is the final reading resistance.

    Then by substituting (2) in (1) and rearranging the equation, show:

    (see the PDF for correct calculations)

    (b) By multiplying the rhs brackets and collecting terms, show the effect of the leads is given by:

    (see the PDF for correct calculations)

    i.e. = effect with no leads — ratio of initial and final readings
    x lead resistance

    (c) Determine the distance to the fault by modifying the expression in (b)

    (see the PDF for correct calculations)

    where x is the cable distance to the fault
    and L is the length of a cable core.
    Derive an expression for x, the distance to the fault.

    (d) Using R = pi, A
    where p is the resistivity,
    L is the length
    and A is the cross-sectional area of a cable core

    (see the PDF for correct calculations)

    and by substituting for R1 show that the distance to the fault is given by:

    (see the PDF for correct calculations)

    (e) Determine the distance to a fault on a 200 m, 120 mm2 copper cable R.
    if copper 10 mm2 test leads of length 10 m are used and = 0.2.

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    Solution Summary

    This solution addresses the calculations required for determining the effect of leads on the Varley bridge as well as the computation of fault distance.