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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, â€” 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
2R, = R f â€” 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 â€” ratio of initial and final readings

(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.