How Does Varley Loop Testing Calculate Fault Distance in Cables?

[swr]

Homework Statement

A Varley Bridge is connected to a faulty three-core copper cable by two identical copper leads of resistance Rl.

(a) Show that for the initial reading (connection to earth);

2Rx = 2Rc – Ri ........ 1

where Rc 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:

2Rc = R f – 2Rl ........  2

where Rl is a lead resistance
Rf is the final reading resistance.

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

Rx + Rl =  R f R–f Ri  Rc + Rl 

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

R = Rf–Ri R – Rl Ri

x c Rf
Rf
i.e. = effect with no leads – ratio of initial and final readings

× lead resistance(c) Determine the distance to the fault by modifying the expression in (b) and using Rx = x

Rc L

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=ρL/A

where ρ is the resistivity,
L is the length
and A is the cross-sectional area of a cable core
show that
Rl=RcAcLl/AlLc

Homework Equations

The Attempt at a Solution

I can work out all the way to section d, but then have no idea what formula to start with

 

[magoo]

It would help if you provided a diagram with the various resistances labelled. I remember seeing a Varley bridge many years ago, but I don't remember the basic circuitry and how it is connected to cable.

 

[swr]

This is how the varley bridge circuit looks.
I just cannot see which of my existing formulae or how to create a new to show Rl=RcAcLl/AlLc

 

[Babadag]

https://www.physicsforums.com/threads/varley-bridge.951609/

 

[Babadag]

In a) take Ra=Rb. Point b) it is very difficult to guess what the actual formulae are [what is written it is only gibberish].

Point d) I guess Lc=cable length, LL=lead length and ρc=ρL=ρ

Rc=ρ.Lc/Ac ;ρ=Rc.Ac/Lc; RL=ρ.LL/AL