Varley loop R=pL/A formula

  • Thread starter swr
  • Start date
  • #1
swr
2
0

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
 

Answers and Replies

  • #2
166
45
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.
 
  • #3
swr
2
0
upload_2018-7-18_22-44-4-png.png


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
 

Attachments

  • upload_2018-7-18_22-44-4-png.png
    upload_2018-7-18_22-44-4-png.png
    44.5 KB · Views: 675
  • #5
473
126
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
 

Related Threads on Varley loop R=pL/A formula

  • Last Post
Replies
14
Views
2K
Replies
1
Views
1K
Replies
20
Views
1K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
4K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
2K
Top