By multiplying the rhs brackets and collecting terms show

Question

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);

                                                2R_x = 2R_c - R_i      

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

R_x = (R_f-R_i/R_f) R_c-(R_iR_i/R_f)

(c) Determine the distance to the fault by modifying the expression in (b) and using R_x/R_c = x/L 

(d) Using  R = ΡL/A

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