A DC 2-wire feeder supplies a constant load with a sending-end voltage of 220 V. Calculate the saving in copper if this voltage is doubled with power transmitted remaining the same.

The correct answer is option 3):(50%)

Concept:

 Let L = Length of each conductor in metre

σ = Current density in A/m²

P = Power supplied in watts

A = Area of Conductor

The volume of Cu required for both conductors is V = 2 × A × L

Calculation:

Given

V = 220 V

Supply Current per feeder conductor

I = P / 220

The area of conductor required

A = \( I\over σ\)  =  \(P\over 220σ\)

The volume of Cu required for both conductors is

 = 2 × A × L

Vol₁= \({2 × P\times L \over 200\sigma }\)

if voltage doubled 

Volume of Cu required for both conductors is

 Vol2= 2 × A× L

= \({2 × P\times L \over 440\sigma }\)

\({Vol_1 - Vol_2 \over Vol_1} \times 100 = { {2 × P\times L \over 220\sigma } - { 2P\times L \over 440\sigma } \over {2 × P\times L \over 220\sigma }} \times 100\)

= 50%