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The line voltage of a 2-wire direct current system is increased from 100 V to 200 V. If the same amount of the same electric power is transmitted over the same distance, what will be the percentage savings in copper?
1. 150%
2. 50%
3. 125%
4. 75%

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Correct Answer - Option 2 : 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

Volume of Cu required for both conductors is

V = 2 × A × L

Calculation:

(i) 100 V Supply

Current per feeder conductor I1 = P/100

Area of conductor required A1 = I1/σ = P/100σ

Volume of Cu required for both conductors is

V1 = 2 × A× L  = \( {2 × P\times L \over 100\sigma }\) 

(ii) 200 V Supply

Current per feeder conductor I2 = P/200

Area of conductor required A= I2/σ = P/200σ

Volume of Cu required for both conductors is

V2 = 2 × A2 × L  = \( {2 × P\times L \over 200\sigma } = { P\times L \over 100\sigma } \) 

%age saving in Cu = \( {V_1 - V_2 \over V_1} \times 100 = { {2 × P\times L \over 100\sigma } - { P\times L \over 100\sigma } \over {2 × P\times L \over 100\sigma }} \times 100\)

= 50 %

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