As compared to a 2-wire DC distributor, 3 wire distributor with same maximum voltage to earth use only-

Two-wire DC system with one conductor earthed

Max. voltage between conductors = V_m

Power to be transmitted = P

Load current, \(I_1={P\over V_m}\)

If R₁ is the resistance of each line conductor, then \(R_1={\rho l\over a_1}\)

Line losses, \(W=2I_1^2R_1=2({P\over V_m})^2({\rho l\over a_1})\)

∴ Area of X-section, \(a_1={2P^2\rho l\over WV_m^2}\)

Volume of conductor material required = 2a₁l

\((Volume)_1=2({2P^2\rho l\over WV_m^2})l={4P^2\rho l^2\over WV_m^2}=K\)

Three-wire DC system

Load current, \(I_3={P\over 2V_m}\)

Line losses, \(W=2I_1^2R_1=2({P\over 2V_m})^2({\rho l\over a_3})\)

∴ Area of X-section, \(a_3={P^2\rho l\over 2WV_m^2}\)

Assuming the area of the  X-section of neutral wire to be half that of the outer wire.

Volume of conductor material required = 2.5a3l

\((Volume)_2=2.5({P^2\rho l\over 2WV_m^2})l={2.5P^2\rho l^2\over 2WV_m^2}={5\over 16}(Volume)_1\)

A 3-wire DC distributor, compared to a 2-wire DC distributor with the same maximum voltage to earth, uses only 31.25% of the copper.