What is the length of the wire for the following problem?

[iVenky]

Here's the question:

A twin- core cable is used to supply a 1kW load. The supply voltage is 100 V ac. The regulations state that the voltage at the load should be within 5% of the supply voltage. Determine the maximum length of cable run that therefore can be used. The resistance of the cable is 6.28 * 10-8 Ω/m and the cross section area of the cable is 1.57 mm^2.


Thanks in advance.:grin:

 

[mister_rf]

Uin=100V,
P = U I = 1000W -> I = 10 A


U _load = 95% Uin=95V
U _cable = 5V
but
U _cable = I * R _cable
R _cable = U _cable/I = 5/10 = 0.5Ω
R _cable = 2 R_wires

R_wires = ρ * l / A

A = 1.57 mm² =1.57 * 10 ^-6 m²
ρ =6.28 * 10^-8 Ω/m
R _wires = 6.28 * 10^-8 * l / 1.57 * 10 ^-6 = 4.331 * 10 ^-2 * l
R _cable/2 = R _wires = 4.331 * 10 ^-2 * l
R _cable = 2* 4.331 * 10 ^-2 * l = 0.5
l = 0.5/(2* 4.331 * 10 ^-2) = 50/8. 662 = 5.77 m