Answer
6 billion meters.
Work Step by Step
Find the initial current from equation 18–9a.
$$P=IV$$
$$I=\frac{P}{V}=\frac{100\times10^3 W}{12\times10^3 V}=8.333A$$
Next in line is the step-up transformer, multiplying the voltage by a factor of 20, therefore lowering the secondary current by the same factor.
$$I_S=8.333A/20 = 0.41667 A$$
Calculate the power lost, which is the dissipated power. We set the power lost to 50 kW.
$$P_{loss}=I^2 R=50\times10^3W=(0.41667 A)^2 (5\times10^{-5}\Omega/m)L$$
Find the length of wire L that loses that much power.
$$L=\frac{50\times10^3W}{(0.41667 A)^2 (5\times10^{-5}\Omega/m)}$$
$$L\approx 6\times10^9 m$$