Minimizing resistance in power lines involves using high voltage and low amperage to reduce power loss due to resistance, as resistance primarily affects amperage rather than voltage. Transformers are essential for stepping up voltage for long-distance transmission and stepping it down for residential use, typically maintaining voltages around 120/240V. While superconducting wires would be ideal, practical solutions include using thick conductors, though this comes with cost considerations. High voltage lines, such as those operating at 500 kV or more, are effective for long distances, but building lines at millions of volts is impractical due to expense and safety concerns. The discussion highlights the importance of understanding the relationship between line resistance and consumer resistance in power distribution.