Problem — room-temperature superconductor

Problem

Imagine that at $20\ ^\circ$C copper wires became superconductors (zero resistance). Discuss in five lines the impact on: (a) long-distance electrical power transmission; (b) consumer electronics and heat dissipation; (c) batteries and electric cars.

Solution

With $R = 0$ in the wires, the power dissipated in the conductors $P = R\,i^2$ vanishes: Joule heating disappears everywhere there is only copper. The consequences:

(a) Long-distance transmission — today, lines lose energy through Joule heating (on the order of $5\text{–}10\%$), which is why transmission occurs at very high voltage (to reduce $i$ and hence $i^2R$). With superconducting wires, line losses vanish: energy could be transmitted at low voltage over any distance without waste, eliminating many transformer substations. A revolution for power grids.

(b) Consumer electronics — copper tracks and cables would no longer heat up, but the active components (transistors, chips, LEDs) and resistors dissipate for their own reasons, and would not disappear: the heat from processors would remain. The main gain would be in power connections (power supplies, distribution), less so in logic. Heating resistors (made specifically to dissipate) would no longer work if made of copper.

(c) Batteries and electric cars — copper cables and motor windings would not dissipate: more efficient motors, less heat to remove, charging at high currents without overheating the cables. However, the battery’s internal resistance (of chemical origin) would remain, as would the losses in windings that are already limited. Range and efficiency would improve significantly.

$\ev{R=0 \Rightarrow \text{no more } i^2R \text{ in the wires: loss-free grids, cold motors/cables; but active components and chemistry unchanged}}$

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Topics: Circuiti elettrici Concepts: Legge di Ohm Skills: Analisi di casi limite e fantafisica