Problem — mains at ten times the voltage

Problem

Imagine that the domestic mains voltage went from $230\ \text{V}$ to $2300\ \text{V}$. What practical implications would this change have? Consider in five lines: transmission losses, conductor dimensions, electrical insulation, safety for people.

Solution

For the same power delivered $P = V\,i$, multiplying the voltage by ten divides the current by ten: $i = P/V$ drops to a tenth.

Transmission losses — line losses are $P_\text{lost} = R_\text{line}\,i^2$; if $i$ is reduced to $1/10$, the losses are reduced to $(1/10)^2 = 1/100$. They collapse by a factor of one hundred. This is exactly why high-voltage lines are used to carry energy over long distances.

Conductor dimensions — the cross-section of the wire is dictated by the current (so it does not overheat). With ten times less current, much thinner conductors can be used (less copper, less weight, less material cost).

Electrical insulation — depends on the voltage, not on the current. At $2300\ \text{V}$ much thicker insulation would be needed, along with greater air gaps to avoid discharges and electrical arcs: sockets, plugs and household appliances would have to be completely redesigned and would become bulkier.

Safety for people — this is the critical point: $2300\ \text{V}$ is extremely dangerous. Such a high voltage easily overcomes the resistance of the skin, causes lethal currents through the body and can trigger arcs even without direct contact. The low-voltage domestic mains exists precisely as a compromise in favour of safety.

$\ev{i \to i/10:\ \text{losses} \times \tfrac{1}{100},\ \text{thinner wires, but hugely greater insulation requirements and danger}}$

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Topics: Circuiti elettrici Concepts: Effetto Joule Skills: Analisi di casi limite e fantafisica