SimonR501 said:
Are you sure big current = big pipe?
Absolutely sure.
Think of spark plug wires. The voltage is very high (tens of thousands of volts) so the insulation is thick to contain the voltage (pressure) but the wire conductor is quite skinny because the current (flow rate) is miniscule, typically a small fraction of an amp.
For a more extensive hydraulic analogy of electrical parametrs:
Current = volume rate of flow (litres per second, CFM, whatever)
Voltage = pressure or static head
Resistance = friction in pipe or other appliance.
Generator = pump
Motor = turbine or impellor
Pipe wall thickness = insulation thickness
capacitor = rubber diaphragm
Coil = er ... dunno, I'll have to think about that. I suppose it's equivalent to a master/slave cylinder arrangement.
OK, the electrical purists will cry out that the analogy doesn't hold up under any kind of close scrutiny, but what analogy does? It's good enough for beginners to come to grips with basic electrics in simple circuits like we have in old motorcycles and cars. Modern vehicles are getting away from simple circuit electrics because of all the computers and semiconductor crap everywhere.
When we transmit electricity over long distances we step voltage up quite a bit to 400,000 Volts, so that is 'big pipe = big pressure (volts) and small flow rate (current) and thus low losses in transmission.
The reason the voltage is stepped up for transmission lines is (as you say) to reduce the current, so smaller conductor can be used, thus reducing cost. Otherwise you would need massive wires that would be ridiculously uneconomical. The wires are still pretty big because EHV transmission lines typically carry a lot of power. The larger the conductor the lower the resistance, so it's a balance between installation cost and power loss.
In a previous life I used to build EHV transmission lines and substations. It was interesting work, especially for a mechanical engineer such as myself.