THOUGHT EXPERIMENTS: Transformer traversing a room

[AussieBruce]

Trigger warning: Highly theoretical.

I’ve pondered this on and off for a long time, even partial answers have been few and far between.

See diagram 1. An engineer is in a sealed room, the legs of a ‘wide’ transformer cross the room so that the coils and everything attached to them are inaccessible. A full range of tools and test gear is available, and the engineer can do anything required to measure the power being passed through the transformer to the resistive load.

One solution is in Diagram 3. Cut the core legs and complete the magnetic path with new coils, join the coils with an ammeter and voltmeter in the circuit, job done. But that approach bypasses the question of what’s happening within the transformer core to pass the power.

For a partial clue, consider Diagram 2., The engineer is in the room with a rotating shaft transmitting mechanical energy from a motor to a generator with a load. Once again, without some sort of invasive action only part of the required information – the rotational speed – is available. To determine the power, the shaft must be cut, and a torque measuring device inserted.

This relates to stuff that I encountered doing my degree at uni, decades ago. Lagrangian theory, and intensive/extensive variables. In that context, what are the two variables that determine the power passing through the transformer core, and how do you measure them? Or is the idea of power passing through the core invalid?

[Someone]

Shafts can have their wind-up measured directly (or optically) to get the power in real time:
https://www.imc-tm.com.au/products/sensor-solutions/telemetry/dx/mechanical-power-measuring/

Its a little trickier with a magnetic field as they aren't particularly well controlled in their spatial distribution.