Constraint relationships

Constraints say what cannot be the case

Constraint relationships express knowledge about snapshots, about states.

Current and potential difference cannot be varied independently. You make a choice about how to assemble the circuit and that puts in place a connection between the current and the potential difference: the values of these quantities are tied together or constrained. This constraint is a statement of some thing that you know about the world. Of what electrical circuits cannot do.

Trade-off relationships

To set power switched or energy shifted, there is a choice to make in how much to alter the values of the appropriate physical quantities. To set a certain power in an electrical pathway you can choose pairs of values of potential difference and current. You cannot choose any values, so the choice is constrained.

These trade-offs are a subset of constraint relationships, but are useful to understand energy.

In reasoning about electrical circuits you come across a densely interwoven set of constraint relationships, some of which are trade-offs. Having a way to describe what you are doing might be expected to be helpful in keeping them in order.

Both constraint and trade off relationships are atemporal, true at an instant: that's the significance of the assertion of equality that lies at the core of these relationships. Both describe possibilities and impossibilities – they formalise empirical or theoretical connections between physical quantities but don't predict how those quantities evolve over time. For that, you need a different class of relationship: an accumulation relationship.