The power in a pathway determines the quantity of energy shifted to a store each second
Connect up a circuit and leave it running in a steady state – lamps glow and resistors warm. How much they glow or warm depends both on the electrical current and on the electrical potential difference.
So much for the physical description; now to re-describe it in terms of pathways.
Electrical working at a constant rate occurs in an electrical loop in which there is a constant electrical current. Every device in this loop that has a potential difference across it shifts energy. The power in the electrical pathway tells you how much energy is shifted every second by that device. This power is set by the potential difference across the device and the current through the device.
Power in a pathway here can be equal to power in a pathway over there
The power in this pathway shifts energy to or from a store, adding to or subtracting from the energy already in the store. So a constant power in a pathway leads to a steady accumulation in a store. This accumulation can be either positive or negative.
As a starting example, use a simple large-scale electrical loop that does something useful: a hydro-electric generator, deep in the Welsh countryside, lights a domestic lamp in the West Midlands. Model the circuit, simplifying as much as possible, with wires of negligible (as near to zero as makes no difference) resistance. Then there are only two devices in the circuit – places where pathways are switched. The system is designed to optimise the following switches: at the generator, from the mechanical pathway to the electrical pathway; at the lamp, from the electrical pathway to the heating by radiation pathway (again, visible radiations only – that is our particular interest because of how we evolved).
In both locations the device will not be perfect – there will be some switching to other pathways, chiefly heating by particles as the water is warmed by churning through the turbine, and the wires in the generator are warmed by the current driven through them, as the air surrounding the lamp is warmed.
Describing the process in terms of energy shifted, you end up with an even more abstract picture, as the gravitational store is depleted and the thermal store augmented. This is the view that was emphasised in the earlier SPT: Energy and SPT: Electric circuits topics.
Constant power implies steady rate of accumulation
A larger constant power in any pathway accumulates energy in a store at a larger steady rate. This accumulation can be either positive or negative, thereby augmenting or depleting the energy in the store.
For the electrical pathway, you choose how to make the power larger: set the character of the pathway by using either a larger current or a larger potential difference, or both.
Accumulating over more time, at the same constant rate, also leads to larger quantities of energy being shifted to or from stores.