Voltage and current in a resistor

[sophiecentaur]

Sophie -not to be contrarian- IMO if the force applied is being equally reacted ( steady state as with drag / friction / resistance ) --- then the F applied = F reaction -- and work is done(power loss) . I agree to the inductor - this is the case where energy is stored in the system - inductors / capacitors... in these cases we are using Impedance - and we are talking about time varying cases - but regardless of the time - the Total force applied (Voltage) at any point in time is equal to the sum of each of the elements "reactive" force. ( really KVL right ?- the total sum =0, although the OP may ONLY see KVL as a mathematical tool - it is a (the) fundamental issue)
Consider a motor - not a resistor - looks like an inductor, then the back emf - is proportional to the mechanical force ( torque) and the power is the EMF ( Volts) * current... if there are resistors capacitors - what ever else in the circuit --- the back EMF becomes one of the SUM of forces - resisting the flow of current ( as I say pushing back).
This is my understanding - I do not consider this an analogy, but the fundamental principal. The same principal can be applied to many ( if not most) classical physical systems. Water in pipes, springs, gravity and friction blocs...

Either way round, it is not a good idea to try to equate Potential Difference (an Energy quantity) with Force. Using the right quantities and believing what the Maths delivers is usually the best way forward.
Volts are only allowed to be called a 'force' in the context of "emf", which is an ancient tradition and the term is used with fingers crossed.