Analogies can be a very good way for us to imagine things but we must always bear in mind they may only be helpful in a certain way and by no means totally accurate and often have the ability to mislead us.
True. However, I think we need tio remember that our 'understanding' of many of these things (e.g. gravity, 'centrifugal force', the 'structure of an atom' etc. etc.) are really just theories which reasonably explain what we can observe, even though we don't really know the truth about the 'underlying facts'. In that sense, many of these theories are not much different from 'analogies'.
Regarding power factor. I have found that even some electricians etc tend not to grasp it, some even make some big mistakes.
Years ago I too struggled with the concept of power factor.
It seems that a lot of people have difficulty with PF and I think it is probably easier for those who have an understanding of the underlying maths.
However, although it is in some senses a flawed analogy, I've had a fair degree of success in explaining PF and related concepts, by using a ('mechanical') analogy which helps people to understand how the amount of energy (c.f. electrical power x time) required to make something move a certain distance (c.f. electrical current flow) is critically dependent upon the 'phase relationship' between the direction of the force being worked against (c.f. electrical voltage) and the direction of the movement (c.f. direction of current flow).....
Consider a fairly heavy object (hence a fairly large 'force of gravity' trying to 'pull it down') sitting on an extremely low friction surface.
First consider the situation in which the 'force being worked against' and the direction of movement caused by the applied force) being 'in phase' - i.e. one wants to lift the object upwards, against the force of gravity trying to resist that movement. One would apply an appreciable ('upwards') force, and an appreciable amount of energy would be required to do that moving.
Now move to the situation in which there was a 90° 'phase difference - i.e. one wants to move the object sideways. This would require very little ('sideways') force (hence energy) since the only thing resisting the movement would be the (very low) friction afforded by the surface. Most people can understand that as the friction gets smaller and smaller, one approaches the ultimate situation in which it would require zero force (and energy) to move the object sideways.
If one gets that far (with 'understanding') then it's usually not too difficult to get people to understand that as the direction of the applied force (hence movement) moves from being ';in phase' with the movement (i.e. zero 'phase difference') to 90° out-of-phase, the amount of energy required to move the object a given distance progressively decreases from a fairly high value (c.f. "PF=1) to reach 'near zero' (true zero if no friction at all) when the phase difference is 90° (c.f. "PF=0").
Reduced to a conceptual statement, this means that the 'true power' depends to the extent on which the direction of movement (current flow) is 'in sync' with the force resisting the movement, being at its greatest when they were totally 'in sync' (as they would be with a resistive circuit) but approaching zero as the approached being "90° out-of-sync' (i.e. 'perpendicular to one another).
However, that analogy does not work for everyone, so it may not work for you!".
Obviously it is totally wrong, not least because I am thinking in DC and this subject only concerns AC. However if you think in DC then think of quickly disconnecting the battery then connecting again in the opposite polarity I suppose it makes it a little bit more acceptable.
Indeed - similar to what I recently wrote.
When I went to school we were taught about Centrifugal Force. Nowadays we are told that Centrifugal Force does not exist. But the calculations we used to make about Centrifugal Force still hold us in good stead. I wonder if we can think of those as an analogy?
You are saying exactly what I did at the very start, above. Our 'understanding' about these things are theories, that reasonable fit the observed facts (hence the calculations based on the theories 'work'), even if the theories do not correspond to 'the truth' - so, yes, as I said, I think such theories can be described as a type of ('useful') 'analogy'.
Kind Regards, John