# Why are voltage and current directly proportional? [closed]

So, I thought I had an understanding of Ohm's law, but after thinking deeply about it, the direct proportionality between voltage and current doesn't make a lot of intuitive sense to me.

So, when I first learned about circuits, voltage in a circuit was compared to the height of a waterfall. However, according to Ohm's law, given a constant resistance, increasing voltage should increase current. But with the waterfall analogy, it doesn't make sense that a higher height would make more water flow per second. Simply making the waterfall taller shouldn't make water fall from the top any faster than it would if it were shorter. Also, the greater height giving the water more time to accelerate to a faster final velocity also shouldn't make for more current, because wouldn't that mean the individual water droplets would get more and more spaced out as they fell, so the amount of water passing a point per second would stay the same since the higher velocity of the water droplets is counteracted by a greater distance between them? So, why does simply increasing the difference in how much potential energy a coulomb of charge has between two points increase the amount of charge passing between those two points? I am having a bit of trouble wrapping my head around this, and I would greatly appreciate an intuitive answer to help me fully understand Ohm's law.

• If you need a water flow analogy think of a water pipe system with a pump as the pressure control (voltage). The more pumping pressure the more water volume (current) flows through a restricted pipe (resistor) per a fixed time interval. – Nedd Feb 19 '18 at 9:39
• A waterfall is a really bad analogy, it's a pity that you learned that way. Much better is a pipe, then the water analogy works really well, as long as you stay with laminar flow. If the flow becomes turbulent, the analogy stops working so well, it can't be pushed that far. – Neil_UK Feb 19 '18 at 9:59
• The disadvantages of analogies far outweigh the advantages. – Chu Feb 19 '18 at 14:45
• George Ohm measured this relationship using a powerful Volta pile battery, in the Cavendish lab in early 1800s. The results were close enough to a straight line the Brits took over the math, forbade any curve fitting for all future generations, and 200 years later we are still suffering the indignity of "slope" as the only variable allowed for Ohms Las. – analogsystemsrf Feb 20 '18 at 2:52
• Drude model gives the intuition about why current is proportional to voltage. – leventov Oct 18 '20 at 15:47

The problem with the waterfall analogy is that the attraction force that takes water over the edge is gravity and this isn't changing as the height of the waterfall increases so yes, the analogy is flawed as are all analogies.

Voltage is a strange and elusive force - it isn't like current where you could envisage counting the net number of electrons passing a fixed point in a certain time and although nobody ever would do this you'd be happy with the concept. Voltage is harder to grasp and it's probably best asking on physics stack exchange for a decent answer.

Regards: -

Why are voltage and current directly proportional?

The simple answer is "they are not" except for the basic case of a resistor. Inductors and capacitors are different for instance; the voltage across an inductor is inductance times the rate of change of current with time. It follows from this that if the current is a sinewave, the voltage has to be a cosine wave and these two are not proportional in time.

Hosepipe analogy - the higher the pressure the more water flows per second. The higher the potential difference (voltage), the more electrons flow per second (current).

Don,t think of a waterfall think of a pipe. A waterfall is effectively a short circuit it will take as much current as you can throw at it. The pressure from one end of the pipe to the other is voltage the friction of the water on the pipe walls is resistance. The analogy is not perfect, that friction is not linear, however as a thought experiment it is good enough.

So your pipe comes out of the bottom of a bucket of water. Keeping the length (resistance) of the pipe the same. If there is only a small drop (voltage) from one end of the pipe to the other water trickles out but if you let the pipe drop vertically it comes out much faster.

If V = I * R and R is constant then any change in V will cause proportional change in I.

The height of the water fall is not helpful unless you only look at the energy that can be collected by a pelton wheel at the bottom where Power =Qh * 10000 where Q is litres/sec, 10000 is gravity and density - gravity can be assumed to be 10 here as there are otger losses...

The water analogy is not always the most helpful in some situations... IMHO...