# Why does more voltage mean more current?

So, I get that voltage is the difference in electrical potential energy per unit charge between two points. However, many textbooks and online resources compare voltage to the height of a waterfall to point out that you need a difference in height to produce a current. That makes sense. What doesn't make sense is why increasing the height (which is supposed to correspond to voltage) would increase the rate of the flow of the water. The water is not leaving the top of the waterfall any faster than before, so why would current increase? I know that the water has more height to fall and its final velocity will be higher because it has more time to accelerate, but wouldn't that just mean the water droplets just get spaced out further apart, so the actual amount of water passing a point per second won't increase? So, why would increasing the difference in how much electric potential energy each coulomb of charge has between two points mean more current will flow between those two points?

Sorry if this is an extremely basic question. I can do circuit analysis and apply Ohm's law, but I am just trying to get a full picture of the intuition behind Ohm's law rather than just accepting it and moving on (the inverse relationship between current and resistance makes perfect sense to me, though, so I'm good with that).

## 2 Answers

You may have found a small glitch in that water fall analogy. An analogy I like much better is to think of water through pipes.

The voltage (potential difference) corresponds to the pressure difference between two points. A higher pressure in one spot means a larger "push" on the water. For charges in a circuit, the voltage is the "push" that squeezed them forward through the obstacles in the form of resistors and other circuit components.

Such a pressure difference is directly corresponding to a larger potential energy difference. This is why the water fall analogy is often used, because it is a more intuitive way to think of potential energy. But when you are increasing the voltage across two points in a circuit, then this corresponds to not a higher "pressure" difference from the top to the bottom of the water fall, but rather to a larger potential difference. And such a higher potential difference means a higher water fall, because the potential energy we are comparing with here is gravitational.

So, the increase in height of the water fall is analogous to an increase in charge accumulation in an electric circuit. The distance is changing in that analogy so the speeds are not really comparable. But they would be in the pipe-analogy.

Current in a circuit, like movement of links in a circulating bicycle chain, does not vary from one location (like the top of a waterfall) to another. The 'liquid flow' analogy is just.. an analogy, but there's another reason: the current is not measured in velocity, meters per second, but in flow, LITERS per second. The same number of liters that departs the top of the waterfall, in any given time, reaches the bottom soon after. The water stream gets thinner as it gains velocity, keeping the current constant.

The lazy mill pond and the fast-flowing flume hold the same current.

Ohm's law is (approximately) true for a variety of current-carriers, and always (because of thermodynamics) is expected to have a positive current in a positive field (voltage drop), reflecting the fact that energy loss to heat is never negative in a closed system. That's another reason that more voltage generally means more current: no parts of the system have negative resistance except in a local-small-fluctuation in the flow (like an eddy in a stream might include some uphill water movement, but not NET uphill water movement).