# Water wheel model to describe current flow in a circuit

1. Aug 30, 2015

### Barclay

1. The problem statement, all variables and given/known data
There is a diagram in a book that shows a water pump sending water down a hill that then rotates a water wheel. The water reaches the bottom reservoir and is then carried back up the hill by the pump to start the cycle again.

Q1. Use this model to describe an ammeter, voltmeter, current and potential difference.

Q2. How is this model flawed?

2. Relevant equations
I'm trying to get a full an answer as possible and have gone overboard compared with the answer in the book. Please can you check my answer.

3. The attempt at a solution

A1. The pump represents the cell that is carrying electrons (water) up a hill and is the source of electrical energy. It gives the electrons (water) potential energy by lifting them to a higher level.

Wires are represented by pipes allowing the water to flow.

The current is the amount of water (electrons) flowing.

The potential difference is the height that water (electrons) is pumped up.

The ammeter is represented by the waterwheel. The number of rotations/unit-of-time measures the amount of water flowing past the waterwheel (current). The current is the amount of water (say buckets) passing the wheel each second.

The waterwheel can also represent a bulb where energy is being transferred when it rotates (symbolising light) as water moves past it.

As the water passes the wheel (coulombs of charged electrons) they rotate it and fall to a lower level and lose potential energy.

The height of the hill is the potential available. The height of the drop to the wheel (the component in the circuit) hill is the voltage drop.

Water (electrons) regains its potential energy (potential to do work) as it moves through the pump and is pushed to a higher level (higher potential).

A2. The book says that the model does not show the way current is affected by resistance.
I do not know how this model could show this. Isn't resistance just heat? Heat could be shown as a leaky pipe?
Resistance impedes flow of the water. Perhaps this would be by narrowing the pipes in certain sections of the stream.

2. Aug 30, 2015

### andrewkirk

Something is needed in the analogy that converts kinetic energy of the water into heat energy. Something that makes the flow turbulent and slows it down might do it. Say lots of little projections from the inside walls of the pipes that break up the flow and make many more particle collisions that become heat in the pipes themselves, which is lost to the environment. It would be best to have the projections not aligned with one another so that there isn't an easy path that allows water to smoothly avoid them all.

3. Aug 31, 2015

### Barclay

Thanks for the idea. The projections would be the resistance

The heat has to be shown as something. A leaky pipe suggests coulombs of energy is lost?

4. Aug 31, 2015

### andrewkirk

No, not a leaky pipe. The heat from the circuit corresponds to heat in the water analog as well.
The impact of increased resistance, given a fixed potential difference, is
(1) a lower rate of current (a lower rate of electron flow), because I = V/R
(2) creation of heat
In this analog that equates to a
(1) a lower rate of water flow, and
(2) creation of heat

The analog of a leaky pipe would be electrons escaping the circuit out into the environment, which is not what resistance does. The analog of a leaky pipe would be a circuit in which some wires had holes in their insulating coating and are in contact with a conducting or semi-conducting material, so that current flows out of the circuit, eg to ground.