# Relating Work, Energy, Power, Voltage, Current, and Resistance

How do these things relate?

# Work, Energy, Power

Work is how much force directly caused how much displacement. Energy is the *ability* to do work. Work and energy use the same unit (joule), but they look at things from a slightly different perspective.

Energy is never created nor destroyed, it is just transformed from one form to another, and in the process work is done. I.e. usually when you convert energy from one form to another, work is done in that process.

The formula for work is:

```
work = force * displacement
```

There are two things that you need in order for any work to be done.

- You need to apply a force.
- That force must be directly responsible for displacement (along the direction of the force).
- If the displacement is exactly in the opposite direction, then you are doing negative work.

If you are missing any of the above, you are not doing work. I.e. if you apply a giant force on an object, but this force causes no displacement of the object, then no work was done!

As I mentioned, joule is the unit for work/energy. Let’s get an idea of “how much” work/energy 1 joule is. When you apply 1 Newton of force on an object and cause 1 meter of displacement, it is said that you’ve done 1 joule of work. So let’s say that you have a 1 kg object. You apply a 1 N force on it for 1 second. A 1 N force accelerates a 1 kg object 1 m/s/s. Thus in 1 second, the object will go from 0 m/s to 1 m/s, thus it will travel 1 m in 1 second. Thus 1 joule of work can move a 1 kg object 1 m in 1 second.

Just so you know, 1 Calorie is rougly 4000 joules. That is an *incredible* amount of energy, thus an incredible amount of work that can be done with it before it is “burned”!

Power is just work/energy per time. In other words, power is the rate of work (usually when we say rate, we mean with respect to time). The unit used for power is Watt. 1 Watt is 1 joule per second. So, if you are doing 1 joule of work per second, you are using 1 watt of power.

# Voltage, Current, Resistance

## Current

Atoms in a conducting material allow their valence shell electrons (their outter most, most weakly held electrons) to flow from atom to atom. Electricity is basically the flow of atoms in a conducting wire, all in one direction. The amount of electrons that flows past a certain point in your wire per time is called the current. The unit for current is Amps. 1 Amp is 1 coulomb of electrons per second. 1 coulomb of electrons is just a really, really large amount of electrons (roughly 6 times 10 to the 18th electrons).

We can study electron flow through a system of wires at a macro level, similar to how we study the flow of water though a pipe system at a macro level (i.e. looking at properties/relationships on a bigger scale than the relationships/interactions between individual water molecules). In fact, the relationships we see when we consider electron flow through a system of wires is strongly analogous to the relationships we see when we consider water flow through a system of pipes.

## Voltage

In order to have electron flow, we must have some “motivator”, something that will “convince” the electrons to move. We call this the electromotive force, often we just call it voltage. Voltage is the *difference* in potential between two points in the wire system. If there is a difference in potential between two points in the wire system, then electrons will flow from higher potential to lower (given that they have a path). The bigger this difference, the more electrons will flow per unit of time. In other words, the greater the voltage, the greater the current. Additionally, the greater the voltage (potential gradient), the more energy will be given off as the electrons move down the gradient. Thus power, depends on two things:

- Current (i.e. rate of electron flow).
- Voltage (i.e. potential gradient, i.e. how much energy per electron)

If there are more electrons flowing, or if the electrons give off more energy as they flow down, then you have more power. One way to look at 1 volt (the unit for voltage), is when 1 coulomb of charge moves down a potential gradient and gives off 1 joule of energy, we say that is a 1 volt potential gradient. In other words, voltage tells you how much energy (in joules) each coulomb of charge travelling down the potential gradient will give off.

## Resistance

However there can be “clots” or “hard to travel” areas along the system of wires (analogous to rocks stuck in some pipes). We term these kind of things “resistance”. The more the resistance, the less the current. Thus voltage helps the current, resistance harms it.

The full relationship between current, voltage, and resistance is:

```
current = voltage / resistance
```

# Puttin’ it all Together

When you have a circuit (system of wires) with a potential difference (voltage), electrons will flow from higher potential, down to lower potential, and in the process you can “drive” some work. For example, if you have 1 voltage potential gradient, each coulomb of electrons traveling through your circut can donate 1 joule of energy. Let’s say that your current is 1 amp (1 coulomb per second). Thus you have 1 coulomb of electrons traveling down your gradient per second and each coulomb can donate 1 joule of energy. Thus you have 1 joule per second of energy, or in other words, 1 watt of power that these electrons can do for you!

# Terminology Summary

**work**is how much force caused how much of a displacement.**energy**is the ability to do work.**power**is the rate of work (i.e. work/energy per time).**current**is electrons traveling down a potential gradient.**voltage**is what we call this potential gradient (1 volt means each coulomb of electrons traveling down the gradient have 1 joule of energy available)**resistance**is a measure of how difficult it is for the electrons to flow

# Relationship Summary

`work = force * displacement done by the force`

`power = work or energy / time`

`current = voltage / resistance`

# Todo

- review this article (is kind of a 1st draft)