# Potential Dividers

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## Potential Dividers

As charge flows around a circuit it uses up its energy (its **electrical potential energy**) and turns it into other forms, such as heat and light.

Fortunately for us, electrons use **more** energy going through **larger** resistances and **less** energy going through **smaller** resistances. This means the larger the resistor, the greater the voltage needed across it for the same current to flow through it. In maths language, **the ratio of resistances gives you the ratio of voltages.**

*Let me show you with a simple example:*

Imagine, the current leaves the cell with 3V. Now, it has to get through a 1Ω and 2Ω resistor. In this simple example the current will use 2V to get through the 2Ω resistor and 1V to get through the 1Ω resistor.

**Note the voltage is in proportion to the resistance.**

There is a total of 12 ohms resistance in this circuit.

Let's look at the voltage available at each part of the circuit - or the **potential** as we call it!

*A more complex example:*

So at any point in a circuit you can find the **'potential'** - the amount of energy that each coulomb of charge has still got stored, ready to use.

Have a go at the more complex example above.

**Can you work out how much potential is used in each resistor?**

In this circuit you have a long piece of resistance wire.

As the charge passes through the wire it uses up its potential. Note this simple connection:-

**Halfway** through the wire it has used **half** the potential

**1/4** of the way through the wire it's used a **1/4** of the potential.

**1/8** of the way through the wire it's used an **1/8** of the potential.

See it! (Who said A-level physics was hard?!)

**You can write this as a ratio:**

**Or in this circuit:**

if V is the potential used going from A to B.

You can extend that because the **length** of wire is directly proportioned to the **resistance** of the wire.

**If instead of a wire we use resistors the equation can be taken one step further:**

*Now:*

If R_{1} was a variable resistor, then the voltage across it could be easily changed, by altering its resistance. That means that we can use this as a variable voltage supply, as any component placed in parallel with R_{1} will have this variable voltage across it.

Light dependent resistors and thermistors are often used in these circuits to control light and heat systems by varying the output voltage as their resistance changes.

**Here's a question for you to try:**

In the day time the LDR has a resistance of 200Ω. At night the LDR has a resistance of 5000Ω. The lighting system needs at least 8 V to operate.

Potential dividers are used in many systems to control voltage outputs for controls - for example, hi-fi controls.