# Lesson 7: Resistance and Ohm's Law

## Introduction

In this lesson we'll introduce the idea of resistance. We'll try and explain what electrical resistance is and what causes it.

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We'll see how resistance is related to Ohm's Law and we'll do some experiments to see how the resistance of a bulb, thermistor, light dependent resistor and diode change as the current through them changes.

## What is electrical resistance?

There are several ways of looking at electrical resistance. We're going to look at it from the point of view of energy.

Electrical resistance tells us something about how much energy you need when you move charges through a component, like a bulb. If you need lots of energy then the resistance of the bulb is high. If you don't need very much then it's low.

The opposite of resistance is conductance. This means if something has a high resistance then it has a low conductance.

## Resistance and the brightness of bulbs

Another way of looking at resistance is to think about three different bulbs connected to the same number of batteries. All three bulbs will have the same voltage across them but the current through them will be different.

The bulb with the biggest current flowing through it will be brightest. This bulb has the lowest resistance because you get the biggest current for a given voltage.

The bulb with the smallest current flowing through it will be dimmest. This bulb has the highest resistance because you get the smallest current for a given voltage.

It's a common misconception that high resistance bulbs are brightest.

## Why is the resistance of a bulb important?

In a simple series circuit we assume that the leads and the battery have a very low resistance. The resistance of the battery we call the internal resistance because you can't change it. Internal resistance is often ignored to simplify things.

The filament of the bulb has a higher resistance than the leads. This means that most of the energy is converted in the filament rather than in the leads. It also means that the current around the circuit mostly depends on the resistance of the filament rather than the leads.

So we want the filament of a bulb to have a higher resistance than the leads but not so high that the bulb is dim.

To understand how we design the bulb filament to have the right resistance it'll be useful to know about how the resistance of a piece of wire depends on what it's made of, its length and its thickness.

## How resistance depends on material, length, thickness and temperature

All metals are good conductors so all metal wires have a relatively low resistance. However some metals are better conductors than others, for example copper and silver. The reason why some metals are better conductors than others is to do with the way their free electrons move. Bulb filaments are often made from tungsten, which has a very high melting point.

The longer a piece of wire the higher its resistance. Double the length means double the resistance. You can think of a long piece of wire as being like lots of resistors in series but there is also a more formal explanation. The filament of a bulb may seem pretty short but if you look closely you can see that it's often a very thin piece of wire that has been tightly coiled up. It may be up to half a meter long when its unwound.

The resistance of a piece of wire also depends on its thickness. Double the area means half the resistance. A thin wire has a higher resistance than the same thick piece. There are a few misconceptions about resistance and thickness. The most important point is that the speed of the charges only depends on the voltage, not the thickness of the wire. But with a thick wire more charges can move side-by-side so the charge flowing past a point each second is greater.

The final thing the resistance of a piece of wire depends on is its temperature. The higher the temperature the higher the resistance. A simple explanation involves imagining that the ions vibrate more so the electrons find it more difficult to get between them. A fuller explanation uses similar reasoning to the ideas about the resistance of wires made from different metals.

## How to calculate resistance

When you calculate resistance you're really asking 'How much voltage do I need to make 1 amp flow?'

The unit of resistance is the ohm, named after the early 19th century German physicist Georg Ohm. The symbol for the ohm is Ω (the Greek capital letter omega). O for omega, o for ohm, so it makes sense. So if you see 'the resistance was 40Ω' read it as 'the resistance was 40 ohms'.

If you need 1 volt to make 1 amp flow, the resistance is 1 ohm. If you need 2 volts, the resistance is 2 ohms and so on. If a bulb needs 6 V for 2 A to flow through it, the resistance is 3 ohms.

## Current vs. voltage curve for a filament bulb

The basic relationship for all conductors is that big voltages cause big currents.

To find the detailed relationship between voltage and current you normally need to do an experiment where you change the voltage across the component and measure the current through it.

When we plot current vs. voltage for a filament (rather than a fluorescent) bulb we get a curve. If we calculate the resistance at each data point using resistance = voltage/current we find that the resistance increases. This is because the bigger the voltage, the hotter the filament. We've seen above that the resistance of a metal increases as the temperature increases.

The fact that the voltage vs. current graph is curved rather than a straight line shows that the resistance changes with changing current.

Sometimes the graph is plotted the wrong way round with voltage on the y-axis and current on the x-axis. In this case a steeper slope means a bigger resistance. But you need to be careful because the value of the slope is not numerically equal to the value of the resistance if the line is a curve.

## Current vs. voltage curve for a resistor

If you do the same experiment with a resistor the graph is a straight line. If you calculate the resistance you'll see that it doesn't change. A resistor is designed so that it's resistance doesn't change as long as the voltage across it isn't too big.

## Ohm's law

If a component obeys Ohm's law then *the current through it is proportional to the voltage across it.* Another way of thinking about Ohm's law is simply to say that the resistance stays constant when you change the voltage.

In other words doubling the voltage exactly doubles the current, tripling the voltage exactly triples the current, and so on. A wire obeys Ohm's law unless it gets too hot. The same goes for resistors.

Ohm's law is often written as

V = IR

voltage = current x resistance

## Ohm's law and straight-line graphs

If current is proportional to voltage then a graph of current vs. voltage should give a straight line through the origin.

If you plot the graph with the axes the wrong way round (voltage on the y-axis) then the steeper the straight line the bigger the resistance.

In this case the gradient of the line is numerically equal to the resistance but you need to be very careful with this idea.

## Using Ohm's law to calculate voltage and current

Since voltage = current x resistance if you know the resistance of a component and the current through it then you can calculate what voltage you'll need.

If you rearrange the equation you can get current = voltage/resistance so if you know the voltage and the resistance you can calculate the current.

## Current vs. voltage for a diode

A diode acts like a valve for current. It allows current to pass through it in one direction but not the other. So it's as if it has infinite resistance one way and zero resistance when you turn it round.

In fact you find that the current through a diode rises rapidly once you get near some 'threshold' voltage, typically about 0.3 V. If the current rises rapidly for a small change in voltage then the resistance must be decreasing.

## Resistance of a light dependent resistor (LDR)

The resistance of an LDR decreases the more light that falls on it. To show this you typically keep the voltage constant, change the brightness of the light falling on the LDR and measure the current through it.

An LDR might have a resistance of a few thousand ohms in the dark and a few tens of ohms in bright light.

The resistance drops because photons of light can give some electrons enough of a boost to break free from their atoms. The more free electrons the lower the resistance.

## Resistance of a thermistor

The resistance of a thermistor changes with temperature. Normally higher temperature means lower resistance.

Again a typical experiment involves keeping the voltage constant, changing the temperature of the thermistor and measuring the current through it.

The higher the temperature the more free electrons are shaken free and so the lower the resistance. This process overwhelms any tendency for the resistance to increase by the same process as in metals.