Ohm’s law-
For many useful conductors there is a simple rule, which connects current, voltage and resistance. If you double the applied voltage, the current is doubled. If you halve the voltage, the current is halved. This effect doesn’t work with all conductors, but is true for metals and for carbon, if they don’t get too hot.
For most circuits we can use the rule to calculate what will happen when things change.
The rule is – The voltage across a metal resistor is proportional to the current through it, provided its temperature is constant. This rule/statement is called Ohm’s law.
Because V is proportional to I, we can say that:
V / I = a constant
This means doubling the voltage, doubles the current. Trebling the voltage trebles the current and so on. The larger the resistance, the greater is the voltage needed to push each ampere of current through it.
Above shows voltage-current graphs for three different circuit components- a resistor at constant temperature, a filament lamp and a thermistor (LDR).
From the graphs you can see that the filament lamp and thermistor do not obey Ohm’s law (voltage is not proportional to the current). These are known as non-ohmic conductors to differentiate them from ohmic conductors- resistor at constant temperature.
The current through a resistor (at constant temperature) is proportional to the voltage. The voltage-current graph is straight line, V/I is constant and therefore the resistance is constant.
For the filament lamp, the voltage-current graph curves upwards as current increases. This means the gradient of the voltage-current graph rises, V/I increases therefore the resistance increases as the current increases. The filament lamp is made of very thin metal wire. As the current through the filament wire increases, the temperature rises sharply. With this increase in temperature, metal atoms in the wire vibrate faster and impede the flow of electrons, which make up the electric current. So the resistance of a filament lamp increases as the current increases due to the increase in filament temperature.
At very low temperatures, the atoms in a metal vibrate very little. At extremely low temperatures, the electrons in some metals are not really impeded in any way and they become superconductors. For the thermistor, the voltage-current graph curves over as the current increases. This means that V/I and therefore resistance, decreases as the current increases.
Resistance ( ) = Voltage ( ) / Current ( )
Prediction-
To make my prediction I have to consider several factors that affect resistance. The factors affecting resistance are length, material, width/thickness and temperature.
Length of the wire-
Length of the wire affects resistance. If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this the length increase should be proportional to the resistance increase.
In a short wire electrons can travel to the opposite side quicker as there is a shorter distance and less ions to pass. In a long wire electrons take longer to reach the opposite side, as there is a longer distance to travel. Also there will be more ions present, so it will be harder for them to pass through and there will be more collisions, which results to more energy in electrons. Therefore as the wire gets longer the resistance increases.
Width of the wire-
Width of wire affects resistance. If the width is increased the resistance will decrease. This is due to the increase in the space for the electrons to travel through. Due to increased space between atoms there should be less collisions. Below is a diagram to explain this-
In a thin wire there are less metal ions, so therefore there are less routes for the electrons to travel through. So it takes longer for the electrons to get around, therefore resistance increases. In a thick wire there are more metal ions, so therefore there are more routes for the electrons to get around. There are more routes so therefore it takes a shorter time for electrons to get around. So the current increases and resistance decreases.
Material of the wire-
Material of wire can affect resistance. The type of material will affect the amount of free electrons, which will be able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms there must be more electrons available. If the material has a high number of atoms there will be a high number of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase.
Temperature of the wire-
Temperature of wire affects resistance. If the wire is heated up the atoms in the will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of electrons. This increase in collisions means an increase in resistance. But the wire can burn out if temperature rises too much. Below is a diagram to explain this.
Final Prediction-
Looking at all the information in my introduction, prediction (factors affecting resistance) and preliminary experiment results (next page) I can now be able to make a sensible final prediction. I predict as the length of the wire increases the resistance will increase. As you increase the length there will be an increase in voltage and a decrease in current, which results to an increase in resistance. I predict this because the longer the wire the more atoms so it is more likely that the electrons will collide with the atoms. So more collisions occur and therefore resistance increases. I also used my preliminary results (next page). In a series circuit as you add more resistors the resistance increases, very similar to the increase of length.
Collision theory, preliminary work and background knowledge has helped me make a sensible prediction, which is as I increase the length resistance will increase.
I can also predict what my graph will look like if the experiment is successful-
Preliminary experiment-
In my preliminary experiment I will do an experiment on series circuits and parallel circuits. I will do three series circuit experiments, I will add more resistors each time and see what affect it has on the resistance. I will do the same with a parallel circuit, I will add more resistors and see what affect it has on the resistance.
Apparatus-
- Power pack
- Resistors
- Crocodile clip wires
- Voltmeter
- Ammeter
Method (preliminary experiment)-
- I will first get all the equipment listed on my apparatus.
- Then I will set up the series circuit, I will set up three (one with one resistor, another with two resistors and the final one with three resistors).
- I will then record the results.
- Then I will set up the parallel circuits, I will also set up three (one with one resistor, another with two resistors and the final one with three resistors).
- I will then record the results.
As you add more resistors in a series circuit, the resistance increases. If the length of the wire increases the resistance increases.
As you add more resistors in the parallel circuit the resistance decreases. This is similar to increasing the length, as wire gets thicker the resistance decreases.
In the preliminary experiment I used (4V) because if we use higher/lower the wire becomes to hot and it can burn out. The precautions I took were division error, parallax error, zero error and I used (4V).
When resistors are connected in series, the total resistance is-
When resistors are parallel the total resistance is-
Method-
Apparatus-
Below is a list of the apparatus I will be using in my final experiment-
- Two 1 meter rulers
- Constantan wire
- Power pack
- Voltmeter
- Ammeter
- Clear sticky tape
- Micrometer
- Calculator
- Crocodile clips
- Wires
Variables-
The only variable I will be controlling in this experiment is the length of the wire, as I am investigating how length affects resistance. All the other variables I will be keeping constantly the same, I have to make sure that they stay the same throughout the whole experiment to ensure it is a fair test. These are the material of the wire, width of the wire and the temperature.
I will change the length by increasing the length by 10cm and I will take 10 readings, these are 20cm, 40cm, 60cm, 80cm, 100cm, 120cm, 140cm, 160cm, 180cm and 200cm. I will repeat the experiment three times.
Fair test-
I will make my experiment a fair test by doing the following things-
- Make sure I measure the lengths of wire with accuracy.
- I will use the same wire and same material.
- I will make sure the temperature stays constant by keeping the power pack on (4V). I will also do the experiment on the same day. I will have to keep the temperature constant because if temperature increases more collisions will occur between atoms and electrons, which will increase resistance. Also if temperature is increased the wire can burn out and it will not obey ohm’s law, as the temperature must remain constant to obey it. The wire I am using is the constantan wire, its resistance stays the same when it becomes fairly hot.
- I will read the ammeter and voltmeter directly above the pointer to avoid parallax error.
- I will make sure the crocodile clip is accurately on the correct interval on the ruler.
- I will make sure that the pointers on the ammeter and voltmeter on 0 to avoid 0 error.
- I will use a micrometer to make sure the width of the wire is the same as width affects resistance.
- I will stick to correct measurements.
- I will try to straighten the wire to get rid of kinks.
Safety precautions-
- Before I start my experiment I will make sure my coat and bag is put away safely away from the workbench to avoid any danger.
- I will then double check everything before I turn on the power pack as electricity is involved.
- I will not touch the wire, as it will be hot.
- I will not keep any of the equipment near the water tap.
- I will make sure no equipment is near the edge of the workbench.
- If any danger is in place with electricity I will make sure I go on turn the electricity off from the mains.
Method (final experiment)-
- I will clear the workbench and collect all the equipment.
- I will set all the apparatus out on the workbench appropriately.
- Clear things near the workbench, (example-bag)
- I will get my power pack and plug it in, and put my meter ruler straight.
- I will connect the circuit with the crocodile clip wires, ammeter and voltmeter.
- I will straighten the constantan wire, and put it straight on the ruler, then tape it so it doesn’t move.
- I will put one crocodile clip on one end of the ruler where it will stay still constantly through the experiment.
- One crocodile clip will move down the ruler to each measurement.
- I will draw the results table up.
- Before I start the experiment I will make sure everything is working to plan and all the apparatus is working.
- I will then repeat the whole experiment two more times.
This is what my results table will look like-
Below is a diagram of my apparatus-