When the electrons in the metal get energy they jump in the Conduction Band. The highest Band containing electrons is only partly filled. So the electrons in this band can easily move to unfilled levels rather than up the band. These electrons have broken free from individual atoms, and are able to move through the material. So this band is called the Conduction Band. The Valence Band is just is immediately below the conduction band. Electrons in the Valence Band are firmly attached to individual atoms. In Good Conductors, the valence Band and Conduction Band are almost overlapping. In Poor Conductors the gap between the Conduction and Valence Band is higher, and thus the electrons need more energy to flow through the metal.
Non-Ohmic Conductors
Filament Lamp
A filament Lamp is simply a small metal wire that is glowing with heat. The metal used in filament lamps is tungsten. This is important because tungsten is solid at very high temperatures. Electricity flowing through the wire causes it to heat up due to the increasing resistance. The heat energy due to the resistance goes into electrons of the tungsten atoms. The energy pushes the electrons farther away from the nucleus of the atoms. As the electrons fall back, they give off photons,which are little bits of light.
Current (I) V
I
Voltage (V)
In a filament lamp, the graph of I against V becomes less and less steep as the current increases from zero. So the value of V/I increases as the current increases. Hence the resistance of the filament increases with increasing temperature. So its resistance increases with increased temperature.
The resistance can be calculated by the gradient, where :
Gradient = Current but Resistance= Voltage
Voltage Current
Therefore; Resistance = 1
Gradient
As the Gradient decreases, the current increases.
Semi-conductors
Semiconductors are a special class of materials with the common feature that they all conduct electricity better with an increase in temperature. Most semiconductor materials are metal oxides whose resistance decreases rapidly, as temperature increases. This is because as the voltage increases, the temperature increases, and this extra energy is used to liberate more electrons in the semiconductor. As more electrons flow, current increases.
Current (I)
Voltage (V)
As voltage increases, the temperature increases, the resistance decreases, and hence the graph gets steeper.
Resistance (Ω)
Temperature (oC)
The resistance of a semiconductor decreases as the temperature increases.
I will now experiment to see if my predictions based on my knowledge of the different kinds of conductors are correct. In this section, I will plan my experiments. I am going to investigate the characteristics of Ohmic and non-ohmic conductors by experiments.
For this, I am going to first experiment with a metal, a filament lamp, and a thermistor.
The basic Apparatus I will need is:
- A cell with a power supply of 1.5v
- A voltmeter (0-2 V)
- An Ammeter which shows up to 1 amp
- A variable resistor
- 2 metal wires: Copper and Nichrome, 25 cm each, with a cross sectional area of 0.5 mm
- A filament lamp
- Thermistor
- Thermometer
- Beaker with water
- Bunsen Burner
Experiment 1
Metal Wires
For my first experiment I will be connecting the circuit as in the diagram shown above. I will first set the Variable Resistor as at its maximum value. The variable resistor will be used to supply varying voltage to the wire. Then I shall take down the readings of Current at different voltages at intervals of 0.2 V. I will take down at least 10 sets of values to investigate the varying current according to the voltage to find out the resistance in a Copper wire. I will take down the results in a table like the one below.
The experiment will then be repeated, and the current will be taken, at intervals of 0.2 V, in ascending order so as to avoid errors and obtain reliable results.
I will repeat the experiment with a Nichrome wire, to see how the resistance is different in wires of different materials. The Nichrome wire will be of the same length and width. All other factors will also be kept constant. I will take the readings for Current, as I vary the voltage, in the same manner, backward and then forward.
Precautions:
To ensure that the test is fair,
- I have to ensure that the temperature of the wire is kept constant. For this, I will have to make sure that the circuit is not switched on for too long, and I will have to work swiftly.
- I will also have to make sure that a parallax error is avoided, while reading the current, from an analogue Ammeter.
Experiment 2:
For my second experiment, I will be connecting the circuit, as in the diagram shown above. The experiment will be carried out in the same way as the previous one. A filament lamp will be in place of the metal wire, and the temperature won’t remain constant. In this experiment, I will be noting the Current for the various Voltages at intervals of 0.2 V, in the same manner as I did for the previous experiment, in descending order, and then in ascending order. The average of he two will then be taken, to obtain reliable results.
Experiment 3:
In my third experiment, I will be investigating the increase in current, as the voltage increases in a thermistor. The circuit will be connected as shown in the circuit diagram above, and 10 sets of voltage and current will be noted, at intervals of 0.2 V. The results will be recorded in a table like the one below:
In the same experiment, I will investigate how the current increases on external heating of the thermistor.
In this experiment, the thermistor will be placed in a water bath, as shown above. I will be using distilled water, to ensure that there are no ions in the water to conduct electricity, even if there is a fault in the insulation. The beaker will be placed over a Bunsen burner, and a thermometer will be suspended into the water, to check the temperature of the water. The readings of current will be taken at intervals of 5 oC as the water is heated. And then again the current will be noted at intervals of 5 oC as it cools. The average of the two currents will then be taken, to ensure that out results are reliable. In this experiment, the voltage will be kept constant, at 0.5 V, because we want to investigate how the current increases on external heating only.
The results will be recorded in a table like the one shown below:
Precautions:
Stirring is needed, so that convection currents in the water heat the thermistor. Stirring will also ensure that heating is uniform, and the thermistor is at the same temperature as the water.
I will also have to make sure that the thermometer is suspended in the water, and it does not touch the bottom of the beaker, or else the thermometer won’t show the correct temperature of the water.
While reading the thermometer, a parallax error should be avoided. Standing exactly in front of the thermometer while reading the temperature can do help avoid this.
Prior Test Results
Before carrying out the actually experiment, I conducted a prior test, to know exactly how my main experiment would be like. My Prior test was a little different from what I had planned.
- In the trial test I used digital ammeters and voltmeters were used.
- For my test, I used a filament lamp.
- The readings I entered in the table this time contain the intervals of 0.2 from the voltage range of 0-2 Volts
Experimenting
These are the results I obtained from my experiments.
- Instead of a Copper wire I used Constantan. The thickness of the wires is 0.4mm and the length of the wire is 80 cm.
Constantan
Length: 80 cm
Width: 0.45mm
Gradient = Current
Voltage
Gradient = 0.3
Resistance = 1/0.3 = 3.33 ohms
Nichrome
Length: 80cm
Width: 0.45mm
Gradient = Current
Voltage
Gradient= 0.167
Resistance= 1/0.167 = 5.98 ohms
Filament Lamp
Thermistor
Thermistor Heating
Voltage: 1 V
Thermistor Cooling
Voltage: 1 V
In this section, I am going to analyze my results and draw a conclusion. From the results, I can see that Current increases with Voltage for all the graphs. But the way in which it increases is different.
Any difference in reading may be due to some error, which I will account for in evaluation.
Ohmic Conductors
For both the metal wires, Current increases with Voltage at a steady rate. Current and Voltage are directly proportional. We can note that when Voltage doubles, the corresponding value for current also doubles.
Nichrome
Constantan
For both wires, since all the readings for resistance are constant, and the graph is a straight line passing through the origin, we can say that the values are directly proportional. Resistance is constant throughout, and thus it proves that the metal wires are ohmic conductors.
Non-Ohmic Conductors
Filament Lamp
From the graph and table for the filament lamp, I have noted, that as voltage increases, current increases too, but at a smaller rate.
When Voltage is doubled, Current increases too, but it is less that double.
For eg. :
When Voltage is 0.2 V, Current is 9.2 mA;
When Voltage is 0.4 V, Current is 12.1 mA. (Instead of doubling to 18.4 mA)
This graph shows a complete curve. At the beginning of the graph the current is increasing at a high rate (the voltage is also increase but not at the same rate as the current). But by the end the current decreases, causing the graph to become less steep. Voltage and current have a non-linear relationship. At the beginning of the graph, resistance is constant, but towards the end, resistance increases with voltage, as the temperature increases.
Thermistor
From my results, for the thermistor experiments, I can see that when voltage increases, current increases too, but not proportionally. When voltage doubles, current doesn’t double, it more than doubles.
At a higher current, resistance decreases. Though, in this voltage range, the heating wasn’t sufficient for us to observe a curve. Thus, we heated it externally, keeping the voltage constant.
Thermistor Heating
As it is heated, we note that current increases, and resistance decreases.
Thermistor Cooling
As the thermistor cools, we note that resistance increases, and current decreases.
Conclusion
My analysis and conclusions can also be supported by scientific theory, of free electrons in conductors.
The allowed energy levels in a single atom are discrete and spaced widely apart. In the solid state, a large number of atoms are packed closely together, and the electrons are influenced strongly by the assembly of the nuclei. . In the upper energy band (the conduction band) the electrons are free to move between atoms and become charge carriers. In the lower energy band (valence band) electrons are tightly bound to their atoms and are not to free to move about. In some circumstances it is possible for an electron in the lower band to gain enough energy to jump into the higher band and become a charge carrier.
As the temperature of the conductor rises, the amplitude of vibration of the atoms increases and drifting electrons then make more collisions with atoms. The time between the collisions, which can be called the relaxation time, decreases.
Ohmic conductors
Ohms law states that the current flowing through a metal wire is proportional to the potential difference across it (provided the temperature remains constant).
This is because as the voltage increases, more electrons have the energy to flow through the conductor, causing the current to increase simultaneously, (provided the temperature of the conductor remains constant).
In metals, the valence and conduction band can over lap. The electrons in the overlapping region of energy are conduction electrons.
I
Non-Ohmic Conductors
Filament Lamp:
In a filament lamp, the conductor used is usually Tungsten, which has very high resistance. When current flows through the wire, the electrons flowing through, collide with atoms. As Current increases, electrons gain more energy, and thus electrons collide more often with the atoms, transferring energy to them, causing them to vibrate more vigorously, and causing less electrons to flow through easily. In a filament lamp, as temperature increases with voltage, the electrons gain more energy, but at the same time the atoms vibrate more, and hence resistance increases.
Thermistor:
In Semi-conductors, as voltage increases, the energy in the semi-conductor is used to liberate more electrons. If there are more electrons free to move, this may outweigh the effect due to the vibrating atoms, and thus the flow of electrons, or the current, will increase. Thus the resistance decreases. Let me explain this theory using energy bands:
Semiconductors have a narrow forbidden band between the valence and conduction bands. At normal temperature, the thermal energy of some valenc electrons, is sufficient for them to reach the conduction band, where they may become conduction electrons. The increase in thermal energy of the valence electrons due to temperature rise enables more of them to break the covalent bonds and become free electrons.
I will now evaluate the method I used for my experiments. Looking at the results from the experiment, I can say that my method was good, because:
There were very few points outside the line of best fit.
I used a variable resistor as a voltage divider, which is a convenient way of controlling the voltage applied.
I also used digital multi meters to check the reading for Voltage and current. These are better than voltmeters or ammeters, because we can specify the range of voltage we need, and the units we want to measure current and voltage. Digital multi meters are also known for their precise degree of accuracy.
I repeated each experiment twice to ensure the reliability of my results.
For the ohmic conductors, I used a small voltage range, which was appropriate, because otherwise the heating of he wires would take place.
In spite of taking precautions, there were a few sources of error present:
The heating of the thermistor may not be so accurate, because the oil was heated too soon, and thermal equilibrium could not be obtained. The readings of temperature were that of the water. So I assume that the thermistor was not the same temperature as the oil, in spite of stirring and slow heating. I think the cooling of the thermistor was more reliable, because it cooled at a slow pace.
Even though I tried to keep the temperature of the wires constant, as the voltage increased, there would have been some heating of the wire. This may also have resulted in some error.
My experiment would have been even better, and accurate if:
I had used digital thermometers for accurate readings.
The heating could have been even slower
I could have also used a filament lamp and thermistor with a higher voltage range.
My experiment is pretty reliable, because I conducted each experiment twice, and I have not found too many sources of error present. All my conclusions matched with my prediction. However, to ensure the accuracy of my results, I can calculate Resistivity of the conductors. Resistivity is constant for a material. I am going to calculate all my values for resistivity, and compare it with the standard values for resistivity.
Resistance ∝ Length
Area
Resistance = P x length
Area
P = Resistance x Area
Length
Nichrome
Resistance = 5.98 ohms
Length = 80 cm = 0.8 m
Diameter = 0.45 mm = 0.45 x 10-3 = 4.5 x 10-4
Radius = (4.5 x 10-4) / 2
Area of cross-section = π r2
= 3.14 x (2.25 x 10-4) 2
= 1.58 x 10-7 m2
P = Resistance x Area
Length
= 5.98 x (1.58 x 10-7 )
0.8
= 1.18105 x 10-6Ωm
= 1.2 x 10-6Ωm
Constantan
P = Resistance x Area
Length
= 3.33 x (1.58 x 10-7 )
0.8
= 6.57675 x 10-7Ωm
= 6.6 x 10-7Ωm
The standard value for Nichrome is: 1.2 x 10-6Ωm
The standard value for Constantan is: 4.9 x 10-7Ωm
The values I got are very close to the standard value, so I can say that my results are reliable.
Identifying any anomalous errors present and offering a solution:
For my filament lamp and thermistor graphs, I got a few points outside the line of best fit. This shows that there was an error present this may be because I didn’t wait for them to heat before taking the current readings. This could have been avoided by waiting a little while before taking a reading.
My metal wires weren’t completely ohmic. Even though precautions were taken, by using a small voltage range, the temperature could not have been kept completely constant.
The heating for the thermistor was too fast. There was a lack of thermal equilibrium between the thermistor and the oil bath. The points I got weren’t on the line of best fit at all. The cooling was more reliable.
Suggesting A new Experiment:
An LDR is a special type of resistor, which changes its resistance based on the amount light falling on it. A photoresistor is made of a high resistance semiconductor. If light falling on the device is of high enough frequency, absorbed by the semiconductor give bound enough energy to jump into the . The resulting free electron (and its partner) conduct electricity, thereby lowering resistance. LDRs are used in electronic circuits to operate light-sensitive switches.
For this experiment, we will need:
- Ammeter
- Voltmeter
- LDR
- Filament Lamp
- Connecting Wires
- Crocodile clips
- 2 Batteries
The Apparatus will be set up as shown below:
The results I expect, are shown below:
Voltage(V)
Wattage
I will first set the Variable Resistor as at its maximum value. The variable resistor will be used to supply varying voltage to the filament lamp. Then I shall take down the readings of Voltage of the LDR at different voltages at intervals of 0.2 Vof the filament lamp. I will take down at least 10 sets of values to investigate the varying current according to the voltage to find out the resistance in an LDR. I will take down the results in a table like the one below.
The experiment will then be repeated, and the current will be taken, at intervals of 0.2 V, in ascending order so as to avoid errors and obtain reliable results.
Final Conclusion
Thus, from my experiments, I have found:
- Current always increases with voltage, but the rate at which it increases varies.
- When temperature is constant, current is proportional to voltage.
- As voltage increases in a filament lamp, current doesn’t increase proportionally. It increases at a slower rate. Hence, filament lamps should be used with a high voltage, as they will then be brighter.
- As voltage and temperature increases in a thermistor, current increases at a higher rate.
- A Light dependant Resistor’s resistance varies with the amount of light falling on it.
