Resistance of an LDR

In this essay, my aim is to examine the physics behind a Light dependent resistor by measuring the voltages across it when exposed to bulbs of various wattages. As with all experiments, it is necessary to make an initial prediction. I believe that the voltage across the LDR will increase if a higher wattage of bulb is used. However, we find ourselves asking the question, ‘Why should the voltage change across this component just because the light intensity around it varies? ‘ In order to answer this question we have to examine the physics behind an LDR.

The LDR: ‘Success in Electronics’ (Tom Duncan 1983) provides this symbol as the representation of an LDR and tells us that this component, sometimes called a Photoresistor, varies its resistance according to light levels. The resistance of an LDR depends upon the amount of Charge Carriers inside the component. Charge carriers are particles which are capable of carrying charge (! ) and are free to move across electron levels. According to Ohm’s law, the resistance falls in the LDR as the current throughout the circuit increases.

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The reason for this increase in current is due to the greater number of charge carriers in the semi-conductor inside the resistor. In this case, the charge carriers are electrons. This increased number of electrons when light intensity increases, raises the semi-conductor’s Conductivity and therefore lowers its Resistivity as the two values are inversely proportional. It is only reasonable to say that as the current through the circuit increases, so too will the voltage across the LDR. A Quantum Explanation for the behaviour of an LDR

I have already said that the increased voltage across an LDR is due to an increased number of electrons in the LDR’s material but I have offered no justification for WHY the number of Charge carriers increase with light intensity. Not to Scale In the diagram above I have tried to represent an atom in the semi-conductor of the LDR. The stylised arrow represents a single photon striking an electron in the lowest electron level of the atom. Note how the electron levels in the diagram come closer together as we move further away from the nucleus. This is true in real atoms also.

When light strikes an electron, enough energy can be transferred so that it has enough energy to move to a free outer shell i. e. one that is not full. The vertical arrow represents the movement of the electron below it, to an empty outer shell after the photon strikes it. Note that this movement is continuous. The electron cannot occupy as shell that is already full. To this end, it does not stop as it passes through any of the other shells and if, as in this case the first shells are full, it will fall into a new electron level that was previously empty.

A voltage increase is seen across the LDR when bulbs of increasing Wattage are placed next to it. We can see this in retrospect from the results table and the graph. However, it is not true to say that the resistance of the LDR is affected by light intensity only. When light (a photon) strikes the electron, enough energy is transferred to move it to the outer shell, as we have already discussed. The more photons there are the more electrons will be struck. This means that more electrons are free to carry charge and therefore the voltage increases.

In this way we can see how light intensity can affect the voltage. However, the amount of energy transferred to each electron by a single photon is dependent on the FREQUENCY of the light (multiplied by Planck’s constant). E=hf The reason why the voltage increases with light intensity is that the bulbs used in the experiment emitted white light, which contains all frequencies of light. The electrons in the semi-conductor all responded to the same frequency of light (i. e the amount needed for the electron to transfer to the outer electron level.

Therefore each electron receives the correct amount of energy but the higher amount of electrons means more electrons are freed, which as I have explained increases the overall voltage within the circuit. These facts (which incidentally I obtained from The Art of Electronics by Horowitz Hill 1980), went a long way to reassure me that my results were accurate. Imagine we are thinking of a non-quantum explanation for why the voltage across the LDR varies. We assume then, that it is the intensity of these light bulbs solely which will control the resistance of the LDR.

This inaccurate theory taken into account let us then examine two of my results. I obtained an average voltage across the LDR for a 20 Watt bulb of 1. 58. For a bulb of 100 Watts I obtained an average reading of 1. 92. Imagine my thinking at the beginning of this experiment. I thought that the voltage across the LDR was directly proportional to the intensity of light falling on it solely. I performed the method you will read later and then plotted my results table. Imagine then my confusion when I examined my results.

If the voltage reading depended on light intensity solely, why wasn’t the voltage across the 100W roughly 5 times (5*20=100) that of the 20W bulb? The non-quantum theory I mentioned above had to be discarded, as based upon this explanation, the voltage should double every time the light intensity doubles. The results did not bear this theory out so I realised that there must be another factor which was affecting the voltage across the component. What was initially a simple and mundane experiment developed into great significance.

Either there was a gigantic margin for error (a point I will discuss in my evaluation) or the Quantum explanation I have given for the behaviour of the LDR was true i. e. that the electrons in the semi-conductor were in fact all responding to the same frequency of light, with the same amount of energy, hence the similarity of the readings. Planning and Method for an Experiment to investigate changes in Resistance of an LDR Notes: In this experiment I experiment using various types of resistor, including a 1 Ohm and 30K Ohm component.

I found that a 1k Ohm resistor suits my purposes best as lower resistors tend to burn out or give wide-ranging results making the difficult to graph and the voltage changes in larger resistor are to small to measure given that the digital voltmeter is only precise to 3 significant figures. I initially performed this experiment in the Lab, compensating for the amount of background light by measuring light intensity before turning the bulb on and subtracting this value from the voltage reading after the light was turned on.

However I realised that as there were large windows in the laboratory, the background amount of light would never be the same from one minute to the next. To this end I decided to perform the experiment in a darkroom to minimise any extraneous light so only the light intensity of the bulb in question would be measured. I realised also that light intensity will naturally vary as the distance between the bulb and the LDR changes. In order to remove this margin of error from the experiment, I placed the clamp directly above the LDR with the bulb facing downwards.