# Cross-sectional area - Sample Essay

This coursework assignment is to investigate resistance. To investigate it, we must first understand it. What is it? Where does it come from? The most fundamental basis to understanding resistance is to know about current. Electric current is a flow of electric charges. Like water in a heating system, the charged particles are already in the conductors. Most electrons in a conductor (e. g. copper) are held tightly to their atoms, but each atom in a conductor has a couple of electrons that are loosely held.

Since the electrons are negatively charged, an atom that loses an electron is left with a positive charge (since the protons remain), and is called an ion. This means that copper (and all similar conductors) consist of a lattice of ions surrounded by ‘free electrons’. The ions can only vibrate in their current state, but the electrons can move randomly throughout the lattice. All metals (conductors) are made this way. When a battery is attached to a metal, the free electrons are repelled by the negative terminal and attracted by the positive one.

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They still move randomly, but they all move slowly in the same direction with a steady drift velocity. This is a flow of charge, an electric current. Current is measured in Amps (I). A simple circuit through a conductor looks like this: The greater the resistance of a component, the harder it is for charge to flow through it. In a conductor with a higher resistance, the electrons have more collisions with the ions than if they were flowing through a conductor with lower resistance. If there is a potential difference (Voltage, V) across a conductor, a current (Amps, I) goes through it.

But when you apply the same potential difference across different conductors, the currents are different. For example, if we put a potential difference of 230V across a kettle and toaster, the current in the kettle is 10A, whereas the current in the toaster is only 5A. The current is smaller in the toaster so it must have a higher resistance. Resistance is measured in ohms (? ) and has this definition: “The resistance of a conductor is the ratio of potential difference applied across it, to the current passing through it” So the formula for resistance is: Resistance, R = Potential difference across the conductor, V (volts)

(? ) Current through the conductor, I (amps) or R = V or V = I R I As the potential difference doubles, so does the current. This means the resistance of a wire is constant. This rule was discovered by Georg Ohm and is true for all metals at a constant temperature. “As long as a metal is kept at a constant temperature, the current through a conductor is directly proportional to the potential difference across it” This is ohm’s law, and it can help us to get good results. There are a number of factors affecting how much resistance a conductor has. They are these:

Type of material – Different conductors have different levels of resistivity. E. g. Copper has a much lower resistance than nichrome.  Length – A short wire has less resistance than a long one. The free electrons have to travel a farther distance in the long wire, passing between more ions. This increases the chances of an electron hitting one, therefore there are more collisions, thus a higher resistance.  Cross-sectional area – A thin wire has more resistance than a thick one. This is simple due to the fact that more electrons can flow through a thicker wire, similar to the way more water can pass through a wider pipe.

Temperature – In metals, a hot wire has more resistance than a cold one. This is because, as a metal eats up, the ions vibrate more. This increases the chance of them colliding with electrons, thus there is a higher resistance. The resistance of a wire at constant temperature depends on its dimensions, and the material from which it is made. Every material has a property called its resistivity (p). It is measured in ohm metres (? m). The higher the resistivity, the harder it is to charge flow through the material. Conductors have low resistivities and insulators have very high ones.

If we know the resistivity, the cross-sectional area and the length of a sample material, we can calculate its resistance thus: Resistance, R = Resistivity, p (? m) x length, l (m) or R = p l (? ) Cross-sectional area, A (m2) A So now that we understand what resistance what are we going to do with it? Why an experiment of course! I’m going to be investigating how the length of a wire affects the resistance. I will try passing the same voltage through different lengths of the same wire and see how length affects the resistivity. Prediction I predict that the longer the wire is, the higher the resistance.

As shown in this graph: The resistance is directly proportional to the length of the wire (i. e. If the length doubles, so does the resistance). This is because as the length doubles, so does the number of ions in the conductor. With twice as many ions, there are twice as many collisions, thus twice the resistance. I likewise predict that the current passing through will be inversely proportional (i. e. if the length doubles, the current halves) to the length of the wire. I can also predict that, as I am using an ampage of 0. 5A, the resistance will be double the voltage read.

This is because the formula for resistance is R=V/I. Therefore, if I=0. 5A, then V/0. 5 is equal to V x 2. Using to the rule: Resistance, R = Resistivity, p (? m) x length, l (m) or R = p l (? ) Cross-sectional area, A (m2) A I can predict that, whilst retaining the same metal (as all metals have different resistivities) and the same cross-sectional area (keep these variables constant, to ensure that the changes made to the length variable are accurate to the result) then changes in length will affect the resistance. The way that the equation is formed means that if the length increases, so will the resistance (And vice-versa).

This rule backs up my previous prediction so I’m pretty sure that’s what will happen. Method To test the resistance of each different length of wire, I will need this equipment…  Power Pack  Crocodile Clips  An Ammeter  A Voltmeter  A 100cm Length Of 28swg Wire  A Meter ruler Selotape  Two Probes  Double Ended Connector Cables Safety points: In order to make the experiment as safe as possible, I will tuck away all obstructions (bags, coats), keep all metallic objects away from the experiment (to avoid a short circuit) and make sure to be entirely sensible and safety conscious around the apparatus.

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