Neha Shah – 10EC/10PY
Investigating How The Resistance Of A Wire Changes With Length
AIM
To investigate the relationship between the length of wire and its resistance when a voltage is applied.
PREDICTION
If I double the length of a wire I would expect the resistance to approximately double proportionally. If I halve the length of the wire I would expect the resistance to approximately halve proportionally. I predict that as the wire gets hotter, its resistance will increase.
HYPOTHESIS
The wire allows an electric current to flow through it, but it does not allow the current to flow with ideal freedom. Electric current is the flow of electrons. This is a diagram showing atoms in the metal (which are really positive ions) surrounded by a sea of free electrons.
Collisions between the free electrons and positive ions of the conductor (wire) interfere with the flow of electrons from the current. In a collision the electrons collide with the ions in the wire and as a result they lose kinetic energy which is transformed into heat. This prevents the flow of electrons and this effect is known as resistance. The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula:
Voltage
Current
The symbol for ohms is the Greek letter omega, Ω. It is also relevant to know of Ohm’s law, which states the current through the wire at a steady temperature is proportional to the potential difference. Therefore the voltage and current is constant. A temperature increase is the result of heat energy being released. Therefore an increase in the length of the wire causes the temperature to increase. Using Ohm’s law, we find that there will be a decrease in current and an increase in resistance.
The resistance of a piece of wire depends on the affect of the 4 factors: Length, Cross sectional area, Material and Temperature. In this investigation we will be looking at the length.
- Length - The length of the metal conductor can affect the resistance. The longer the length of the wire, the higher the resistance. This is because there are more positive ions in the metal so there is more chance that the electrons will collide with one of the ions therefore there is more resistance. The length of the wire will start off to be 100cm (1m) and then decrease every 10cm down to 20cm. Electrons have a longer distance to travel so there will be more collisions at the beginning and then will reduce, when the wire shortens. The length of the wire will make a difference to the resistance because when you have a long wire, the electrons have to squeeze together for longer to be able to pass through the wire than they do in order to be able to pass through a short wire. The longer the wire, the greater the resistance.
- Cross-sectional area - If the metal conductor has a large cross sectional area then the resistance is likely to be lower because there is more room for electrons to pass through the wire at the same time, therefore allowing more charge to pass through. If the conductor has a small cross sectional area then less electrons can pass through at the same time therefore there will be more resistance. This shows that electrons need a large cross sectional area for a large charge to pass through. In the investigation, I will use a series of different diameters but the same material.
- Material - different materials have different resistances because the atomic structures are different, so some metals have a higher or lower resistance. Metals with a large number of free electrons have a lower resistance. Therefore it is important to keep the same material throughout the investigation. If different materials are used, it will affect the results. Throughout the experiment I will use Constantan wire of two different diameters. The type of material will affect the amount of free electrons that are able to flow through the wire.
- Temperature - When the temperature of the wire increases the resistance of the wire increases. The is because when the temperature increases the kinetic energy of atoms in the metal increase and causes vibrations because of the change in energy. This means the electrons have more difficulty getting through the wire as they collide with the atoms which are in their pathway. This increases the amount of collisions between electrons and ions, therefore there is more resistance. However it is hard to keep the temperature exactly the same, as the room temperature might change. The investigation will be done at room temperature. It cannot be investigated because you cannot control the temperature.
