To investigate how the length (mm) and the cross-sectional (mm2) area of a wire affects its resistance (ohms).

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GCSE Physics Coursework                Abu Shoaib

                5A

GCSE COURSEWORK

PHYSICS : RESISTANCE OF A WIRE

Coursework

Coursework Owner         :         Abu Shoaib

Date Submitted         :         7 November 2003

Form         :         5A

        


TABLE OF CONTENTS

1.        PLAN        

1.1.        Aim:        

1.2.        Background knowledge:        

1.3.        Apparatus:        

1.4.        Safety:        

1.5.        Variables:        

1.5.1.        RESISTANCE (OF ENTIRE CIRCUIT)        

1.5.2.        RESISTANCE (OF RHEOSTAT)        

1.5.3.        LENGTH        

1.5.4.        CROSS-SECTONAL AREA        

1.5.5.        SUBSTANCE        

1.5.6.        TEMPERATURE        

1.6.        Observations to be made:        

1.7.        Theory:        

1.8.        Method:        

1.9.        Prediction:        

1.9.1.        LENGTH:        

1.9.2.        CROSS-SECTIONAL AREA:        

1.10.        Variables table:        

1.11.        Preliminary work:

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  1. PLAN

  1. Aim:

To investigate how the length (mm) and the cross-sectional (mm2) area of a wire affects its resistance (ohms).

  1. Background knowledge:

Electricity, or more specifically, the flow of electrons carrying an electrical charge through a metallic conductor is known as an electrical current. When two objects with different charges touch and redistribute their charges, an electric current flows from one object to the other until the charge is distributed according to the capacitances of the objects. If two objects are connected by an object that lets charge flow easily, such as a copper wire, then an electric current flows from one object to the other through the wire. Electric current is measured in units called amperes (amps). If 1 coulomb of charge flows past each point of a wire every second, the wire is carrying a current of 1 amp. If 2 coulombs flow past each point in a second, the current is 2 amps. The conduction of electric currents in solid substances is made possible by the presence of ‘free’ electrons (electrons that are free to move about). Most of the electrons in a metallic conductor are tightly bound to individual atoms. However, some are free to move from atom to atom, enabling current to flow.

Normally, the motion of the free electrons is random; i.e., as many of them are moving in one direction as in another. However, if a voltage is applied to the two ends of a metallic conductor by means of a battery, the free electrons tend to drift toward one end. This end is said to be at a higher potential and is called the positive end. The other end is said to be at a lower potential and is called the negative end. The function of a battery or other source of electric current is to maintain potential difference. A battery does this by supplying electrons to the negative end of the bar to replace those that drift to the positive end and by absorbing electrons at the positive end. Although the two terminals (positive and negative) are constantly receiving and sending out electrons, the electrons themselves do not move very quickly. It is the current that flows through the electrons at the speed of light and enables instant access to electricity for all parts of the circuit.

  1. Apparatus:

To effectively carry out this experiment and get the most accurate results, I have to ensure that I have the best and most accurate equipment at my disposal. After some contemplation, I have narrowed possible apparatus to the following few:

  • A rheostat
  • Several types of fuse wire (at least 5m)
  • Several insulated electrical wires
  • Two 6V DC batteries
  • An ammeter
  • A Voltmeter
  • A ruler (30 cm)
  • A few pieces of paper to make notes and record the results
  • A pen or pencil
  • A wire clipper
  • Crocodile clips
  • Calculator
  • Electronic weighing scale (in g; 2 d.p.)

These items will be set up in a circuit that will enable me to efficiently investigate the relationship stated in my aim. Since I have to obtain the most accurate results, I have the need for several types of fuse wire. This will enable me to repeat my experiment at least three times with each length of wire. The circuit should look like the following:

Fig. 1.3.1. How to set-up apparatus

The ammeter and voltmeter both read to two decimal places at least so I should get accurate results.

  1. Safety:

Since this experiment involves the use of electricity, there is always a risk of an electric shock, even if the power source in use is not very strong. Therefore, I will have to take into account all the risk factors while planning and applying my procedure.

The most important safety equipment will be the safety goggle. Since I will be using bare wire, there is always a chance of it piercing the eye. I will also always use plastic or rubber gloves while handling the wires because these substances are very good insulators and therefore I will have a low risk of getting an electric shock. As always, I will also wear an apron for safety in general. I will also have to make sure that I wear rubber soled shoes since the quickest way for electricity to flow through to the earth is through me, so if I wear rubber soled shoes, the electricity cannot pass through me.

  1. Variables:

  1. RESISTANCE (of entire circuit)

The resistance is the most important variable in this experiment since this is the one that we are going to investigate. This is the dependent variable since it depends on the length or the cross-sectional area of the wire and the rheostat value. I predict that the resistance is directly proportional to the length and inversely proportional to the cross-sectional area. Since there is no device that can measure the resistance itself, I will have to do it using a mathematical procedure. I will therefore use the variable resistor to change the current in the circuit. This is turn will change the value of the voltage. I will change the value of the variable resistor several times. I can then plot these results on a graph and using the gradient, I can find the resistance. The resistance will be measured in ohms.

  1. RESISTANCE (of rheostat)

This is the resistance of the rheostat or variable resistor. This will be used to change the current in the circuit so that I can plot a graph of a length to find the resistance at the length. This variable will be controlled by me. Since the track in a rheostat is linear, the resistance tapped off is going to be proportional to the distance moved by the sliding contact. This variable can be used as a third independent variable and can be used to effectively change the current going into the fuse wire. This will enable me to investigate my stated aim more deeply. The resistance will be measured in ohms.

  1. LENGTH

This is the length of the fuse wire (mm) that we will use to change the resistance in our experiment. This is the variable that I have decided to change in this experiment. It is one of the independent variables in this experiment. The resistance should increase as the length of the wire increases because as the length of the wire increases, so does the amount of atoms in the wire. This means that as the electrons in the circuit flow around, there are more collisions with atoms in the wire resulting in a greater loss of electrical energy than with a shorter wire. This gives the wire its property of resistance. Therefore, resistance is directly proportional to the length of the wire.

Fig. 1.5.3.1. Electrons in a long wire

Fig. 1.5.3.2. Electrons in a short wire

Since this is my main variable, I will perform the most number of experiments while changing this variable. I will start the experiment by first having the length of the wire at 10 mm. After each measurement (three times), I will increase the length of the wire by 10 mm more. This will continue until I measure the current and voltage at 150 mm. By then, I should have 15 different sets of results for the resistance while changing length.

  1. CROSS-SECTONAL AREA

This can be described as the width of the wire, but scientifically is the cross-sectional area of the wire in mm2. This is the second independent variable that determines the resistance of the wire. The resistance should decrease as the area increases because although the number of atoms increases again with the area, so does the amount of space inside the wire through which the electrons can pass through. Unlike the length where the amount of space says the same, the electrons have a lower chance of colliding with the atoms in the wire thus reducing the amount of electrical energy lost. Therefore, resistance is inversely proportional to the cross-sectional area of the wire.

Fig. 1.5.4.1. Electrons in a thick wire

As you can see in the two diagrams for the length of the wire, two of the six electrons collide with atoms on their way through the wire. In the second diagram, when the width (or cross-sectional area) of the wire is increased, the number of atoms increases as well, but so do the number of spaces for the electrons to safely pass through. This results in no collisions between the electrons and atoms.

Fig. 1.5.4.2. Electrons in a thin wire

The cross-sectional area is my second variable in this experiment, so it is important that I include it in my procedure to gain extensive results. As stated above for length, the procedure is the same, except that I will repeat the procedure a number of times for the different types of fuse wires that have different cross-sectional areas. The most common types of fuse wire available are that of 3A, 5A, and 13A. Clearly, the units for the fuse wire is A or amps. Since I have stated that the units will be mm2, I will have to devise a simple procedure that will enable me to measure the units in mm2.

This procedure will involve the use of reference books. Since I can find out what substance the wire has been made of, I can use a reference book to look up the density of the substance. After noting down the density, I will accurately weigh the wire so that I get a reading in grams to 2 decimal places. Now that I know the density and mass of the wire, I can calculate its volume using Volume = Mass/Density. Once the volume is calculated, I can easily calculate the cross-sectional area of the wire by dividing the volume by the length of the wire. This should give me an accurate figure for the cross-sectional area of the wire in mm2.

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  1. SUBSTANCE

This variable is the type or types of metal of which the wire has been made. Obviously, this is going to be important to influence the absolute resistance of the circuit. This is because different metals have different atomic structures. This means that the atomic arrangements in the wire will be different. Therefore, in some metals, the atoms will be further away from each other simply because they are larger. This allows the electrons to flow through the larger gaps in different metals. This variable is closely related to length and cross-sectional area. Since ...

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