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Investigating Resistance– To investigate if and how a wires length affects the resistance.

Extracts from this document...

Introduction

Investigating Resistance – To investigate if and how a wires length affects the resistance.

Problem:

Altering the number of cells or the voltage supplied from the power pack can change the amount of current flowing through a wire. However, the amount of current will also depend upon the resistance of the wire. The resistance, in turn, depends upon certain characteristics of the wire itself.

Task / Aim:

To investigate if and how a wires length affects the resistance.

Theories & Formulae:

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as

image04.png

The factor in the resistance which takes into account the nature of the material is the resistivity. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

Resistance

image05.png

The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it:

image08.png
If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behaviour of the material. Although the definition above involves DC current and voltage, the same definition holds for the AC application of resistors.

Whether or not a material obeys Ohm's law, its resistance can be described in terms of its bulk resistivity. The resistivity, and thus the resistance, is temperature dependent. Over sizable ranges of temperature, this temperature dependence can be predicted from a temperature coefficient of resistance.

Ohm's Law

For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship:

image07.png

ADVANCED RESEARCH:

Microscopic View of Ohm's Law

image09.png

When electric current in a material is proportional to the voltage across it, the material is said to be "ohmic", or to obey Ohm's law. A microscopic view suggests that this proportionality comes from the fact that an applied electric field superimposes a small drift velocity on the free electrons in a metal. For ordinary currents, this drift velocity is on the order of millimetres per second in contrast to the speeds of the electrons themselves which are on the order of a million meters per second. Even the electron speeds are themselves small compared to the speed of transmission of an electrical signal down a wire, which is on the order of the speed of light, 300 million meters per second.

The current density (electric current per unit area, J=I/A) can be expressed as

image10.png

The number of free electrons, assuming one per atom, is

image11.png

From the standard form of Ohm's law and resistance in terms of resistivity:

image12.png

The next step is to relate the drift velocity to the electron speed, which can be approximated by the Fermi speed:

image13.png

The drift speed can be expressed in terms of the accelerating electric field E, the electron mass, and the characteristic time between collisions.

image14.png

The conductivity of the material can be expressed in terms of the Fermi speed and the mean free path of an electron in the metal.

image06.png

...read more.

Middle

Length of wire.Thickness of wire -> Cross sectional area.Potential difference (Pd).Material of wire.Temperature.

Prediction:
I predict that the length of the wire will be directly proportionate to the resistance. I.e. if the length of the wire is doubled the resistance will also double.

The formula for the relation between the length and resistance of a wire (for more information refer to the research section):image00.png

R = V / I

Where:
R = resistance.
V = Potential difference (Pd) across the conductor (wire).
I = current.

Apparatus:

The apparatus that I will use:

  • Steel wire with a cross sectional diameter of 0.5mm ands a length of 1 metre.
  • Power pack – A/C variable current and voltage.
  • Voltmeter. (Connected in parallel.)
  • Ammeter. (Connected in parallel.)
  • Metre rule – To measure contact distance.
  • Wires to create the circuit.

The apparatus was set up as follows:

image01.png

image02.png

Method:

  1. Gather all equipment required.
  2. Make sure all of the equipment is working correctly.
  3. Cut one metre of wire and attach it securely to a surface.
  4. Connect the circuit – as shown in the diagram.
  5. Ensure the circuit is working correctly.
  6. Ensure the ammeter and voltmeter is displaying correct results.
  7. Perform a trial run of the experiment.
  8. Perform the experiment -
  9. Turn on the power source.
  10. Record the readings displayed on the voltmeter and ammeter.
  11. Measure decrease in current & potential difference.
  12. Move the contact points on the wire 100mm closer together.
  13. Record the readings given.
  14. Repeat steps 8 -10 until the contact points are in contact with each other. (10 moves – length of wire = 1 metre. 10 x 100mm moves.)
  15. Repeat the experiment to ensure accurate results and reliability in the method.

Length (M)

Amps (I)

Volts (V)

R = V   (Ω)

      ---

       I

                                                  V

image03.png

                          A

Safety:

There are many hazards when working in a laboratory. In the series of tests that were performed there were also many hazards:

  • High voltage electricity was use in the experiment. Dew care and attention were always a top priority when performing these experiments.
  • High temperatures: some of the wires used in the experiment grew very hot. We had to be careful not to touch them.
  • Potential for crowding as there were many people.

Fair Test:

To make sure the experiments performed were fair only a few variables were allowed to be changed.

  • The distance between the two contacts was the main variable. This variable we had control over, other variables such as the temperature of the wire, we could not control.

Everything else remained constant.

  • I made sure the apparatus was working correctly.
  • I performed a trial before the real experiment to ensure that the equipment was set up correctly.
  • The final experiment was performed 3 times to ensure accurate and reliable results. (The most accurate set of data was used.)

Reliability:

To ensure that the results are reliable and accurate I will perform the test three times and use the most reliable set of data. I didn’t perform the test more that thrice because it would have taken to long. Also I believe that performing the experiment thrice will provide accurate and reliable results.

Trial: I performed a trial test before performing the series of tests. I did this to ensure that apparatus was performing correctly and to a high level of accuracy. I also did this so I could perform the series of tests more efficiently. Another reason was to help me decide on the observations and measurements to be made in the series of tests that followed.

The Trial was conducted at room temperature (in this case 19°c).

Results of Trial:

Obtaining Evidence

I used a wide range of equipment and materials to obtain the evidence required for this experiment.  I managed their surrounding environment to ensure that I obtained accurate results.

Apparatus & Materials:

  • Steel wire with a cross sectional diameter of 0.5mm ands a length of 1 metre.
  • Power pack – A/C variable current and voltage.
  • Voltmeter. (Connected in parallel.)
  • Ammeter. (Connected in parallel.)
  • Metre rule – To measure contact distance.
  • Wires to create the circuit.
...read more.

Conclusion

There is a formula to display the relationship between the length and the resistance:

R = V / I

Where:
R = resistance.
V = Potential difference (Pd) across the conductor (wire).
I = current.

Here is a graph displaying the direct proportional relationship between a wires length and its resistance.

image00.png

The results prove that the electrical resistance of a wire is greater for a longer wire, less for a wire of larger cross sectional area, depends upon the material out of which the wire is made.

The resistance of a wire can be expressed as:

image04.png

The factor in the resistance which takes into account the nature of the material is the resistivity. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

The results produced from the series of experiment prove Ohm’s law to be correct.

OHM’S LAW

For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterised by such a resistance, then the current can be predicted from the relationship:

image07.png

...read more.

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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