# Ohm’s Law: Out How the Length of and the Width of the Wire Affects the Resistance?

Resistance would be that resistance is the opposition of a conductor to a flow of current. It is when traveling electrons in a wire collide with the atoms of a wire. The collisions between the electrons and the atoms cause the electrons to move slower, which causes resistance. So, resistance would be how hard it is to move electrons through a wire.

Resistance is measured in Ohms: Resistance = resistivity p (ohm metres) x length l.

Cross-sectional area A (square meters) Current flows through a wire by a flow of electric charges.

Wire is made up of a lattice of positive ions, surrounded by ‘free’ electrons. Ions can only vibrate about in their fixed positions but electrons are free to move randomly from one ion to another. When the battery is attached to the wire, the free electrons are repelled by the negative and attracted to the positive. They still have some random movement but they move slowly in the same direction through the wire with a steady drift.

In 1827, a German physicist discovered relationship that the amount of steady current through a large number of materials is directly proportional to the potential difference, or voltage, across the materials. Thus, if the voltage V (in units of volts) between two ends of a wire made from one of these materials is tripled, the current I (amperes) also triples; and the quotient V/I remains constant. The quotient V/I for a given piece of material is called its resistance, R, measured in units named ohms.

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The resistance of materials for which Ohm’s law is valid does not change over enormous ranges of voltage and current.

Ohm’s law may be expressed mathematically as V/I = R. That the resistance, or the ratio of voltage to current, for all or part of an electric circuit at a fixed temperature is generally constant had been established by 1827 as a result of the investigations of the German physicist George Simon Ohm. Alternate statements of Ohm’s law are that the current I in a conductor equals the potential difference V across the conductor divided by the resistance of the conductor, or simply I = V/R, and that the potential difference across a conductor equals the product of the current in the conductor and its resistance, V = IR.

In a circuit in which the potential difference, or voltage, is constant, the current may be decreased by adding more resistance or increased by removing some resistance. Ohm’s law may also be expressed in terms of the electromotive force, or voltage, E, of the source of electric energy, such as a battery. For example, I = E/R. With modifications, Ohm’s law also applies to alternating-current circuits, in which the relation between the voltage and the current is more complicated than for direct currents. Precisely because the current is varying, besides resistance, other forms of opposition to the current arise, called reactance.

The combination of resistance and reactance is called impedance, Z. When the impedance, equivalent to the ratio of voltage to current, in an alternating current circuit is constant, a common occurrence, and Ohm’s law is applicable. For example, V/I = Z. With further modifications Ohm’s law has been extended to the constant ratio of the magneto motive force to the magnetic flux in a magnetic circuit. Resistance values in electronic circuits vary from a few ohms, W, to values in kilohms, kW, (thousands of ohms) and megohms, MW, (millions of ohms). Electronic components designed to have particular resistance values are called resistors.

Hypothesis: Resistance is caused by electron bumping into irons. If the length of the wire is doubled, the electrons bump into twice as many irons so there will be twice as much as resistance (resistance as a length. ). If the cross sectional area of the wire doubles, there will be twice a many irons and twice as many electrons bumping into them, but also twice as many electrons getting through twice as many gaps. If there are twice as any electrons getting through, as there is twice the current, the resistance must have halved. This means that resistance a 1 (cross-sectional are of the wire).

I am assuming that the temperatures are kept constant and that the material is kept constant. We can include this in our equations by adding a constant R=PL/A Where P=Constant R=Resistance L=Length and A=Cross-sectional area of the wire. The equation R=PL/A is found like this: We have 2 equations RAL and RAL/A If we combine them we have RA1 i?? L/A which becomes Ra L/A If we add a constant P then we have our equation R=PL/A Preliminary Work I will use nichrome wire, because it has more resistance compared to nickel and copper. I have chosen to test the length, as it is simple to compare the average resistance when the length has changed.

I tested nichrome, nickel and copper wire and found out that nichrome is the best to use. The resistance of a wire depends on certain factors. Some of these variables are listed below:  Length of wire  Diameter of wire Temperature at which wire is at  The material of which wire is made out of  The potential difference across circuit  Cross sectional area Factors: The factors I believe that will affect what happens in the investigation are:

1. Diameter/Cross sectional area: A good example to illustrate this where two cars are travelling down a dual lane road side by side. As soon as the road changes to become a single lane road, it is impossible for the cars to travel side by side and one must stop and resume behind the other car. This same can be said for electrons in a wire, the larger the diameter/cross section, the more electrons are able to travel trough the wire at the same time.
2. Temperature: When the temperature of a metal increases the resistance of that metal increases. This is because when the temperature increases the atoms of the metal vibrate more vigorously because of the increase in energy. This means that 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 therefore there is more resistance. However it is hard to keep the temperature exactly the same as the room temperature might change from day to day. It is essential to use a low voltage because it means a low current that will not heat up the wires. If a high voltage is used the energy would be in form of heat which would make the experiment unfair. The investigation will be done at room temperature. The temperature cannot be investigated because it is hard to control the range of temperature needed without the correct apparatus.
3. Length of wire: The larger the length of the wire, the larger the resistance. This is because there are more atoms from the metal so there is more chance that the electrons would collide with one of the atoms therefore there is more resistance. The length of wire will be variable throughout the investigation. Electrons have a longer distance to travel when the wire is longer, so there are more collisions . The length of the wire will make a difference to the resistance. This is 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.
4. Type of material: Different materials have different resistances because the materials’ atomic structures are different so some metals have low resistances and some have high resistances. Therefore it is important to keep the material the same throughout the experiment unless a different material is used to check if the conclusion or theory works for all materials.