The aim of this experiment will be to determine the relationships the physical characteristics of constantan have with its resistance. Before this, the variables in the experiment need to be defined which ones can be changed and which should remain the same. Dependent Variables Current- Measured in amperes or amps. I=V/R Current is a dependent variable that will be changed. Resistance- Measured in ohms. R=V/I Voltage- Measured in volts symbol V, V=IR Independent Variables Wire length- the length of the wire is a physical characteristic independent of any other variable does not effect.
Therefore, at least one physical characteristic must be changed. Density will remain constant because constantan will always be used, so length would seem a good physical characteristic to vary- i. e. for each length of wire a reading will be taken for a range of potential differences and then another length of wire will be used. A very simple experiment proves that resistance is directly proportional to wire length- when one light bulb was placed in a circuit and the voltage across and current through recorded, thereby allowing its resistance to be calculated, another was placed in series with it, which doubled the resistance.
In equation this is- R=KL Where K is some constant and L is length. Area of wire- Again this is a physical characteristic that will remain constant regardless of all other variables. However it will be easier to change the length of the wire, as changing the diameter will mean switching to a completely different gauge of wire. However when several ranges of data have been taken for one wire gauge, then this variable could be changed. Cross sectional area of wire is therefore an independent variable that will be changed if time allows.
Increasing the cross sectional area of the wire actually has the opposite effect to lengthening it, that is resistance is inversely proportional to cross sectional area. In effect this is because the current has a “wider” space to flow through, so the probability of collisions with positive ions in the lattice is reduced. Expressed in an equation, this is- R=K1/A Where K is some constant and A is cross sectional area. Resistivity- Resistivity is the measure of the amount of resistance per metre a material exhibits assuming a constant cross sectional area.
Its equation incorporates both length and cross sectional area, giving one equation. Measured in ? /m or ? m-1, it is defined as follows- R=? L/A Where ? equals the resistivity of the material. Redefined with ? as the subject- ?=RA/L Because resistivity for a material is always constant as long as its physical characteristics and temperature remain the same, the resistivity of the wire will only be used to check results. Conductivity is a measure of how well a wire conducts, expressed in the form G. It is the inverse of resistivity measured in siemens, symbol S.
It is defined as- G=1/R Temperature- if temperature varies in a circuit then ohm’s law becomes useless. The more internal energy an object contains the more kinetic energy its atoms hold. This increases the probability of electrons colliding with positive ions in the lattice, so resistance is increased. Therefore it would be pertinent to ensure that temperature remains as constant as possible in the experiment. Temperature is actually a dependent variable, as temperature increases with current thereby increasing resistance.
However, constantan, the type of wire being used, has a low variance in temperature when the voltage range I will be using (0-6) are applied to it. Therefore if constantan is used, temperature should remain constant. Constantan The constantan supplied for the experiment has a Standard Wire Gauge of 26, a diameter of 0. 457mm and a area of 0. 656 mm2. It has a resistance of exactly 3? m-1 which will make it much easier to check results against. Its density is 8. 9g cm-3 and its melting point is 1225-1300 i?? C – well above the temperature ranges the wire will undergo in the experiment. Preliminary Experiment
As well as undertaking the main experiment, it will be useful to take a range of readings of the resistance of constantan with a multi-meter set to the ohm range. This will give a set of readings taken in a different manner to those of the main experiment to cross reference with and ensure anomalous results are spotted. To ensure a fair test, the same piece of wire will be used for each set of readings, but crocodile clips will be placed on it at the appropriate point o incorporate the correct length into the circuit. Apparatus Multi-meter- set to 200-ohm range, allowing readings in this range to be taken accurately.
Due to the miniscule amount of current flowing from the multimeter, temperature change in the wire will be negligible, so readings for lengths as low as 10cm can be taken, unlike in the main experiment. Connecting wires- as short as possible to ensure the resistance added by them to that of the constantan is as low as possible. Crocodile clips- ensure these are in as good a condition as possible. Also ensure that the Constantan is placed right at the tip of each, to minimise resistance from them. Constantan- Standard Wire Gauge of 26. Greater than or equal to 120 cm in length, allowing lengths in 10cm increments up to this length.