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

Extracts from this document...

Introduction

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

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

1.7.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:

2.OBTAINING EVIDENCE

2.1.Preliminary Results:

2.1.1.LENGTH:

2.1.2.CROSS-SECTIONAL AREA:

2.2.Length:

2.3.Cross-sectional area:

3.ANALYSIS

3.1.THEORY/HYPOTHESES:

3.2.LENGTH:

3.3.CROSS-SECTIONAL AREA:

3.4.CONCLUSION:

4.EVALUATION

4.1.LENGTH:

4.2.CROSS-SECTIONAL AREA:

4.3.OVERALL EVALUATION:

5.EXTENSION PLAN

5.1.Aim:

5.2.Apparatus:

5.3.Safety:

5.4.Theory:

5.5.Prediction:

6.GRAPHS - 68

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.

Middle

0.07

0.10

0.09

0.10

0.12

0.16

0.16

0.16

0.25

0.35

0.35

0.35

Table 2.1.1.2. Preliminary table; length 100 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 100.00 0.23 0.03 0.03 0.03 0.28 0.04 0.04 0.04 0.33 0.04 0.05 0.05 0.40 0.05 0.05 0.05 0.45 0.06 0.06 0.06 0.55 0.07 0.07 0.07 0.63 0.09 0.08 0.09
1. ### CROSS-SECTIONAL AREA:

Table 2.1.2.1. Preliminary table; c.s.a. 0.25 mm2

 WIRE CROSS - SECTIONAL AREA (mm2) V (v) I1 (A) I2 (A) Iaverage (A) 0.25 0.05 0.03 0.03 0.03 0.07 0.04 0.04 0.04 0.10 0.05 0.05 0.05 0.11 0.06 0.06 0.06 0.12 0.07 0.06 0.07 0.16 0.08 0.08 0.08 0.25 0.13 0.13 0.13

Table 2.1.2.2. Preliminary table; c.s.a. 0.06 mm2

 WIRE CROSS - SECTIONAL AREA (mm2) V (v) I1 (A) I2 (A) Iaverage (A) 0.06 0.20 0.02 0.02 0.02 0.25 0.03 0.03 0.03 0.30 0.03 0.03 0.03 0.35 0.04 0.04 0.04 0.40 0.05 0.05 0.05 0.45 0.05 0.05 0.05 0.50 0.06 0.06 0.06
1. ## Length:

The following tables contain all the data that I collected for the voltages and currents with wires of various lengths at a thickness of 26 swg (0.45 mm). The cross-sectional area of this wire therefore equals π x ½d2 = 0.16 mm2.

Table 2.2.1. Length 10 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 10.00 0.02 0.03 0.04 0.04 0.03 0.04 0.05 0.05 0.04 0.05 0.06 0.06 0.05 0.07 0.07 0.07 0.07 0.10 0.09 0.10 0.12 0.16 0.16 0.16 0.25 0.35 0.35 0.35

Table 2.2.2. Length 20 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 20.00 0.05 0.04 0.04 0.04 0.07 0.05 0.05 0.05 0.09 0.06 0.06 0.06 0.13 0.09 0.09 0.09 0.20 0.13 0.13 0.13 0.32 0.22 0.23 0.23 0.39 0.27 0.27 0.27

Table 2.2.3. Length 30 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 30.00 0.08 0.03 0.04 0.04 0.10 0.04 0.05 0.05 0.13 0.06 0.06 0.06 0.16 0.08 0.08 0.08 0.22 0.12 0.11 0.12 0.28 0.15 0.15 0.15 0.43 0.22 0.21 0.22

Table 2.2.4. Length 40 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 40.00 0.11 0.03 0.03 0.03 0.14 0.04 0.05 0.05 0.17 0.06 0.06 0.06 0.21 0.07 0.07 0.07 0.25 0.09 0.08 0.09 0.33 0.11 0.11 0.11 0.50 0.16 0.17 0.17

Table 2.2.5. Length 50 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 50.00 0.13 0.03 0.03 0.03 0.15 0.04 0.04 0.04 0.18 0.05 0.05 0.05 0.24 0.06 0.06 0.06 0.30 0.08 0.08 0.08 0.36 0.10 0.10 0.10 0.50 0.14 0.13 0.14

Table 2.2.6. Length 60 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 60.00 0.15 0.03 0.03 0.03 0.18 0.04 0.04 0.04 0.22 0.05 0.05 0.05 0.27 0.06 0.06 0.06 0.30 0.07 0.07 0.07 0.38 0.08 0.08 0.08 0.55 0.12 0.13 0.13

Table 2.2.7. Length 70 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 70.00 0.17 0.03 0.03 0.03 0.21 0.04 0.04 0.04 0.25 0.05 0.05 0.05 0.30 0.06 0.06 0.06 0.36 0.07 0.07 0.07 0.47 0.09 0.09 0.09 0.56 0.11 0.11 0.11

Table 2.2.8. Length 80 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 80.00 0.19 0.03 0.03 0.03 0.25 0.04 0.04 0.04 0.29 0.05 0.05 0.05 0.34 0.06 0.06 0.07 0.41 0.07 0.07 0.07 0.50 0.08 0.09 0.09 0.59 0.10 0.10 0.10

Table 2.2.9. Length 90 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 90.00 0.20 0.03 0.03 0.03 0.28 0.04 0.04 0.04 0.32 0.05 0.05 0.05 0.38 0.06 0.06 0.06 0.44 0.07 0.06 0.07 0.50 0.08 0.07 0.08 0.60 0.09 0.09 0.09

Table 2.2.10. Length 100 cm

 WIRE LENGTH (cm) V (v) I1 (A) I2 (A) Iaverage (A) 100.00 0.23 0.03 0.03 0.03 0.28 0.04 0.04 0.04 0.33 0.04 0.05 0.05 0.40 0.05 0.05 0.05 0.45 0.06 0.06 0.06 0.55 0.07 0.07 0.07 0.63 0.09 0.08 0.09
1. ## Cross-sectional area:

The following tables of cross-sectional area contain all the raw data collected for the five different cross-sectional areas. The length is kept generic for all the five wires at 40cm.

Table 2.3.1. C.S.A. 0.25 mm2

 WIRE CROSS - SECTIONAL AREA (mm2) V (v) I1 (A) I2 (A) Iaverage (A) 0.25 0.05 0.03 0.03 0.03 0.07 0.04 0.04 0.04 0.10 0.05 0.05 0.05 0.11 0.06 0.06 0.06 0.12 0.07 0.06 0.07 0.16 0.08 0.08 0.08 0.25 0.13 0.13 0.13

Conclusion

In the first diagram, e.g. of tungsten, the atoms are very tightly packed together in a crystal lattice, and there are a lot of atoms in a small space; therefore tungsten has a high density. All the electrons in that wire collide with atoms and therefore they lose a lot of energy, which is converted into heat by the atoms. This gives tungsten such a high resistance, and it can be used in filament lamps.

In the second diagram, e.g. of copper, the atoms are packed a lot less loosely together and there are a lot less atoms in the same space; therefore copper has a low density. Only two of the electrons in the diagram collide with atoms, therefore they lose a lot less energy, and this gives copper its low resistance. Copper is the most common element used in electrical wires.

1. ## Prediction:

As I have stated in my theory above, if you increase the density of a wire, you increase the number of atoms, which increases the number of collisions. This results in the wire having a higher resistance. Therefore, I predict that resistance will be directly proportional to density. This is only to a certain extent though, since a substance cannot have infinite density, otherwise it would be a singularity. Therefore my graph would look like the following:

Fig. Predicted graph of resistance against density

I predict that the graph will represent this because although the density can increase forever till it is infinite, the resistance will slow down increasing after a certain point because the atoms will be slow closely packed together, that increasing the density a tiny bit more will not make a difference to the resistance. The electrons will simply not have any space to move and will lose all their energy. But at infinite density, the resistance will have to be infinite as well; therefore the resistance will be directly proportional to density.

1. ## GRAPHS

As attached in the following 1+ 31 sheets

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