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# Investigating Wires

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Introduction

‘Investigating wires’

(D, DCP and CE)

Determining how the length of a nichrome wire changes the resistance

Introduction:

Electrical resistance is a ratio of the degree to which an object opposes an electric current through it. It can also be defined as the ratio of voltage per unit current through it, R=V/I. The unit of electrical resistance is the ohm (Ω). Resistance can be found using the two following formulas.

Resistance= (Potential Difference ÷ Current) ---> (which is more known as Ohm’s law) where the potential difference is measured in Volts (V) and the current can be measured in Amps (A). Another way the resistance can be found is by using the formula R= ( L)/ A. This is where the resistance (R) is related to: cross- sectional area (A), length (L) and material of the wire as R  L/A. The constant of proportionality is called the resistivity ( ).

So R= ( L)/ A

So for our theory work for this experiment, we know that R  L/A. Therefore let’s say that by assuming the wire follows Ohm's Law, the resistance of a wire is directly proportional to its length therefore doubling the length will double the resistance of the wire.

Middle

1 Voltmeter 20/ 20 V ± 0.01 V2 crocodile clipsStopwatchMeter rule6 Connecting wires1 variable resistorNichrome wire- 220 cm altogether

[10cm, 20 cm, 30 cm, 40 cm, 50 cm and 60 cm(Note*- each length was used once)]

Method-

1. Start of by cutting out six different lengths of nichrome wires of the same brand and thickness (10cm, 20 cm, 30 cm, 40 cm, 50 cm and 60 cm respectively) from a reel using a meter ruler. Do Note*- Three wires of each length were cut out i.e. there were three wires of 10cm, three wires of 20 cm and so on.
2. The ammeter, power pack and nichrome wire (about to be tested for resistance) are connected in series using connecting leads.. Basically refer to the diagram displayed below as the experiment set up is exactly similar to that.
3. Connect the voltmeter in parallel to the circuit.
4. Next, turn on the power pack which is adjusted to the voltage we are working with (note, as previously mentioned, the voltage is a controlled variable therefore it is kept constant). At the same time start the stopwatch and begin timing.
5. When thirty seconds have gone by (as mentioned previously, we are working with 30 s time intervals), the readings of the ammeter and the voltmeter must right away be taken.

Conclusion

ngth of wire, the average resistance needs to be calculated and this can be done by using the following formula:

Example 2- Length of wire-0.10m,

Average         =    0.39+0.39+0.39 Ω
3

=0.39 Ω

Table 2: The average resistance for different lengths of wires

 Length (±0.0005 m) Trial 1 Trial 2 Trial 3 Average Resistance(Ω) Resistance(Ω) Resistance(Ω) Resistance(Ω) 0.10 0.39 0.38 0.39 0.39 0.20 0.84 0.84 0.83 0.84 0.30 1.24 1.22 1.22 1.23 0.40 1.76 1.73 1.70 1.73 0.50 2.13 2.15 2.14 2.14 0.60 2.60 2.49 2.54 2.54

The uncertainty for reading of the length of wire was ± 0.0005m. This is because the smallest graduation of readings on a meter rule is 0.001m. In an analogue system the smallest graduation is divided by two to find the uncertainty. The uncertainty for the voltage is ± 0.01 V and the uncertainty for current is ± 0.01 A.

To find the uncertainty for resistance the fractional uncertainty for voltage and current had to be added. The fractional uncertainty is obtained by:

Fractional uncertainty= absolute uncertainty
actual value

Example 4- Trial 1, Length-0.1m

Fractional uncertainty of voltage= absolute uncertainty
actual value

=(0.1/0.97)

=0.103 V

Fractional uncertainty of current= absolute uncertainty
actual value

=(0.1/2.46)

=0.041

Uncertainty for resistance=Fractional uncertainty of voltage+fractional uncertainty of current

=(0.1/0.97)+(0.1/2.46)

=0.144

The average uncertainty was found by the formula

Average uncertainty= Sum of uncertainties
Number of uncertainties

Example 4- Length of wire-0.1m

Average uncertainty= (0.0146+0.0149+0.0148) Ω
3

=0.0147 Ω

Determining the relationship between the length of wire and the resistance:

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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