Investigating Wires

Key Variables-

Independent

• The independent variable in the experiment was the length of the nichrome wires. To do this different lengths of nichrome wire were cut and measured using a meter rule.

Dependent

• The dependent variable for this experiment is the resistance of the nichrome wire connected to the circuit. This is simply because the resistance of the wire will change due to the length of the wire being varied.

Controlled

(In order for the experiment to be fairly executed, some key variables need to be controlled)

Apparatus List-

• 1 Power pack 0-12 V (note these gradations are highly inaccurate)
• 1 Ammeter -20/ 20 A ± 0.01 A
• 1 Voltmeter 20/ 20 V ± 0.01 V
• 2 crocodile clips
• Stopwatch
• Meter rule
• 6 Connecting wires
• 1 variable resistor
• Nichrome 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.
6. This is repeated thrice for each length of nichrome wire since we are experimenting with three wires of the same lengths. Therefore we are going to be recording the data for three trials.
7. After that we primarily repeat steps 4 to 6 for different lengths of nichrome wire.

Diagram-

Raw Data-

Table 1 illustrates the voltage and current readings from different lengths of wires (after 30 seconds)

Qualitative observations-

 There was only one major observation we were able to notice during this experiment. As the current flowed through the wire, it eventually started to become warmer. At one point when the current flowed through the wire for a long duration of time (wire became very hot) or if a high potential difference was applied, then the wire has consequently melted.

Another observation we were able to pick up on was that the current and voltage readings gradually increased after the voltmeter switch was turned on.

Processed Data-

Now, we must calculate the Resistance of each length of wire. This can be done by using the following formula:

Resistance=Voltage/Current (knows as Ohm’s Law)

Example 1-   Trial 1, length 0.10m

Resistance=Voltage/Current

                                =(0.95/2.44) Ω

                =0.39 Ω

As there were three readings which were taken for each length of wire, the average resistance needs to be calculated and this can be done by using the following formula:

Average =    sum of readings 
                    number of readings

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

        

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 Ω

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: