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Introduction

Many physics students complain that their results in practical experiments do not always corresponded exactly to the theoretical values that can be obtained using the relevant physics equations and laws. This report will investigate the claim’ ‘the experimental data results obtained in Physics investigations will always contradict theoretical results without reasonable explanation”. This will be achieved by calculating the theoretical values for resistor and comparing the results to the experimental to find out the difference and give a reasonable explanation for the variance.

There are many different types of Resistor available which can be used in both electrical and electronic circuits to control the flow of current or to produce a voltage drop in many different ways. But in order to do this the actual resistor needs to have some form of “resistive” or “resistance” value. Resistors are available in a range of different resistance values from fractions of an Ohm (?) to millions of Ohms. It would be impractical to have available resistors of every possible, therefore, resistors are manufactured in what are called preferred values with their resistance value printed onto their body in colored ink.

An international and universally accepted resistor color code scheme was developed many years ago as a simple and quick way of identifying a resistors Ohmic value no matter what its size or condition. It consists of a set of individual colored rings or bands in spectral order representing each digit of the resistors value. The chart below shows how to determine the resistance and tolerance for resistors. The table can also be used to specify the color of the bands when the values are known

The Standard Resistor Colour Code Chart.a

https://www.electronics-tutorials.ws/resistor/res_2.html

Colour bands on the 3 unknown resistors

R1- Red Red Brown Gold

R2- Orange Red Brown Gold

R-3 Brown Blue Red Gold

Results

Red is 2 and there are 2 red bands, therefore red indicates 22, brown is the multiplier which is 101 and Gold is the tolerance which is 5% which means R1 is 220±11 Ohms. For R2 Orange is 3, Red is 2, brown is the multiplier which is ?10?^1 and gold is the tolerance which is 5%, which means R2 has a value of 320±5% Ohms. For R3- Brown is 1, Blue is 6, the multiplier is Red which is 100 ? and similarly the tolerance is Gold which is 5% and therefore it is1600±5%.

Circuit 1

In circuit 1, the voltage across the 3 resistors are different and the currents are similarly the same in all the resistors. According to the definition (david, 2017). of if the voltage drop across all resistors present in circuit are the same and the currents vary then the circuit is In parallel. ” Therefore circuit 1 is in a parallel circuit and the diagram below will illustrate one possibility of how the circuit could have been set to produce the same data.

Diagram 1

To be able to find the resistance of the 3 unknown resistors, the experimental data had to be plotted into a graph of Voltage vs Current. If the graph is linear, which it should be if it’s a representation of Ohm’s law, then the resistance can be calculated graphically by finding the gradient. For resistor 1 the trend of the graph is linear as it can be seen on the equation of the graph in graph 1. R2 and R3 also demonstrates a linear graph which shows that the resistors are Ohmic resistors.

Figure 1 current in (A) vs voltage obtained from the experiment

Figure 2

The 3 graphs (figure1,2 and3) shows the equation in the form of y=mx+c, where the gradient is the resistance. From the figure 1 it can be seen that R1 is 220.94 Ohms, R2 is 325.34 Ohms and R3 is 1000 Ohms.

It would be expected for R1 to have the lowest current and R3 to have the highest current, as R1 has a higher resistance and R3 has the lowest. As ohms law indicates, the greater the value of the resistance the smaller the current. When this results are compared with the experimental data they all agree except for resistor 3.The below calculation will compare the theoretical and experimental value and see if the claim of the students is true. This report will prove Ohm’s law by calculating the theoretical value and then comparing it to the experimental value and it will prove that the variance can be reasonably explained, if there are any variance

Resistor 1

Theoretical value

R1=22×10±5%=220±11 Ohms

The theoretical value was found to be 220 ± 11 Ohms which suggests that the Experimental value could be between 209 to 231 Ohms.

Experimental value from the graph = 220.94 Ohms

The experimental data for Resistor 1 was found be 220.94 Ohms as shown in (Figure 1), this value was within the range of the 5% tolerance or errors that was suggested by the theoretical value which seems to contradict with the claims made by the students and obeys Ohms Law.

Resistor 2

Theoretical value

R2=32×10±5%

= 320±5%

R2 is between these ranges: 304 to 336 Ohms

Experimental value obtained from the graph = 325.34 Ohms

The value for Resistor 2 also disproved the claim of the student as illustrated in figure 2. The value 220.94 Ohms (for the resistance) was obtained by plotting the data and then finding the gradient or the resistant from the graph in excel. Because both resistors were between the 5% error range Ohm’s law holds to be true. The ± 5% tolerance is used to account for human errors and other external factors that are not within our control.

Resistor 3

Theoretical value

R3= 16×100±5%

=1600±5%

= between these two 1680 ? or 1520 ?

Experimental value obtained from graph =1000 Ohms

Both R1 and R1 prove that the variance between the theoretical and experimental was within the range of the error. However Resistor 3 was an anomaly, the experimental data for resistor 3 was 1000 Ohms as shown in figure 3 and when this is compared to the theoretical value, there is a variance of 600 ohms, as the theoretical value was calculated to be 1600±80 Ohms.

The total resistance of a parallel circuit can be calculated by the following formula

1/R_T =1/R_1 +1/R_2 +1/R_3

Experimental total resistance: 1/R_T =1/220.94+1/325.34+1/1000= 120.55?

Theoretical total resistance: 1/R_T =1/220+1/320+1/1600= 116.28?

The value of the total experimental resistance is a reasonable result as the total resistance for circuit to be lower than the lowest resister which is R1. To evaluate to comparison of the experimental and theoretical data, first the percentage error has to be calculated, the calculation is done below:

Percentage error=|experimental value-theoretical value|/(theoretical value)×100

If the actual numbers are substituted into the equation for R1 then it would be as it follows

Percentage error=|220.94-220|/220×100=0.43%

The percentage for R1 is found to be 0.43%

Percentage error for R2

Percentage error=|325.34-320|/320×100=1.67%

The percentage error for R2 is found to be 1.67%

Percentage error for R3

Percentage error=|1000-1600|/1600×100=37.5%

After evaluating the percentage error it is clear that both R1 and R2 are within the acceptable error or tolerance of 5% which proved ohms law, however R3 does not follow the same pattern as the two resistors. R3 has a percentage error of 37.5% as showed above which leads the report to into a more profound discussion in attempting to explain the variance with a reasonable explanation. This variance however does suggest that there were errors associated with the R3 voltage and current when conducting the experiment or and collecting the data.

The following section will evaluate the accuracy of Kirchhoff’s Junction and Loop law in circuit 1. This will be achieved by taking the point at which the voltage from the power pack is at 6.

Kirchhoff’s Junction and Loop law was used in this circuit because it was parallel. Kirchhoff’s Junction and Loop law forI_1,I_( 2), and I_( 3) because the percentage error is between the 5% tolerance Kirchhoff’s law is proved to be true. Kirchhoff’s junction rule states that at any circuit junction, the sum of the currents flowing into and out of that junction are equal. (Physics, 2016)

j

I_1=I_3+I_2

Loop ABEFA

1000×I_1-325.34×34×I_2=0

(1000×I_3)/325.34 equation 1

Loop ABEFA

1000×I_3-220.94×I_1=0

I_1 (1000×I_3)/220.94 equation 2

Loop ABGHA

1000×I_3-6

(-6)/1000=I_3=0

Substitute equation 3 into equation 1 and 2 to find I2 and I1.

I_2=(1000×0.006)/?([email protected] @ )

I_2=0.0184A

From equation 2

I_1=(1000×0.006)/220.94

I_1=0.0246

Percentage error for I_1

Percentage error=|experimental value-theoretical value|/(theoretical value)×100

Percentage error=| 0.0246-0.0268|/( 0.0268)×100=0.082%

Percentage error for I_2=(0.0184-0.0181)/0.0181=0.0166%

Loop rule states that in complete circuit the sum of the voltage differences across all of these circuit elements must be zero.

v=IR

v=6V

R1=120.94Ohms

therefore I=v/R1

I=6/120.94Ohms 4.96×?10?^(-2) A

v=IR

v= 4.96×?10?^(-2)×120.94Ohm=5.9v

V_t-R1=0

5.9V-5.9=0

The above calculations proves the loop rule to be true.

Circuit 2

For circuit 2 the current at X and Y are the same but the voltage vary. According to the definition of series circuit: if the current for both resistors are the same and the voltage is different then the circuit is a series circuit. Therefore circuit 2 is in series and the diagram below will illustrate how the experiment could have been set.

Using Ohms law equation V=IR the resistance can be calculated as R=V/I , however this equation holds true only when the graph is a linear graph and where the gradient can be calculated. The graph above is a linear graph which means the gradient can be calculated and the value of the resistance can be determined graphically, therefore circuit 2 is a representation of ohms law. The value for R1 and R2 obtained from the graph is 533.07 Ohms.

In a series circuit the total resistance is equal to the sum of all the resistors

R_T=R_1+R_2

R_T=220+320=540 Ohms

the theoretical value for R1 and R2 is 540 Ohms

Experimental value obtained from the graph= 220.94 + 325.34= 540Ohms

Percentage error Percentage error=| 533.07 -540|/540×100=1.16%

The percentage error for circuit 2 is 1.16%

The calculation when the voltage from the power pack is 6 is presented below. The resistance for R1 and R2 is found using Ohms law formula R=V_1/I_1 =2.4/0.0111=216.2Ohms

The percentage error for R1 = | 216.2 -220|/( 220)×100=1.72%

The percentage error between the theoretical vale and experimental value for R1 is 1.17%

R2=V_1/I_1 =( 3.6)/0.111×100=32.43

The percentage error for R2

Percentage error=|324.32-320|/320×100=1.35%

The percentage between the theoretical error and the experimental error is 1.35%, this is within the range error of 5% tolerance.

R_T=R_1 +R_2=216.22+324.32=540.54Ohms

The percentage for both resistors error was less than the tolerance which means the experiment was carried out successfully with relativity low error associated, circuit proves Ohms law is proven by circuit 2. Kirchhoff’s Junction and Loop law does not apply to circuit 2 as it’s in series.

Kirchhoff’s loop rule states that in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop

V=V_1+V_2

6=2.4+3.6

6=6

In the calculation above, it shows that the voltage on power pack (EMF source) is equal to the sum of the voltage across R1 and R2. It suggest that Kirchhoff’s loop rule has a high validity and it hold true for this circuit.

Circuit 3

The two resistors for circuit 3 have the same voltage across but different currents R1 and R2 which indicates that circuit 3 is in a parallel circuit. The diagram below will show how the circuit was set to produce those data.

The graph above demonstrates that it is a linear which indicates that it is Ohmic graph. The gradient obtained from the equation of the graph is 132.38 Ohms In a parallel circuit, the total resistance of a set of resistors is the sum of the inverse of each resistor and can be calculated by this equation

Theoretical value

1/R_T =1/R1+1/R2

1/220+1/320=130.3

Percentage error for circuit 3

Percentage error=| 132.38-130.3|/(130.3 )×100=1.54%

The percentage error is 1.54

R_1=V_1/I_1 =6/0.0269=223.05 Ohms

The resistor for R1 is 223.05 Ohms

In Parallel circuit the total current is the sum of all the current that is passing through each resistor

I_T=I1+I2

I_T=0.0269+0.0181

I_T=0.045A

R_T=6/0.045

R_T=133.33?

Now that the total resistance is found the resistance for R2 can also be calculated by the following equations

1/R_T =1/R_1 +1/R_2

Rearrange to make R2 the subject of the equation

1/R_2 =1/R_T -1/R_1

1/R_2 =1/133.33-1/223.05

R_2=331.47Ohms

The results are as expected, as the value of resistances for R2 is higher than to that of R1. This was expected because of Ohms law, as it states that if the current passing through one resistor is higher than the other resistor then the resistor with the higher current has a lower resistance value. This can be seen in R1 and R2, as the current passing through R1 is higher than the current passing R2, which indicates that R2 has a higher resistance. Kirchhoff’s Junction and Loop Law applies to circuit 3 as it is in a parallel circuit.

Kirchhoff’s Junction Rule state that the sum of the current that flows into the junction is equal the sum of the current that flows out of the junction. The value of I1 and I2 obtained from Kirchhoff’s loop rule will be used.

I_3=I_1+I_2

I_3=0.0269+0.018

I_3=0.0449A

When using Kirchhoff’s junction rule to find the value of I3, it is almost the same as the theoretical value. Therefore, Kirchhoff’s junction has a high validity and it hold true in this circuit.

Circuit 4

3 resistors are present in circuit 4, R1, R2, and R3. The experimental data shows that R1 and R2 have the same voltage but different currents which means R1 and R2 are in parallel. The result also show that the sum of the voltage in parallel circuit and the voltage across R3 is approximately equal to the total voltage (voltage across combination). Circuit 4 has 2 resistors in parallel and resister 3 is in series. As they are in series, the total current of the parallel will equal to the total current throughout the series circuit. The results show that the sum of X and Y is equal to the total current. And for this reason the ammeter should be placed on the parallel circuit. Because R1 has a higher current it is expected to have lower value of resistance to that of R2 as Ohm’s law state that the smaller the value of the resistance will result in greater current flows through it. The diagram below shows how the circuit might have been set correctly.

In order to determine the value of the total resistance, the graph of the total voltage (voltage across combination) over the total current is produced from experimental results. , V=IR because the graph is linear the circuit is Ohmic graph.

The total resistance of a set of resistors in a parallel circuit is the sum of the inverse of each resistor.

1/R_(T parallel) =1/R_1 +1/R_2

1/R_(T parallel) =1/220+1/320

R_(T parallel)=1/(1/220+1/320)

R_(T parallel)=130.37?

Check the graph

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As R3 is in series with the parallel circuit (R1 and R2), the current flows through R3 will be the same as the current flows in the parallel circuit.

I_3=I_(T parallel)

I_3=0.0053A

Applying Ohm’s law to find resistance R3

R_3=V_3/I_3

R_3=5.4/0.0053

R_3=1018.87?

percentage error=|225-220|/220×100=2.27%

The percentage error between theoretical and experimental value of resistance R1 is 2.27%

percentage error=|342.86-320|/320×100=7.14%

The percentage error between theoretical and experimental value of resistance R2 is 7.14%

percentage error=|1018.87-1600|/1600×100=36.32%

The percentage error between theoretical and experimental value of resistance R3 is 36.32%

The percentage error between theoretical and experimental value of the resistance R1 is within the range of % tolerance. However, the percentage error between theoretical and experimental value of the resistance R2 and R3 exceed the range of -/+5% tolerance. It shows that Ohm’s law does not hold true in this circuit and the experiment was conducted with sources of error.

Kirchhoff’s loop rule state that in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop.

225×I_1-342.86×I_2=0

225×0.0032-342.86×I_2=0

I_2=(225×0.0032)/342.86

I_2=0.0021A

Kirchhoff’s loop rule was used to find the value of I_2 and the value of I_2obtained from Kirchhoff’s loop rule is the same as the experimental result, which show that Kirchhoff’s loop rule hold true for this parallel branch

Errors

In investigating the validity of Ohm’s law, there are some discrepancies between the experimental and theoretical results in which the percentage differences fall higher than the 5% tolerance range. However the most of the errors can be explained with a reasonable explanation. The reason the experimental value often differs from the theoretical value is because of the assumption of Ohms Law. As value for Ohms law is calculated with the assumption that the experiment is conducted without any influence from external factors (such as temperature), the actual wire that was used or parameters used to measure the voltage or and the current. There are many small factors that are not taken into consideration such as the resistivity of the wire, distance between the different resistors, and temperature.

When these factors then add up to produce an error that is often higher than the acceptable 5% tolerance. The equipment that were used to conduct the experiment could also contribute to error. For example most multimeters are guaranteed with the accuracy specification for only one year. After that, it might not keep its accuracy within the published limits and it must be calibrated once a year. This can be seen in circuit 2 where the ammeter is reading higher than the source of the voltage, however it is important to note that this is the same reasons why there is 5% tolerance for most resistors. If the error percentage of error is so like in circuit 4 where the difference between experimental and theoretical value is 36.32 % then it is best explained as a human error, which means the student has made some major error. This could be from reading the wrong value, from connecting the wires in a wrong order to the positioning of the ammeter and voltmeter or the ammeter was not accurate enough to be used in a scientific experiment. But the most simple to error to make is but that would impact the most would be reading the colour band incorrectly.

Recommendation

To make the experiment more reliable conduct the experiment in groups where all the groups are doing the same experiment. By this if one makes errors then the other group can correct the data. Moreover, the equipment need to be checked carefully and the equipment must be consistent in every circuit before conducting the experiment. And finally it is recommended to check the circuits to determine if the positioning of the ammeter.

Conclusion

After investigating the validity of Ohm’s law and Kirchhoff’s law by performing calculation and obtain from graph, it was found that there was some large percentage error between the theoretical and experimental value. However, most of the errors were found to be within the range of 5 % error or tolerance. And even the anomaly can be justified as human errors or errors that are caused by the efficiency of the equipment and the student who is conducting the experiment. Over all it can be concluded that the claim “The experimental results obtained in Physics investigation will always contradict theoretical results without reasonable explanation” is false and not based on facts.

Reference

http://www.instructables.com/lesson/Resistors/ for resistor

https://www.electronics-tutorials.ws/resistor/res_2.html colour

coding

All about circuits. (2017, 5 20). Retrieved from https://www.allaboutcircuits.com/textbook/direct-current/chpt-8/ammeter-impact-measured-circuit/.

Electronics Tutorials. (2017, 5 10). Retrieved from http://www.electronics-tutorials.ws/resistor/res_2.html.