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Lab Report Title: Verification of Ohm’s Law Using a Known Resistor

# Introduction

Ohm’s law explains relationship between voltage and in conductors (Ferry, 2012; Weber et al., 2012). In the case of ideal conductors, it states that voltage is directly proportional to current at a certain temperature. In such a case, the gradient is the conductor resistance which is constant. Such materials are said to be ohmic. If such a relationship is not linear, then such a material is said to be non-ohmic. A plot of voltage versus current is called an I-V characteristic (Leon-Garcia, 2017). The following diagrams shows the two types of I-V characteristics.

 Figure 1: Ohmic material Figure 2: Non-Ohmic material

In the current lab experiment, the overall objective was to verify ohm’s law while demonstrating the understanding of electrical principles usage of digital multimeter. In addition, various electrical symbols were to be studied while building a simple electrical circuit.

# Methodology

## Measurement of resistance

The following procedures was applied to measure the resistance:

1. DMM was first turned OFF.
2. The DMM was turned to ohmmeter.
3. The function switch was slide to Ω and a range of 2 k Ω was dialed.
4. DMM was then turned ON.
5. The probes were connected to each other as shown in figure 3 below.

Figure 3: Checking a zero reading in DMM

1. The 100 Ω resistor was selected from the kit.
2. Actual value of the resistor was then measured as shown by figures 4 and 5 below.
 Figure 4: Best method for measuring resistors Figure 5: Alternative method to hold resistors

## Measuring current

The following procedure was applied while measuring current:

1. DMM was set to 200 m DCA in order to measure current in Amps DC up to 200 mA.
2. Without turning DMM on, the circuit show in figure 6 was built.

Figure 6: Circuit to Measure current

Where the resistor was 100 Ω, and a DC source of 1.5 V.

1. Jumper cable 1 was connected to the negative side of the battery.
2. Jumper cable 2 to the other end of the resistor and the black lead of the DMM.
3. The third jumper cable to (3) the red lead of the DMM and the positive end of the battery holder were connected.
4. All the connections were checked and the DMM turned ON.

## Measuring voltage

1. All the elements in measurement of current were disconnected while making sure that DMM was turned OFF.
2. The knob for DMM was rotated so as to measure volts in DC.
3. A new circuit shown in the figure below was built.

Figure 7: Circuit to measure voltage

The power source is 1.5 V battery and a resistor of 100 Ω.

1. The DMM is then turned ON to read the voltage across the resistor.
2. Steps (i) to (iv) were repeated with two 1.5 V batteries in series.
3. Steps (i) to (iv) were repeated with three 1.5 V batteries in series.

# Results

The following were the results of the experiment:

• Actual resistance of the 100 Ω: 99 Ω
• Current measure for 1.5 V battery connection: 15.7 mA.
• Voltage when 1.5 V battery is connected: 1591mV DC (1.591 VDC)
• Calculated voltage for 1.5 V battery connection:
• Difference between measured and calculated voltage: .
• Measured voltage when DMM leads were reversed: -(-ve) 1591 mV DC (1.591 VDC).

The table below shows current (mA) and voltages (V) measured with various battery configuration.

Table 1: Experimental results

 Battery configuration Measured current (mA) Measured Voltage (V) One 1.5 V battery 15.7 1.59 Two 1.5 V batteries in series 31.1 3.19 Three 1.5 V batteries in series 45.6 4.59

The following figure shows a plot of voltage versus current (that is, V-I characteristics) for the three circuits.

Figure 8: V-I Characteristic

The equation for the best fit was found to be:

This indicates that the slope of the graph is 0.1004.

By calculation:

# Discussion

The actual resistance of the resistor was found to be 99 Ω against a specification of 100 Ω. This was within the manufacturer’s specification of ±5 Ω. Using ohm’s law, voltage is equivalent to the product of current and resistance. When the power source was 1.5 V, the measured voltage was found to be higher than the calculated voltage with an error of 2.33%. This can be attributed to the errors i(Huyett, 2004)n measurement. Such an error can be reduced by multiple measurements and using the averages of such measurements in calculations. Reversing leads of a DMM results to a value which is equal but of opposite sign. Therefore, care should be taken when making circuit connections.

The slope for the V-I characteristic curve gives the slope and the y-intercept. The current resistor resulted to a straight curve and thus it is an ohmic material. However, it was expected that it would have a 0.00 y-intercept which was not the case (Huyett, 2004). This can be attributed to errors during measurements. The calculated slope and the slope read from the graph were found to be the same.

# Conclusion

The objectives of the experiment were met in that various circuits were built and DMM used to measure resistance, various currents, and voltages in all the three circuits. In addition, various electrical symbols were used utilized during the experiment. Ohm’s law was verified for the selected resistance and thus helping to understand the same in detail. However, it was difficult to hand small diameters of wires during building for various circuits during the experiment. Such a difficulty could be the source of error noted in the results. This error can be reduced by having good wire handling mechanisms as well as repeating the measurements several times and using the averages in calculations.

# References

Ferry, D. K. (2012). Ohm’s law in a quantum world. Science. http://doi.org/10.1126/science.1215900

Huyett, G. L. (2004). Engineering Handbook. Textbook (Important), 95. http://doi.org/10.1016/B978-1-85617-689-7.10017-2

Leon-Garcia, A. (2017). Probability, statistics, and random processes for electrical engineering. Retrieved from http://dl.saintgits.org/xmlui/bitstream/handle/123456789/1059/Probability%2C_Statistics%2C_and_Random_Processes_for_Eletrical_Engineerging%2C_3rd_Ed_-_Leon-Garcia.pdf?sequence=1&isAllowed=y

Weber, B., Mahapatra, S., Ryu, H., Lee, S., Fuhrer, A., Reusch, T. C. G., … Simmons, M. Y. (2012). Ohm’s law survives to the atomic scale. Science335(6064), 64–67. http://doi.org/10.1126/science.1214319