Ohm’s Law and Resistivity

By: Alexis Huddleston

 

Introduction:

            The purpose of this experiment was to gain an understanding of Ohm’s law, to experimentally evaluate the validity of the formulas used to determine equivalent resistance, and to find the resistivity of carbon. Ohm’s law, as stated in this activity, is defined as a fundamental rule for analyzing circuits which involve only one voltage, current and resistance in the simplest cases. Interestingly Ohm’s law is named for the relationship between circuits in which Georg Simon Ohm proposed. This relationship is often presented as the equation, V=IR. In the equation, V is voltage, I is current, and R is resistance. Voltage is represented by the unit called volts (V), current is represented by amps (A), and ohms are represented by a symbol called ohm (Ω) respectively. Specifically in reference to Ohm’s law equation, as stated in this activity, resistance can be inferred from how much current flows in a circuit with a fixed voltage.

Importantly, in more complex situations involving circuits, Ohm’s law can be utilized. For instance, in addition to determining resistance of a circuit with one resistor, Ohm’s law can be used to determine the “equivalent” resistance of circuits containing more than one resistor. According to Ohm’s law, the current through each resistor is equal in a series connection and voltage differs in depending upon the value of each resistance. Therefore, in a situation involving two resistors connected in series, the equation that would be used to determine the equivalent resistance would be R1 + R2. Yet, if two resistors are connected in parallel, the equation to determine equivalent resistance would be R1R2/(R1 + R2).

In addition to Ohm’s law, this activity focused on resistivity. Notably, every material contains resistance. In order to determine the amount of resistance that a certain piece of material has, it is important to know the material dependent value called resistivity (ρ), the length (l), and the cross-sectional area (A). Using the equation, R= ρ (l/ A), the resistance contained by a piece of material can be deciphered. It is important to note that the units for resistivity, as stated in this activity, are Ω x m.

Conclusions and Discussion:

During the lab, unfortunately I did not have the opportunity to learn much about Ohm’s law.  Though, my group and I were able to use a multimeter to measure resistance, we were unable to measure voltage and current upon implementing the circuit noted in the activity (pg. 2). After continuing to set up the circuit in many different arrangements, we came to the conclusion that the multimeter was working properly but there seemed to be a shortage in the power supply. The multimeter would work properly for a few seconds and then discontinue working properly when we tried to complete the remainder of the lab activity. We were able to conclude that the multimeter was working correctly because, as noted in the activity, if the multimeter would have measured the current as zero amps even when the circuit was correctly arranged, then it would have been likely that the fuse was blown. In order to try to complete the lab activity accurately, we also tried to use different multimeters. All of the multimeters reacted the same way; they worked properly for a short period of time. Therefore, it was obvious that there was some shortage of power to the multimeter which caused it to discontinue reading the current and voltage measurements correctly.

Due to the problems that we had with the circuit, we were unable to collect accurate data for the lab experiment. This was most evident in the slope that was developed after measuring voltages and currents with the multimeter for five trials. According to Ohm’s law, the slope of the line that was developed should have been a diagonal line where R1 would be a rational number. Instead, our data showed a vertical slope in which the slope was equal to zero; this was obviously incorrect. Another five trials were done in an attempt to find the correct measurements for voltage and current but again, the data that was collected produced a vertical slope. As a result of the inconsistencies in the circuit and several inaccurate readings, we concluded that the lab experiment could not be completed with accuracy.