Day 1 - Introduction and Review of Power, Voltage, Current, Charge, and Energy in Circuits

Topics Discussed

Day one of the Electrical Engineering (ENGR 44) Course introduced and included a review of the many elements learned in previous physics courses (PHYS 4B) in regards to electric current. Among these topics were charge, current, voltage, power, and energy. Additionally, a brief demonstration of breadboards was included which emphasized open-circuits and a short-circuits.

The fundamentals of electricity and circuits were introduced on Day 1. Charge and current were discussed first, as charge is considered the fundamental building block to understanding and "explaining all electric phenomena" (Mason). With this understanding of charge, we derive an understanding of current,  which is essentially a description of the mobility or change of charge over time. Charge is measured in coulombs, with the standard relating to the charge of an electron (1e=-1.602×10^-19C or 1C=6.24×10¹⁸ e) Two different types of currents were also briefly discussed, such as direct current (dc) and alternating current (ac). Direct current is simply a current that remains constant over a set period of time, while alternating current is a current that varies over time in a sinusoidal fashion. Power, energy, and voltage were introduced after, illustrating methods of how graphs could be derived by knowing the behavior of certain elements of a circuit.

Many of the prior relationships learned in previous physics courses were reinforced in the beginning of class. This included the relationship of current to charge, voltage to work and charge, and power to energy.  These relationships would intersect in various situations, and several problems and questions were presented in class that illustrated this merging of concepts. (See Fig. 1)

Fig. 1
In this problem, the graph of current and voltage as functions of time were given. With these graphs, the total energy absorbed by the device was to be found. In order to properly solve the problem, the relationship between energy, voltage, and current had to be derived. A necessary relationship that was noted was that of power to energy, in which power is the change in energy over a period of time. Rearranging this relationship would lead us to understanding that the energy function is equivalent to the integral of power multiplied by time (dt). We could then recall that power is also defined as the product of current and voltage, and by substitution we can derive the equation presented in the lower right corner of Fig. 1. The calculation to find the exact value for the problem was not recorded.

Another important topic discussed in day one was dependent sources of current and voltage and how they apply to the real world compared to the ideal independent voltage and current sources used in previous physics classes. The four dependent types of sources included a voltage-controlled voltage source (VCVS), a current-controlled voltage source (CCVS), a voltage-controlled current source (VCCS), and a current-controlled current source (CCCS). Understanding these dependent sources grants us the ability to solve problems where circuits contain  contain fluctuating current and voltage sources. Additionally, power and a reinforcement of the conservation of energy within a circuit was also discussed. As current moves through a circuit, voltage sources can be used to determine the power absorbed or released at various points across the circuit. We can solve for unknowns by combining this idea with the law of conservation of energy. (See Fig. 2)

Fig. 2
In this problem, we are given a circuit that has an ideal voltage source of 50 volts, creating a current of 3 amperes. At multiple junctions within the circuit, we are given the corresponding currents as the wire is split, as well as the voltage experienced at multiple different points. We are instructed to find the unknown voltage of the circuit element in the center. By using the current at each specific point, as well as the voltage experienced, we are able to find the power absorbed and produced. Applying the Law of Conservation of Energy, we can find the necessary power remaining that needs to be absorbed by the unknown circuit element in the center, and thus we can find the unknown voltage of said circuit element.

Solderless Breadboards, Open-circuits, and Short-circuits Lab

Introduction

The lab performed on Day 1 was intended to allow us to become familiar with breadboards and digital multimeters (DMMs). The electrical resistance experienced by creating these circuits across different holes in the breadboard, which would be connected by jumper wires, would be measured using the DMM (used as an ohmmeter) (Fig. 3)

Fig. 3
By connecting the leads of the ohmmeter to different holes across the breadboard, we were able to measure the resistance across different potential circuits. This would allow us to develop a basic understanding of the functionality of breadboards and how to properly use them in future labs. In this figure, the resistance across holes in the same row is shown.

Procedure

In order to conduct the lab, jumper wires would be placed across several holes in the breadboard and the resistance between the holes would be measured. First, the leads of the ohmmeter would be connected to two holes in the same row on one distinct side of the central channel on the breadboard and the corresponding resistance of that circuit would be recorded (Fig. 4). Next, the leads of the ohmmeter would be connected between two holes in the same row but on opposite sides of central channel and the corresponding resistance of that circuit would be recorded (Fig. 5). Following, the leads of the ohmmeter would be connected across two arbitrary holes across the breadboard and the corresponding resistance of that circuit would be recorded (Fig. 6). Finally, with the leads of the ohmmeter in two arbitrary holes, a jumper wire will connected the rows of the arbitrary holes, and the resistance across this circuit will be measured (Fig. 7). For every circuit, it will be determined whether it is an open-circuit or short-circuit.

Fig. 5
Circuit connected by holes on same row on opposite
 sides of channel, resulting in infinite resistance. 

Fig. 4
Circuit connected by holes on same row on same side
channel, resulting in relatively low resistance.

Fig. 7
Circuit connected by jumper while on same row of corresponding
arbitrary holes, resulting in relatively low resistance.

Fig. 6
Circuit connected by arbitrary holes,
 resulting in infinite resistance

Data and Results 
Among the separate trials, it was found that in instances of low resistance (or any numerical reading of resistance) a circuit was being properly created and we would classify this as a closed circuit. If the resistance was found to be extremely high/infinite (See Fig. 8), this signified an open circuit. Data table with measurements can be found in Fig. 9.

Fig. 8
This reading occurred during the trial of two holes in the same row on
opposite sides of the central channel and the trial of two arbitrary holes.

Fig. 9

Conclusion

In this lab, we familiarized ourselves with the proper use of breadboards and what type of circuits would be created in a multitude of situations. It was found that closed circuits were created when two wires were attached to holes in the same row on the same side of the central channel. In any other  instances where a circuit was created by connecting holes that were NOT in the same row and NOT on the same side of the central channel simultaneously, open circuit conditions would be observed. However, in this instance, if a jumper cable connected the two rows of these holes separated by row or by central channel, then a short circuit would be created. Understanding how the breadboard behaves will allow us to became more efficient in more complex experiments in the future.