Electric Circuits I

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Tulane University *

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Electrical Engineering

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Apr 3, 2024

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Electric Circuits I Introduction It is well known that all atoms are composed of a nucleus (containing protons and neutrons) and electrons, which orbit the nucleus. Objects can become positively or negatively charged when electrons are added or removed from the atoms in the object. For example basic storage batteries move electrons via a chemical reaction from one terminal to another, creating a difference in charge between the two terminals. This difference in charge creates potential energy in the electrons, as they want to move from like charge to unlike charges (i.e. from the negative terminal to the positive terminal. When discussing the potential energy of electric charges, we normally refer to the amount of energy per charge, which is called the electric potential (or voltage ) of the system. The more voltage a system has, the more potential energy each electron has. The electrons in metallic objects easily move within the object when influenced by an electric potential. A wire that connects two regions of differing potential, such as two battery terminals, will allow electrons to flow from the excess electron terminal (-), to the deficient electron terminal (+). This is known as a current , and its flow is measured in Amperes (which is the same as a Coulomb / second or 6.25 × 10 18 electrons / second). The current flow is opposite to the electron flow . This is by convention when it was thought that the positive charges were the main charge carriers. It was not until the discovery of the electron in 1897 by J. J. Thomson that it was realized that electrons are the mobile charge carriers in circuits. The current in a circuit loses energy in varying amounts due to the circuit's resistance to current flow, normally as the result of electron- atom collisions which occur in the course of the current flow. This impedance to the flow of current is called resistance . The unit of resistance is the Ohm and its symbol is Ω , the Greek letter omega. Resistance is a derived quantity and is related to voltage and current by the relation Resistance = Volts / Amperes , or R = V / I . This relationship is known as Ohm’s Law . Physical Quantity Units Charge Coulomb Current Ampere [= Coulombs / second] Electric Potential (Voltage) Volt [= Joules / Coulomb] Resistance Ohm ( Ω ) [= Volts / Ampere] Table 1: SI units for electrical circuits.

Experiment – Ohm’s Law In this experiment we will create an electric current by producing a voltage difference between the ends of a circuit. The current will flow through a resistor, which removes energy from the electrons, resulting in a voltage drop between when the electrons enter and leave the resistor. By measuring this voltage drop and the amount of current flowing through the resistor, we will verify Ohm’s Law and determine the resistance of the resistor in the circuit. Procedure [1] Create a simple, one-resistor circuit by connecting two jumper wires and power from the power supply around the 180 Ω resistor as shown in Figure 1. [2] Open the file “Circuits.cmbl” and ensure that both the voltage and current probes are connected to the LabPro interface. Zero the sensors. [3] Turn on the power supply and adjust the voltage to 5 volts. To measure the voltage of the power supply, connect the positive and negative voltage probes to the wires attached to the power supply. This is the voltage difference being applied to ends of the circuit. [4] Measure the voltage drop across the resistor. Do this by placing one lead from the voltage probe on each end of the resistor piece, as shown in Figure 2. Record this value. [5] Remove the second jumper from the circuit and place one lead from the current probe in each hole that the connector filled as shown in Figure 3. This measures the current through the circuit. Record this value. Note: do not connect the current probe directly to the resistor as you did with the voltage probe. This will damage the probe. [6] Connect both the voltage and current probes to the circuit (Figure 4). Click “Collect” and use the dial on the power supply to vary the voltage between 0 and 6 volts. Save the graph. [7] Repeat the voltage and current measurements for the 240 Ω and 390 Ω resistors. Fig. 1 – A basic circuit with positive (red) and negative (black) power across the 180 Ω resistor. Fig. 4 – Measuring both voltage and current flow through the 180 Ω resistor. Fig. 2 – Measuring the voltage drop across a resistor. Fig. 3 – Measuring the current flow through a resistor. Current must be measured in series, meaning the current probe has to be part of the circuit. In order to measure current you have to replace a component with the current probe.

Data Analysis Using your plot of Voltage vs. Current measurements, fit a line to your function by using the Linear Fit tool. What does the slope of the line represent? Use this data to show how resistance is related to voltage and current. Use the data from your plot to determine the calculated resistance of the resistor in the circuit. How does this value compare to the stated resistance of 180 Ω ? Create a table to hold your data from the first part of the experiment and calculate the resistance using the relationship you just determined. How do these values compare to the stated resistances? Measure the actual resistance of each of the resistors using the small multimeter. Set the multimeter dial to the “2000 Ω ” setting and place the probes on either side of the resistor. How do these values compare to your other values? What does this tell us about resistors in general? Why do you think it is essential to measure current in series instead of in parallel? What would happen if you simply connected the current probe to opposite sides of the resistor?

Experiment – Resistors in a Series Circuit We can add multiple resistors to a single circuit in two different ways. The simplest way is to add one resistor after another in the circuits and have the current flow through each of the successively. This is referred to as a “Series Circuit” (as there is a series of resistors). Procedure [1] Create a series circuit including both the 180 Ω resistor, and the 240 Ω resistor by completing the circuit as shown in Fig. 5, then placing the negative power supply wire in front of the unknown resistor (connect jumpers (a) and (b), and plug the negative power supply wire into (b)). [2] Set the voltage for the power supply to 5 volts, and verify it with the voltage probe. [3] Measure and record the voltage across each resistor using the same method as in experiment one. Measure the amount of current before and after each resistor and record these values. [4] Expand the circuit to include the third resistor (??? Ω ) in series, so that you have a three resistor series circuit (as shown in Figure 3). Measure and record the voltage and current through each resistor. Data Analysis Organize your measurements in a table for each series circuit. Which resistor gave the biggest voltage drop? What is the total voltage drop across all three resistors? How does it compare to the voltage of the power supply? How does the current through each resistor compare to each other, and to the total current entering and leaving the circuit? If the voltage is dropping as the charges pass through each resistor, how much voltage is remaining before the charges enter the final resistor? Using your data, create a plot that shows how adding a resistor in series affects the total resistance of the circuit. Use this plot to find an equation for determining the total resistance of a series circuit. If we were to replace these three resistors with one resistor, what would be the resistance of that resistor? Verify this by measuring the total resistance across the entire circuit using the small Fig. 5 – Three resistors arranged in a series circuit. (a) (b) (c)

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