Electric Circuits I

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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 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 and 390 resistors. Fig. 1 – A basic circuit with positive (red) and negative (black) power across the 180 resistor. Fig. 4 – Measuring both voltage and current flow through the 180 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 ? 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 ” 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?
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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 resistor, and the 240 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 (??? ) 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)
multimeter. Test your theory by using a single resistor instead of the three and measuring the voltage and current again. What is the overall trend of adding resistors in series? As you continue to add resistors in series, what happens to the overall resistance of the system? If a circuit is composed of N resistors, and each resistor has equal resistance R . What is the total resistance if all resistors are in series?
Experiment – Resistors in a Parallel Circuit The second way to add multiple resistors to a single circuit is by providing multiple paths for the current to flow through, with each path having its own resistor. This is referred to as a “Parallel Circuit”, because each resistor provides parallel paths for the current to flow. With this type of setup the moving charges have multiple paths to choose from and thus only pass through one resistor instead of all of them. Procedure [1] Build a circuit with two resistors in parallel similar to the one shown in Figure 6, using the 180 and 240 resistors (Connect jumpers (a) and (b), but do not connect jumper (c)). [2] Set the power supply voltage to 5 volts and verify the voltage using the voltage probe. [3] Measure and record the voltage across each of the resistors, then measure the current through each resistor, as well as the total current flowing into and out of the circuit. [4] Add a third parallel resistor (??? ) to the circuit and repeat the measurements from step [3]. Data Analysis Organize your measurements in a table for each parallel 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? Using your data, create a plot that shows how adding a resistor in parallel affects the total resistance of the circuit. Use this plot to find an equation for determining the total resistance of a parallel 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 multimeter. Test your theory by using a single resistor instead of the three and measuring the voltage and current again. What is the overall trend of adding resistors in parallel? As you continue to add resistors in series, what happens to the overall resistance of the system? If a circuit is composed of N resistors, Fig. 6 – Three resistors arranged in a parallel circuit. (a) (b) (c)
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and each resistor has equal resistance R . What is the total resistance if all resistors are in parallel? How do you think this applies to the practical warnings against plugging too many devices into a single outlet in your home? How do we protect against this in homes? resistor? How can we calculate the total resistance of each circuit?
Experiment –Kirchoff’s Rules When working with simple DC circuits which may have combinations of series and parallel resistors, Kirchoff’s Rules give us a simple means for calculating the resistive loads and currents flowing through each part of the circuit. Kirchoff’s Junction Rule describes current flows through different branches (or junctions) of the circuit. It simply states that the sum of all currents entering a junction must be equal to the sum of all currents leaving a junction. In the diagram shown in Figure 7, Kirchoff’s Junction Rule states that I 1 = I 2 + I 3 . Kirchoff’s Loop Rule describes changes in the energy of the moving charges as they flow around the complete loop of a circuit. Specifically, for any complete loop of the circuit, the change in voltage due to resistors and power supplies must add up to zero. Any decreases in voltage due to the presence of a resistor must be compensated for by an increase in voltage from a power supply or other component (Figure 8). You may need to review the sections of your textbook that describe Kirchoff’s Rules to understand how to use them to calculate circuit properties. I 1 I 2 I 3 I 3 I 1 I 1 = I 2 + I 3 Fig. 7 – Kirchoff’s Junction Rule. Δ V 1 = -I 1 R 1 Δ V 2 = -I 2 R 2 Δ V 3 = +V Δ V 1 + Δ V 2 + Δ V 3 = 0 Fig. 8 – Kirchoff’s Loop Rule. Fig. 9 – Series and parallel circuit for measuring Kirchoff’s Rules.
Procedure [1] Build a circuit using four resistors like the one shown in Figure 9. [2] Apply 5V as the voltage source from the power supply and verify the voltage using the voltage probe. [3] Measure the voltage drop through each resistor and the current flowing through each resistor, including the total current flowing into and out of the circuit. Data Analysis Organize your measurements in a table, and make sure that you clearly identify to what each measurement is referring. Label your measurements on a schematic of the circuit. (Hint: It may help to redraw the circuit in a different shape.) Identify all of the loops and junctions on your schematic. Show that the sum of currents entering each junction is the same as the sum of currents leaving each junction. Calculate the change in potentials around each complete loop, and show that they add up to zero. Use this information to determine the resistance of the unknown resistor. Show that this calculation is verified by Ohm’s Law and by measuring the resistance of the unknown resistor. If this circuit were replaced by a single resistor, what would be the resistance of that resistor? What is the total measured resistance of the circuit?
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