Basic DC Circuits Current and voltage can be difficult to understand, because the flow of electrons and potential differences cannot be observed by the unaided human eye. To clarify these terms, some people make the comparison between electrical circuits and water flowing in pipes. Here is a chart of the three electrical units you will study in this experiment. Electrical Quantity Voltage or Potential Difference Current Resistance Description Unit A measure of the Energy Volt (V) difference per unit charge between two points in a circuit. A measure of the flow of Ampere (A) charge through a cross-­‐
section in a circuit. A measure of how Ohm (Ω) difficult it is for current to flow in a circuit. Water Analogy Water Pressure Amount of water flowing per unit time. A measure of how difficult it is for water to flow through a pipe. This experiment studies three rules which are essential to understanding DC circuits: Ohm’s Law, Resistors in Series, and Resistors in Parallel. Objectives There are three primary results which you will determine in this lab, and address in your abstract. Part 1: Ohm’s Law • Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit. Part 2: Voltage and Resistance in Series and Parallel Circuits • Study the voltages across resistors in series and parallel circuits. • Use Ohm’s law to calculate equivalent resistance of series and parallel circuits. Part 3: Current in Series and Parallel Circuits • Study the current flow through resistors in series and parallel circuits. 22 - 1
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Materials Computer Vernier computer interface Logger Pro Vernier Circuit Board Multimeter Part 1a: Using an Ohmmeter Vernier Current Probe Vernier Differential Voltage Probe Adjustable low voltage DC power supply Alligator clips 1. For each of the three resistor values you are using in this experiment, note the tolerance rating. Tolerance is a percent rating, showing how much the actual resistance could vary from the labeled value. This value is labeled on the resistor or indicated with a color code. Calculate the range of resistance values that fall in this tolerance range. 2. Ensure the external supply is disconnected, and use the multimeter on the resistance measurement setting (Ω) to measure the resistance of each resistor, filling in the final column of the table below. CAUTION: The ohmmeter must never be used when the resistors are connected to a source of power as the internal circuitry of the meter (which in ohmmeter mode includes its own battery), could be seriously damaged if connected to another power source. Labeled resistor value (Ω) Tolerance (%) 10 Minimum resistance (Ω) Maximum resistance (Ω) Measured resistance (Ω) 51 68 Part 1b: Ohm’s Law Georg Simon Ohm discovered the fundamental relationship among these three important electrical quantities: current, voltage, and resistance. Ohm’s Law and the unit of electrical resistance, the ohm, were both named for him to commemorate his contribution to physics. Ohm’s law states that the current through a resistor is proportional to the voltage across the resistor. Resistance, R, is then defined as R = V/I 22 - 2
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where V is the potential across a resistor, and I is the current through the resistor. R is measured in ohms (Ω), where 1 Ω = 1 V/A. In this experiment you will see if Ohm’s law is applicable to a resistor, and you will use measurements of current and voltage to determine resistance. Procedure 1.
Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the computer interface. 2.
Open the file “22 Ohms Law” in the Physics with Vernier folder. A table and a graph of potential vs. current will be displayed. The meter displays potential and current readings. 3.
With the power supply turned off, connect the 10 Ω resistor, wires, and clips as shown in Figure 1, noting the pin numbers. Take care that the positive lead from the power supply and the red terminal from the Current & Voltage Probe are connected as shown in Figure 1. Note: Attach the red connectors electrically closer to the positive side of the power supply. 4.
With voltage and current turned off, zero your probes. 5.
Record the value of the resistance (10 Ω) you will be using, in the first row of the data table below. 6.
Make sure the power supply is set to 0 V. Click to begin data collection. Use the momentary switch (red top) to energize the circuit and monitor the voltage and current. Click while holding the switch. The voltage and current will be automatically plotted for you. Figure 1 22 - 3
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7.
Release the switch when the data point has been measured, and increase the voltage on the power supply to approximately 0.2 V. Using the switch, energize the circuit and click again . 8.
Increase the voltage again by about 0.2 V. Click again until you reach a voltage of 3.0 V. 9.
Click V. . Repeat this process to end your data collection, and then set the power supply back to 0 10. Are the voltage and current proportional? Click the Linear Fit button, , and record the slope of the regression line in the data table below. Data Table Part 1b. Ohm’s Law Resistor (Ω) Slope of regression line (V/A) Y-­‐intercept of regression line (V) Analysis of Results in Part 1 1.
Compare the slope of the regression line to the ohmmeter-­‐measured resistance for that resistor. 2.
Does your resistor adhere to Ohm’s law? Base your answer on your experimental data. 22 - 4
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Part 2: Voltages and Currents in Series and Parallel Circuits Components in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel. Series Circuit Parallel Circuit You can monitor these circuits using a Current Probe and a Voltage Probe and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors. Procedure Part 2a. Voltages in Series Circuits 1.
Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the interface. 2.
Open the file “23a Series Parallel Circ” in the “Physics with Vernier” folder. Current and voltage readings will be displayed in the bottom-­‐left meter area of the window. 3.
Connect together the two voltage leads (red and black) of the Voltage Probe and zero the sensors. 4.
Connect the series circuit shown in Figure 2 using a 10 Ω resistor for R1 and a 51 Ω resistor for R2. Notice the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. Turn the power supply up to 5 V. 5.
Briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit. 22 - 5
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6.
Press on the switch to complete the circuit again and read the current (I) and total voltage (VTOT). Record the values shown in the software’s Voltage and Current windows in the data table below. 7.
Connect the leads of the Voltage Probe across R1. Press on the switch to complete the circuit and read this voltage (V1). Record this value in the data table. 8.
Connect the leads of the Voltage Probe across R2. Press on the switch to complete the circuit and read this voltage (V2). Record this value in the data table. 9.
Repeat this and continue to fill in the rest of the table. Data Table Part 2a: Voltages in Series Circuits R1 (Ω) R2 (Ω) R3 (Ω) I (A) VTOT (V) V1 (V) V2 (V) V3 (V) Req (Ω) 10 51 -­‐ -­‐ 10 68 -­‐ -­‐ 51 68 -­‐ -­‐ 10 51 68 Analysis of Results of Part 2a 22 - 6
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1.
2.
Using the measurements made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the series circuit with the two resistors you tested, and fill in the appropriate column above. What seems to be the relationship between readings V1, V2, V3 (where applicable), and VTOT? How are these values dependent on the values of your resistors? Part 2b: Voltages in Parallel Circuits 1.
Connect the parallel circuit shown below, with a 51 Ω resistor for R1 and a 68 Ω resistor for R2. As in the previous circuit, the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. The Current Probe is used to measure the total current in the circuit. Figure 3. Parallel resistors. 2.
As in Part 2a, you can take readings from the meter at any time by briefly pressing the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit. 3.
Press the switch to complete the circuit again and read the total current (I) and total voltage (VTOT). Record the values in the data table. 4.
Connect the leads of the Voltage Probe across R1. Press on the switch to complete the circuit and read the voltage (V1) across R1. Record this value in the data table. 5.
Connect the leads of the Voltage Probe across R2. Press on the switch to complete the circuit and read the voltage (V2) across R2. Record this value in the data table. 6.
Repeat Steps 1-­‐5 for the remainder of the resistor values in the table. 22 - 7
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Data Table Part 2b. Voltages in parallel circuits R1 (Ω) R2 (Ω) R3 (Ω) I (A) VTOT (V) V1 (V) V2 (V) V3 (V) Req (Ω) 51 68 -­‐ -­‐ 10 10 -­‐ -­‐ 10 51 -­‐ -­‐ 10 51 68 Analysis of Results of Part 2b 1.
Using the measurements made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the parallel circuit with the resistors you tested. 2.
If the resistance of resistors in parallel is given by 1
1 1
= + +...
Rtot R1 R2
does your result in (1) agree with the values of the resistors you used in your parallel circuit? 3.
What seems to be the relationship between the voltage readings V1, V2, and V3 (where applicable), and VTOT in a parallel circuit? Part 3: Currents in Series and Parallel Circuits In Part 3, we investigate the flow of current through series and parallel resistors. 1. For Part 3. of the experiment, you will use two Current Probes. Open the experiment
file “23b Series Parallel Circ.” Two graphs of current vs. time are displayed.
2. Disconnect the Voltage Probe and, into the same channel, connect a second Current
Probe. Connect a third current probe into channel 3. Zero all three probes before
connecting to the circuit.
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3. Connect the series circuit shown in Figure 4 using the 10 Ω and the 51 Ω resistors.
Figure 4
4. Click on the
button, wait a second or two, then press on the switch to complete
the circuit. Release the switch just before the graph is completed.
5. Select the region of the graph where the switch was on by dragging the cursor over it.
Use the Statistics button to determine and record the average current in the data table
for currents at Ia, Ib, and Ic.
6. Connect the parallel circuit as shown in Figure 5 using the 51 Ω resistor and the 68 Ω
resistor.
Figure 5
7. As with the series circuit, begin collecting the data and hold the switch. When
complete, record the average currents Ia, Ib, and Ic in the data table. 22 - 9
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DATA TABLE Part 3. Currents in Series and Parallel Circuits R1 & R2 Series R1 & R2 Parallel R1 (Ω) 10 51 R2 (Ω) Ia (A) 51 68 Ib (A) Ic (A) Analysis of Results of Part 3 1. What did you discover about the current flow in a series circuit? 2. What did you discover about the current flow in a parallel circuit? 3. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why? 4. According to Kirchoff’s Current Rule, the current into a junction must be equal to the current out of a junction. Are your observations for the parallel resistors in agreement with this rule? 22 - 10
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