LU6_Kirchhoff's Rules

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Name ______________________ Class Section ________ Date _____________ PHY 242 – Laboratory LABORATORY 6: KIRCHHOFF’S RULES Objectives:  build circuits from schematic drawings.  measure the differences in potential and currents in series and parallel combinations of resistors.  demonstrate Kirchhoff’s Rules for electrical circuits. Materials Required: Computer with Excel and access to simulation Circuit Construction Kit : https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc Software Requirements : Windows Macintosh Chromebook Linux iPad Mobile Phone Chrome, Edge Chrome, Safari Chrome Not recommended Safari Not recommended Introduction: Circuits consisting of just one battery and one load resistance are simple to analyze, but they are not often found in practical applications. Usually, circuits have more than two components connected together. There are two basic ways in which to connect more than two circuit components: series and parallel. The defining characteristic of a series circuit is that there is only one path for electrons to flow. The defining characteristic of a parallel circuit is that all components are connected between the same set of electrically common points, therefore they experience the same difference in potential. There are many paths for electrons to flow, but only one voltage across all components. Series and parallel resistor configurations have very different electrical properties. A multi-loop circuit may have more than one battery in different branches of the circuit. A junction (node) in a circuit is a point where at least three circuit paths meet. A branch is a path connecting two junctions (nodes). To analyze such a circuit and to find the currents in all branches of the multi-loop circuit one must use Kirchhoff's rules. a) Kirchhoff's first rule (junction rule): At any junction point in a circuit where the current can divide, the sum of the currents into the junction (node) must equal the sum of the currents out of the junction (this is a consequence of charge conservation). 1

b) Kirchhoff's second rule (loop rule): When any closed-circuit loop is traversed, the algebraic sum of the changes in the potential must equal zero (this is a consequence of conservation of energy). Activity 1: Voltages in Series Circuits 1. Start the Circuit Construction Kit PhET simulation, Lab tab, and explore it. Make sure that you check the Show Current (conventional), Labels , and Values boxes. Hints for the use of various elements of circuit:  Right-click on the circuit element to change a property (e.g. resistance) or to delete it.  Right-click on junctions to disconnect pieces. 2. Build a simple circuit with a battery, wires, and three resistors of different resistances. Connect the three resistors into the series circuit shown below carefully noting which wire is connected to the negative and which is connected to the positive terminal of the battery. Use the sliders (after clicking on the element of circuit) to choose different values for the resistance of resistors and the voltage of the battery. 3. Use the voltmeter to measure the voltages across the individual resistors and then across the combinations of resistors. Be careful to observe the polarity of the leads (red is +, black is -). Record your readings below. R 1 = 10 R 2 = 20 R 3 = 30 R 12 = 30 R 23 = 50 R 123 = 60 V 1 = 5 V 2 = 10 V 3 = 15 V 12 = 15 V 23 = 25 V 123 = 30 4. According to your data, what is the pattern for how voltage gets distributed in a series circuit with unequal resistances? The pattern for how voltage gets distributed in a series circuit is that voltage across each individual resistors is proportional, having the highest resistor have the highest voltage. And when they are combined the voltage is half to the sum of the resistor. And across the resistor the voltage equals to the voltage of the battery. 2

5. Is there any relationship between the size of the resistance and the size of the resulting voltage? Yes when the bigger the resistance the bigger voltage there will be and the same if the resistance is small. Activity 2: Voltages in Parallel Circuits 6. Connect the three resistors into the parallel circuit shown below. 7. Connect the wires to the battery, carefully noting which wire is connected to the negative and which is connected to the positive. 8. Use the voltmeter to measure the voltages across the individual resistors and then across the combinations of resistors. Be careful to observe the polarity of the leads (red is +, black is -). Record your readings below. R 1 = 10 R 2 = 20 R 3 = 30 R 123 = 30 V 1 = 30 V 2 = 30 V 3 = 30 V 123 = 30 9. According to your data, what is the pattern for how voltage gets distributed in a parallel circuit with unequal resistances? The voltage in a parallel circuit is equal through out no matter how much or the difference between the resistor. 10. Is there any relationship between the size of the resistance and the size of the resulting voltage? No the voltage is equal between the different size of the resistance. Activity 3: Kirchhoff’s Rules 11. Connect five resistors (of different resistances) in a circuit as the one shown in the figure. 3

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12. Record each resistance value in the space below. The total resistance R total of the circuit between points A and B, will be calculated using Ohm’s law R total = V total / I total once you measure the difference in potential and the current in each resistor. 0 0 0 0 0 150 13.73 26.27 16.12 = 23.88 2.39 = 82.39 13. On the circuit diagram in the figure above indicate which side of each of the resistors is at a higher potential relative to the other end by placing a “+” at that end. 14. Use the ammeter to measure the current through each of the resistors. Make sure you record each of the individual currents, as well as the current flow into or out of the main part of the circuit, I total . 15. Based on your data, calculate the net current flow into or out of each of the four “nodes” in the circuit (add all the currents entering the nodes and subtract the currents leaving the node. Write down the net current flow in or out of each of the four “nodes” in the circuit below. Node A: 2.687 A positive Node B: 1.134 A positive Node C: 5.231 A positive Node D: 5.779 A positive 16. For at least three (3) of the six closed loops, calculate the net voltage drop based on your collected data. Show your work in the space below. Note: if the potential goes up, treat the voltage drop as positive (+), while if the potential goes down, treat it as negative (-). Loop 1: R1 = 13.73 R2 = 26.27 R3 = 16.12 = +56.12 V Loop 2: R1 = 13.73 R2 = 26.27 = +40 V Loop 3: R3 = 16.12 R4 = 23.88 = +40 V 4

17. Use your results from the previous two steps to analyze the circuit in terms of Kirchhoff’s Rules. State the evidence for your conclusions. To conclude, the evidence from the calculation does reflect and are consistent with Kirchhoff’s Rules. Since the positive net voltage drops around closed loops and the positive net current flows at nodes both making it the support for the principles of KVL and KCL. Making the circuit follow the electrical fundamental laws. References: CC-BY license, PhET Interactive Simulations, University of Colorado Boulder, http://phet.colorado.edu 5

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