Online-Lab-7_Kirchhoff-Laws

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University of Texas, Arlington *

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1402

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Electrical Engineering

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Apr 3, 2024

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PHYS 1402 Lab 7: Kirchhoff’s Laws Name: _____________________ Objective To understand Kirchhoff’s circuit rules and use them to determine the currents that flow in various parts of DC circuits. Overview Consider a circuit that has many components wired together in a complex array. Suppose you want to calculate the currents in various branches of this circuit. The rules for combining resistors are convenient in circuits made up only of resistors that are connected in series or in parallel. While it may be possible in some cases to simplify parts of a circuit with the series and parallel rules, complete simplification to an equivalent resistance is often impossible. The application of Kirchhoff’s rules can help us to understand complex circuits with more than one battery. Kirchhoff circuit rules applied to circuits are based on two conservation laws – conservation of energy and conservation of charge. To analyze the circuits, we define few terms: 1) Branch: A branch is a portion of the circuit in which the current is the same through all the circuit elements. 2) Junction or Node: A junction in a circuit is a place where two or more wires are connected. It is the point of connection between two or more branches. 3) Loop: A loop is any closed path in a circuit. Kirchhoff’s rules : 1. Junction Rule: The sum of the currents entering a junction equals the sum of the currents leaving out of the same junction. Junction rules is based on charge conservation. 2. Loop Rule: The sum of the changes in electric potential around a closed loop is zero. Let us consider the circuit shown below. Figure 1 1

Question 1: How many unknown currents are flowing in the circuit? Question 2: Mark Junction (or Junctions) on the figure. We will use PhET simulation Circuit Construction Kit: DC - Virtual Lab (https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab) 1. Open the PhET simulation Circuit Construction Kit: DC - Virtual Lab 2. Set-up the circuit shown in the above figure 1. 3. Set the resistances values: R 1 = 56 W , R 2 = 35 W , and R 3 = 110 W . Click on the resistor; you will be able to see the value of resistance and then change it using the slider switch. 4. Choose the following battery voltages: ℇ 1 = 10 V ∧ ℇ 2 = 30 V Take a screenshot after you connect the circuit and paste it. Question 3: Apply the Junction rule to one of the junctions. Do you get a different equation when you apply the rule to the other junction? Equation 1: Question 4: Assuming that the internal resistances of the batteries are negligible, apply loop rule to any two closed loops. Write down the equations for each loop. Equation 2: Equation 3: 5. Solve these three equations for the three unknown currents, I 1 , I 2 , and I 3 in amperes. Show your calculations below. 6. Modify the circuit to measure currents flowing through each resistor. You must use an ammeter to measure current. 7. Take a screenshot after you connect the ammeters in the circuit and paste it below. 8. Set battery emf E 1 = 10 V and note down the voltage across each resistor (V 1 , V 2 , and V 3 ) using voltmeter in the table below. Note the currents flowing through each resistor (I 1 , I 2 , and I 3 ) using an ammeter. Ammeter must be connected in series to the resistor. 9. Vary the battery emf E 1 . Each time you vary battery emf E 1 , note down the voltage across each resistor and currents flowing through each resistor in the table below. 10. Using Ohm’s law, V = IR, calculate the currents flowing through each resistor. I 1 (calculated) = V 1 / R 1 ; I 2 (calculated) = V 2 / R 2 ; I 3 (calculated) = V 3 / R 3 . 2

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