10Vdc. Figure 1. Schematics for verifying Kirchhoff's Laws

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1 ECE 231 Laboratory Exercise 2 Laboratory Group (Names) OBJECTVE Verify Kirchhoff s voltage law Verify Kirchhoff s current law Gain experience in using both an ammeter and voltmeter Construct two (2) circuits as shown in Figure 1 and Figure 2. A 1Vdc Ammeter V1 B R1 C R2 D 1Vdc Ammeter V1 R1 R2 1 2 R3 3 E R3 Parallel Circuit Series Circuit EQUPMENT REQURED Figure 1. Schematics for verifying Kirchhoff's Laws ECE 231 Circuit Board (n Stock room) Two banana cables (one for DC power supply and one for DMM) One lot of colored clip leads (students must supply their own clip leads) DMM (digital multimeter) DC power supply BACKGROUND Gustav Kirchhoff first described his laws in His first law KCL simply stated is that current into a node must equal the current leaving a node where a node is the point where two or more components are connected together. n Figure 1 above, the three currents 1, 2, and 3 leave the top node and go through the three resistors and then merge on the ground circuit. The 1

2 voltage across any parallel resistors is always the same. Current through any resistor can be determined by using Ohm's law. = V R = Voltage across a resistor Resistance or by measuring the current through each resistor using an ammeter. n Kirchhoff's Current Law (KCL) k=1 k = where is the n is the number of branches at a node. n Kirchhoff's Voltage Law (KVL) k=1 V k = where is the n is the number of components (resistors and voltage sources) in a loop. Kirchhoff's second law is like going on a hike from your car around a mountain (independent of path). When you get back to your car, your net change in potential energy is zero. No matter how you measure voltages around a circuit, when you return to your starting point the change in voltage is zero. Figure 2. Protoboard connection for the series circuit PROCEDURE 2

3 Part 1 Select three adjacent resistors and connect them in SERES with your power supply. Now measure the voltage at each node (A thru E) in your circuit. 1. Measure the voltages at all of the nodes relative to the power supply ground. Show that the sum of the voltages ACROSS all of the components in a loop complies with Kirchhoff s voltage law. Complete Table 1. Table 1. Voltages across each component and current through each resistor V EA V AB V BC V CD V DE Calculated R1 = Calculated R2 = Calculated R3 = Measured R1 = Measured R2 = Measured R3 = Power Power Power Power Power 2. Now measure the node voltages relative to node C. For example, Vca = -Vac which says that the voltage from c to a = minus the voltage from a to c. The voltages at the nodes relative to ground will not add to zero to prove Kirchhoff s voltage law. t is the sum of the voltages across each component in a series that add to zero NOT the sum of the node voltages. Remember, the reference node in a circuit can be anywhere you want in a real circuit. Table 2. Node voltages relative to node C (i.e. C is connect to the black meter lead) V CA V CB V CC V CD V CE NOTE Remember, the reference node in a circuit can be anywhere you want in a real circuit; therefore the voltage at a node will most likely change depending upon your reference. 3

4 3. Calculate the power delivered by the power supply. Show that it is equal to the power consumed by the resistors. Enter the power into Table 1. CAUTON Never connect an ammeter in parallel with the component you are trying to measure the current through. The ammeter is in essence a short circuit and must be in series with the components through which current is being measured. An error in the connection could seriously damage the ammeter and other circuit components. Part 2. Select three resistors and connect them in PARALLEL with your power supply. Now measure the current from the power supply. This procedure is NOT shown in Figure 2. t is up to you to figure out the connection scheme since only the power supply ammeter connection is shown in Figure 1. You only have one ammeter. Therefore, rewire each branch circuit with the ammeter in SERES with the branch circuit resistor. Verify the ammeter reading using the calculation method and a voltmeter. 1. Measure the source current and the branch currents 1, 2, and 3. Show that the currents comply with Kirchhoff s current law. f you read any negative currents with your ammeter, what did you do wrong? 2. Calculate the power delivered by the power supply. Show that it is equal to the power consumed by the three resistors. Table 3. Currents in the parallel circuit of Figure 1. Source = Measured = Measured= Measured= Measured= Calculated= Calculated= Calculated= Power= Power= Power= Power= 4

5 Write a professional comprehensive lab report using a word processor. Show your results and include a comprehensive conclusion. There are lots of sample lab reports on the internet. Conclusion 5