EMNG1001_Lab6_CombinationCircuits_InClass

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George Brown College Canada *

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EMNG1001

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Electrical Engineering

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Feb 20, 2024

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Student First Name: ……………………………………… Student Last Name: ……………………………………… Student Number: …………………………………………. Submission Date: ………………………………………… General Notes: 1. Type your name, student ID, and the submission date of the lab in the above fields. 2. Practice safety at all times. Carefully follow the directions of the lab. Do not use broken power cords or broken devices powered directly from the mains such as the DC supply. 3. Use only the electronic kit and devices provided by George brown college. Also, ensure that all equipment in the kit stays in good working condition. 4. Carefully read and follow ALL lab instructions provided in the lab write-up. 5. Complete all measurements, calculations, tables, drawings, and images required for all labs. 6. Answer all questions neatly and concisely in the spaces provided (preferably in bold red). 7. All Labs must be submitted by their due dates in Blackboard and cannot be made up. A grade of “Zero” will be assigned for missed labs. 8. The mark and possible feedback will be posted in Blackboard after the due date of each lab. Submission: This original word document with answers included in full is required to be submitted in Blackboard by the due date. It is not allowed to submit another separate document that includes only answers to the questions. Lab 6 Combination Circuits Objectives Upon completion of this lab, students will be able to: 1. Learn to recognize and construct combination series-parallel circuits. 2. Compute voltages and currents of combination series-parallel circuits. 3. Apply the concept of equivalent circuits to simplify combination circuits. 4. Verify computations through measurements. Introduction Real-life systems and applications involve series-parallel circuits which are commonly referred to as combination circuits. The key to solving combination type circuits is to form equivalent circuits of the Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 1 EMNG1001 Circuit Analysis Lab 6 Combination Circuits

series and parallel elements. The goal is to reduce a complex combination circuit into a simple series or parallel circuit. To do so, the student must recognize circuit elements which are connected in series and parallel to form the equivalent circuit. To identify whether components are in series or parallel remember that:  For components to be considered in series, they must be connected end-to-end and the identical amount of current must flow through them.  For components to be considered in parallel, both ends of one component must be directly attached to both ends of other components. Take as an example the combination circuit of Figure 1. Figure 1 Combination circuit example. In Figure 1, R 2 is in series with R 3 and they can be replaced with an equivalent resistance equals to R a = R 2 + R 3 = 11.5 k Ω . The circuit can then be simplified as shown in Figure 2. Figure 2 Simplification of the circuit of Figure 1. In Figure 2, R 1 is in parallel with R a and they can be replaced by the equivalent total resistance as follows and as shown in Figure 3: Figure 3 Total equivalent resistance of the circuit of Figure 1. Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 2

R T = [ 1 R 1 + 1 R a ] − 1 ≈ 2.564 k Ω Part 1 Procedure 1. From your tool kit obtain the following resistors: 2.2KΩ, 4.7KΩ, 5.6 KΩ, and 10KΩ. 2. Use the DMM to measure the resistance of each resistor and record the measured values below in Table 1. Table 1 Measuring resistances. Resistor Nominal Resistance (KΩ) Measured Resistance (KΩ) R 1 2.2 R 2 4.7 R 3 5.6 R 4 10 3. Using the resistors from Table 1, construct the combination circuit shown in Figure 4 below. Adjust the DC power source to 12 V. Figure 4 Experimental combination circuit of Part 1. 4. Identify the topology of the combination circuit of Figure 4: a. Indicate which resistors will have identical current flowing through them (i.e. which resistors are connected in series?). Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 3

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Answer: ………………………….. b. Indicate which resistors have both ends connected (i.e. which resistors are connected in parallel so that they receive the same voltage?). Answer: ………………………….. 5. Measure the DC source voltage as it is applied to the circuit: V s = ¿ ………………………….. 6. Utilizing the measured values of the resistances as in Table 1 and the measures supply voltage as in step 5, theoretically analyze the combination circuit of Figure 4 as follows and fill in the computed values in Table 2: a. Replace R 2 and R 3 with an equivalent resistance called R 2,3 . Determine the value of R 2,3 : R 2,3 = R 2 R 3 R 2 + R 3 ………………………….. b. Determine the total resistance of the resulted simplified series circuit: R T = R 1 + R 2,3 + R 4 = ¿ ………………………….. c. Apply Ohm’s law to find the total current of the circuit: I T = V s R T = ¿ ………………………….. d. Proceed using Ohm’s law to find the voltage drops of the different resistors and the currents of the resistors R 2 and R 3 : V R 1 = I T R 1 = ¿ ………………………….. V R 2,3 = V R 2 = V R 3 = ¿ I T R 2,3 = ¿¿ ………………………….. V R 4 = I T R 4 = ¿ ………………………….. I R 2 = V R 2,3 R 2 = ¿ ………………………….. I R 3 = V R 2,3 R 3 = ¿ ………………………….. 7. Disconnect the constructed combination circuit of Figure 4 from the DC power supply and use the DMM as an ohmmeter to verify the total resistance and record the value in Table 2. 8. Connect the circuit to the DC power supply and using the DMM measure all required voltage drops and currents as per Table 2. 9. In Table 2, do the theoretically calculated values agree with the measured values? Comment on the differences. Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 4

..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Table 2 Analysis and measurement results of the circuit of Figure 4. Parameter Calculated Values Measured Values R T ( k Ω ) I T ( mA ) V R 1 ( V ) V R 2,3 ( V ) V R 4 ( V ) I R 2 ( mA ) I R 3 ( mA ) Part 2 Procedure 1. Using the resistors from Table 1, construct the combination circuit shown in Figure 5. Adjust the DC power source to 12 V. Figure 5 Experimental combination circuit of Part 2. Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 5

2. Measure the DC source voltage as it is applied to the circuit: V s = ¿ ………………………….. 3. Utilizing the measured values of the resistances as in Table 1 and the measures supply voltage as in step 2 of this part, theoretically analyze the combination circuit of Figure 5 as follows and fill in the computed values in Table 3: a. Replace R 1 and R 2 which are connected in series with an equivalent resistance called R 1,2 . Determine the value of R 1,2 : R 1,2 = R 1 + R 2 = ¿ ………………………….. b. Replace R 3 and R 4 which are connected in series with an equivalent resistance called R 3,4 . Determine the value of R 3,4 : R 3,4 = R 3 + R 4 = ¿ ………………………….. c. Determine the total resistance of the resulted simplified parallel circuit: R T = R 1,2 R 3,4 R 1,2 + R 3,4 = ¿ ………………………….. d. Apply Ohm’s law to find the different currents and voltage drops of the circuit elements: I R 1,2 = V s R 1,2 = ¿ ………………………….. I R 3,4 = V s R 3,4 = ¿ ………………………….. I T = V s R T = ¿ ………………………….. V R 1 = I R 1,2 R 1 = ¿ ………………………….. V R 2 = I R 1,2 R 2 = ¿ ………………………….. V R 3 = I R 3,4 R 3 = ¿ ………………………….. V R 4 = I R 3,4 R 4 = ¿ ………………………….. 4. Disconnect the constructed combination circuit of Figure 5 from the DC power supply and use the DMM as an ohmmeter to verify the total resistance and the resistance of each parallel branch of the circuit and record the values in Table 3. 5. Connect the circuit to the DC power supply and using the DMM measure all required voltage drops and currents as per Table 3. Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 6

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6. In Table 3, do the theoretically calculated values agree with the measured values? Comment on the differences. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 7

Table 3 Analysis and measurement results of the circuit of Figure 5. Parameter Calculated Values Measured Values R 1,2 ( k Ω ) R 3,4 ( k Ω ) R T ( k Ω ) I R 1,2 ( mA ) I R 3,4 ( mA ) I T ( mA ) V R 1 ( V ) V R 2 ( V ) V R 3 ( V ) V R 4 ( V ) Part 3 Questions & Answers 1. In your own words, describe what is a combination circuit. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 2. What is the definition of an equivalent circuit? ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 3. What is the purpose of an equivalent circuit? ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 4. Apply KCL to the measurement results of Table 2 for the circuit of Figure 4. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 5. Apply KVL to the measurement results of Table 2 for the circuit of Figure 4. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 6. Apply KCL to the measurement results of Table 3 for the circuit of Figure 5. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... 7. Apply KVL to the measurement results of Table 3 for the circuit of Figure 5. ..................................................................................................................................................... Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 8

..................................................................................................................................................... Ali A. Hussein, Ph.D., P. Eng. EMNG 1001, Circuit Analysis Lab Page 9

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