ECE210-Experiment#06

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University of Illinois at Chicago Department of Electrical and Computer Engineering ECE 210 – Circuit Analysis Spring 2023 Semester Experiment #6 K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS Circle Lab Section: Tu8 Tu2 Th11 Th2 F8 F11 Name: UIN: Signature: By signing, I (we) attest that the document submitted is my (our) own original work. Name: UIN: Signature: By signing, I (we) attest that the document submitted is my (our) own original work. Name: UIN: Signature: By signing, I (we) attest that the document submitted is my (our) own original work. Circle Lecture Session: 2pm 4pm Circle Lecture Session: 2pm 4pm Circle Lecture Session: 2pm 4pm

ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago Preliminary Lab Assignment Please complete the preliminary lab (prelab) assignments that are highlighted as ( Prelab: ). Purpose To verify Kirchhoff’s laws theoretically and experimentally. Equipment • RIGOL DM3058E Digital Multimeter (DMM) • RIGOL DP 831 DC Power Supply • Universal Breadbox 1 Introduction In this experiment, you will measure voltages and currents using all of the techniques we have learned this semester. The resistive circuit shown in Figure 1 will be used for theoretical calculations for the prelab questions and these results will be compared to actual measurements. + + + + - - - - A B C D V s 1 V s 2 I Vs 1 I Vs 2 I 1 I 2 I 3 100 Ω 680 Ω 470 Ω 1 k Ω V 100 V 680 V 470 V 1k I 100 I 680 I 470 I 1k Figure 1: A 4-node, 3-loop, resistive circuit with two voltage sources. 2 of 8

ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago Prelab: Consider the circuit in Figure 1 and let V s 1 = 10 V and V s 2 = 6 V. Use mesh analysis to determine mesh currents I 1 , I 2 , and I 3 . Show your work in the space provided and record the your results in Row 1 of the table shown below. Theoretical Mesh Currents Row V s 1 V s 1 I 1 I 2 I 3 1 10 V 6 V 3 of 8

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ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago Prelab: Calculate the currents through each of the four resistors and the two voltage sources. Please note that all of element voltages and currents in Figure 1 have already been marked according to passive sign convention (PSC). All of the element currents can be derived using KCL and the calculated mesh currents. For example, I Vs 1 = - I 1 , I 470 = I 1 - I 3 , I Vs 2 = I 2 - I 3 , etc. Hint: For this circuit, the currents will be negative for the voltage sources and positive for the resistors . Show your work in the space provided and record the your results in Row 2 of the table shown below. I Vs 1 = - I 1 = I Vs 2 = I 2 - I 3 = I 1 k = I 680 = I 470 = I 1 - I 3 = I 100 = Theoretical Element Currents Row I Vs 1 I Vs 2 I 1 k I 680 I 470 I 100 2 Prelab: Use Ohm’s Law to calculate the voltage drops across each resistor. Use the nominal (ideal) resistor values and calculated resistor currents from Row 2. (show all work) Show your work in the space provided and record the your results in Row 3 of the table shown below. V 1 k = V 680 = V 470 = V 100 = Theoretical Resistor Voltages Row V s 1 V s 2 V 1 k V 680 V 470 V 100 3 10 V 6 V 4 of 8

ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago 2 Verification of KCL, KVL, and Power Balance for a Linear Circuit Before proceeding to the experimental portion of the experiment, it is important to note that if a circuit branch contains a resistor, the best way to measure the branch current is to measure the voltage across the resistor and divide by the resistance R . However, this gives a value which is only as accurate as the value of the resistance R . As a result, start this investigation by using the digital multimeter (DMM) to accurately measure the values of all resistors which will be used in the experiment. IMPORTANT : The resistors must be as accurate as possible in this experiment. Discard any resistors with a tolerance greater than ± 5%. Obtain replacements if necessary. Measure the four resistors and record their resistances in Row 4 of the table shown below. Row Theoretical 1.0 k Ω 680 Ω 470 Ω 100 Ω 4 Measured Now setup the circuit in Figure 1 using the selected resistors. Use the dc power supply and set Output1 to 10 V for V s 1 and Output2 to 6 V for V s 2 . Set the current limits for each output to 100 mA. Use the DMM for measurements. We are now in a position to make the appropriate voltage measurements to verify KVL around loops 1, 2, and 3, and the outer loop (perimeter) of the circuit. You will find that you must understand the sign convention for voltages, and you must understand what the DMM tells you about the sign of a measured voltage, in order to do this. Measure and record the voltages shown in the following table and compute the percent error with respect to the calculated theoretical values. Hint : All of the values in this table should be positive. Row type V s 1 V s 2 V 1k V 680 V 470 V 100 5 DMM Measured 6 % Error Note : The percent error in Row 6 is computed by using Row 5 (measured) and Row 3 (calculated) using: Percent Error = parenleftbigg Measured Value - Calculated Value Calculated Value parenrightbigg 100% 2.1 Verification of KVL We will now verify KVL for each of the loops using the DMM-measured values from Row 5. You will notice that each KVL equation is written in the clockwise direction (same as the loop current direction) using the form Σ v drops = 0. KVL for Loop 1: - V s 1 + V 470 + V 680 ? = 0 5 of 8

ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago KVL for Loop 2: - V 680 + V s 2 + V 100 ? = 0 KVL for Loop 3: V 1k - V s 2 - V 470 ? = 0 Comment on whether KVL is satisfied for each of these three loops. 2.2 Verification of KCL Next, we will verify KCL at each of the four nodes: A , B , C , and D as shown in Figure 1. As mentioned previously, the resistor currents can be determined by measuring the resistor voltage and dividing by the resistor value. If a branch of a circuit contains no resistors, the current in that branch must be measured directly with a DMM by using it as an ammeter and connecting it in series with the branch. Complete the following table by using I R = V R / R where V R is the measured resistor voltage from Row 5 and R is the measured resistor value from Row 4. For the currents through the voltage sources, use the DMM as an ammeter in series with the source to complete the table. Be careful with the signs! Row type I Vs 1 I Vs 2 I 1k I 680 I 470 I 100 7 DMM Measured 8 % Error Note : The percent error in Row 8 is computed by using Row 7 (measured) and Row 2 (calculated) using: Percent Error = parenleftbigg Measured Value - Calculated Value Calculated Value parenrightbigg 100% 6 of 8

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ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago We will now verify KCL for each of the nodes using the DMM-measured values from Row 7. You will notice that each KCL equation is written using the form Σ i out = 0. KCL for node A : I Vs 1 + I 470 + I 1k ? = 0 KCL for node B : - I 1k - I Vs 2 + I 100 ? = 0 KCL for node C : - I 470 + I 680 + I Vs 2 ? = 0 KCL for node D : - I Vs 1 - I 680 - I 100 ? = 0 Comment on whether KCL is satisfied at each of the four nodes. 7 of 8

ECE 210 C IRCUIT A NALYSIS Experiment #6 – K IRCHHOFF ’ S C URRENT AND V OLTAGE L AWS University of Illinois at Chicago 2.3 Verification of Conservation of Power Now we will calculate the power absorbed by all elements in the circuit, including the voltage sources by using P = IV (with I and V assigned according to PSC). Compute the power absorbed by each element using the measured values from Row 5 and Row 7 and record them in Row 9 in the table shown below. Note: The power absorbed by each of the resistors should be positive while the power absorbed by each of the voltage sources should be negative (since each is generating power in this circuit). Power Absorbed by Each Element Row P Vs 1 P Vs 2 P 1 k P 680 P 470 P 100 4 Conservation of Power: P Vs 1 + P Vs 2 + P 1k + P 680 + P 470 + P 100 ? = 0 Is Conservation of Power satisfied? Comment on whether the total power generated (delivered) by the sources is equal to the total power absorbed (dissipated) by the resistors. 3 Conclusion Please comment on the key outcomes of this experiment. 8 of 8