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Experiment 2: Analysis and Measurement of Resistive Circuit

Parameters Report Due In-class on Wed., Mar. 28, 2018

Pre-lab must be completed prior to lab.

1.0 PURPOSE

To (i) verify Kirchhoff's laws experimentally; ii) investigate the concept of power absorption and power delivery; and iii) demonstrate experimentally the principle of superposition in circuit analysis.

2.0 INTRODUCTION Certain network principles and theorems can be used to considerably simplify the analysis of complex circuits. Circuits with multiple independent sources can often be analyzed by considering the effects of the independent sources one at a time. In the design of circuits, the principle of superposition allows the desired response of a complex circuit to be expressed as the sum of the responses due to each independent source. This approach allows the designer to reduce the design of the complex circuit to the design of simple circuits. It is important to note that, for circuits with multiple independent sources, some power sources may absorb power while other sources may deliver power. Once a complex multi-source circuit is divided into multiple simple circuits where each circuit has a single power source, basic circuit analysis approaches can be applied to evaluate all voltages and current associated with each element in the circuit. In addition, Ohm's Law, Kirchhoff’s current law and Kirchhoff’s voltage law are simple but sufficient laws that form the basis for electric circuit analysis and synthesis. Kirchhoff’s laws apply to the interconnection of elements rather than to individual elements. The laws describe the inherent constraints on voltage and current variables by virtue of interconnections. Essentially, these laws follow from the conservation of energy and continuity of current (or conservation of charge) principle. 2.1 The Electric Circuit An electric circuit consists of circuit elements, such as energy sources and resistors, connected by electrical conductors or leads to form a closed path or combination of paths through which current can flow. A point at which two or more elements have a common connection is called a NODE. A two-terminal circuit element connected between two nodes is called a BRANCH. A branch may

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contain more than one element between the same nodes. When two or more circuit elements are connected together an ELECTRIC NETWORK is formed. If the network contains at least one closed path, the network is called an ELECTRIC CIRCUIT.

2.2 Kirchhoff's Laws  

2.2.1 Kirchhoff's Current Law (KCL) Kirchhoff's current law describes current relations at any node in a network. It states that the algebraic sum of the currents at any node is zero. Kirchhoff's current law relates to the conservation of charge since a node cannot store, destroy or generate charge. It follows that the charge flowing out of a node exactly equals the charge flowing into the node. An equivalent way of saying this is to say that the current at a node is continuous. 2.2.2 Kirchhoff's Voltage Law (KVL) Kirchhoff's voltage law describes voltage relations in any closed path in a network. It states that the algebraic sum of the voltages around any closed path is zero. Kirchhoff's voltage law expresses the principle of conservation of energy in terms of the voltages around a closed path. Thus, the energy lost by a charge travelling around a closed path is equal to the energy gain.

2.3 Principle of Superposition The principle of superposition states that the response (a desired current or voltage) at any point in a linear circuit having more than one independent source can be obtained as the algebraic sum of the responses caused by each independent source acting alone, i.e., with all other independent sources set to zero. An independent voltage source is set to zero by replacing it with a short circuit, and an independent current source is set to zero by replacing it with an open circuit. Note that the principle of superposition is a consequence of linearity and hence applicable only to linear circuits. Superposition allows us to analyze linear circuits with more than one independent source by analyzing separately single-source circuits.

2.4 Power Calculation The power associated with a basic circuit element is given by

𝑝 = 𝑣𝑖 (1)

where p is the power in watts, v is the voltage in volts, and i is the current in amperes.

   

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Resistors always absorb energy and dissipate power. Power sources, on the other hand, can either deliver or absorb power. From our circuit analysis, we should be able to determine whether power is being delivered to a given electrical element or extracted from it. We can use passive sign convention to achieve this objective as follows:

1. If the reference direction for the current is in the direction of the voltage drop across the terminals of the element as shown in Figure 1,

Figure 1

then

𝑝!"# = 𝑣𝑖 (2)

2. If the reference direction for the current is in the direction of the voltage rise across the terminals of the element as shown in Figure 2

Figure 2

then

𝑝!"# = 𝑣𝑖 (3)

To summarize, when positive charges move through a drop in voltage, they lose energy, and as they move through a rise in voltage, they gain energy.

2.5 References [1] J.W. Nilsson and S.A. Riedel, Electric Circuits, 10th edition, Pearson Learning Solutions, 2015.

[2]. E. Gill, H. Heys, J. E. Quaicoe, and V. Ramachandran, Lab manuals from previous offering of courses ENGI 1040 and ENG 1333.

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2  

+  

−  𝑣  

𝑖  1  

2  

−  

+  𝑣  

𝑖  

1  

2  

−  

+  𝑣  

𝑖  1  

2  

+  

−  𝑣  

𝑖  

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3.0 PRELAB

Prelab must be completed prior to the lab and signed by a TA at the start of the lab.  

3.1 Read the Introduction of the lab instructions and, from the course text book, the following sections:

Chapter 1, Section 6: “Power and Energy”, Chapter 2, Section 2: “Electrical Resistance”, Chapter 2, Section 4: “Kirchhoff’s Laws”, and Chapter 4, Section 13: “Superposition”.

3.2 The components of the circuit of Figure 3 have the following values: 𝑣!! = 10  𝑉, 𝑣!! = 2.5  𝑉, 𝑅! = 270Ω, 𝑅! = 680Ω, 𝑅! = 510Ω and 𝑅! = 1.5𝑘Ω.

 

Figure 3: Resistive circuit with multiple sources

3.2.1 Replace 𝑣!! with a short circuit and calculate the voltages and currents indicated in the circuit. Record your results in column 2 of Table 1 on p. 9. Determine the equivalent resistance “seen” by 𝑣!!. Record this value as 𝑅!"! in column 2 of Table 2 on p. 10.

3.2.2 Replace 𝑣!! with a short circuit and calculate the voltages and currents indicated in the circuit. Record your results in column 3 of Table 1. Determine the equivalent resistance “seen” by 𝑣!!. Record this values as 𝑅!"! in column 2 of Table 2.

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3.2.3 Record the algebraic sum of the voltages and currents in 3.2.1 and 3.2.2 in column 4 of Table 1.

3.2.4 Using the results in column 4 of Table 1, calculate the power supplied by each source and record on p. 9. Clearly state whether a source delivers or absorbs power.

Be sure to attach Prelab calculations to the lab report, in addition to completed tables in Section 6.0.

4.0 APPARATUS AND MATERIALS  

(1) 1 Fluke 8010A Digital Multimeter (DMM) (2) 1 Sun Equipment Powered Breadboard: Model PBB-4060B (3) Standard Resistors: 270Ω, 680Ω, 510Ω, 1.5𝑘Ω (4) Two rechargeable AA batteries and a battery holder (5) Various connecting wires

…continued on next page

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5.0 EXPERIMENT  

5.0 Prelab Signature

5.0.1 Have your Prelab signed by a TA.

 

5.1 Resistance Measurement Using the DMM  

5.1.1 With the DMM set to measure RESISTANCE, measure and record in Table 2 (in Section 6.1), the resistance of each resistor (selected based on the standard value) needed to construct the circuit of Figure 3. Note that the resistance of each resistor must be measured separately. Also, record the standard values.

5.1.2 Construct the circuit of Figure 3 on the breadboard provided. Do not connect the voltage sources to the circuit (that is, leave a-c and b-c as open). Set the DMM to read RESISTANCE.

5.1.3 Place a short circuit between nodes 𝑏 and 𝑐, and connect the DMM to nodes 𝑎 and 𝑐 to measure the equivalent resistance of the resistive circuit as ‘seen’ by voltage source 𝑣!!. Record the value as the measured 𝑅!"! in Table 2.

5.1.4 Remove the short circuit between nodes 𝑏 and 𝑐. Place a short circuit between nodes 𝑎 and 𝑐. Connect the DMM to nodes 𝑏 and 𝑐 to measure the equivalent resistance of the resistive circuit as ‘seen’ by voltage source  𝑣!!. Record the value as the measured 𝑅!"! in Table 2.

5.2 Voltage and Current Measurements Using the DMM 5.2.1 Set the DMM to read dc volts, and adjust the 0 to 16 V voltage source from the  

breadboard to give a +10 V dc reading on the DMM. Record this as 𝑣!! in column 2 of Table 2. Note:  It may not be possible to adjust the source to read exactly +10 V; simply record the closest value that you are able to obtain.

5.2.2 Turn off the power (voltage source) on the breadboard. Connect the breadboard voltage source to the resistive circuit at points 𝑎 (red lead) and 𝑐 (black lead).

DO NOT POWER ON the voltage source.

5.2.3 Place two AA batteries inside the battery holder. DO NOT SHORT CIRCUIT the two terminals of the battery holder. With the DMM set on dc volts, measure and record the total voltage of the battery pack. Record this value as 𝑣!! in column 2 of Table 2.

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5.2.4 Connect the battery pack to the resistive circuit at points 𝑏 (red wire) and 𝑐 (black wire). Now turn on the voltage source.

5.2.5 Recall the voltage measurement technique from the information given in Experiment 1. Measure and record, in column 2 of Table 2, the dc voltages across the resistors in the circuit of Figure 3 with the polarities as specified. Set the DMM on the most appropriate range for these measurements.

5.2.6 Recall the current measurement technique from the information given in Experiment 1. With the DMM set on dc amps, measure the current flowing in each resistor with the directions specified in Figure 3. Recall that the ammeter is connected with the presumption that the current flows into the red lead and out of the black lead. Record the results in column 2 of Table 2.

5.3 Principle of Superposition in Linear Circuits. 5.3.1 Turn off the power supply and remove 𝑣!! from the circuit. Replace it with a short circuit

across terminals 𝑏  and 𝑐. DO NOT SHORT OUT 𝒗𝑺𝟐 DIRECTLY.

5.3.2 Measure the voltage (v2) across resistor 𝑅! in Figure 3 with the polarities as specified and record it as 𝑣!!! in Section 6.2.1.

5.3.3 Turn off the power supply. Remove 𝑣!! from the circuit and replace it with a short circuit across terminals 𝑎 and 𝑐. DO NOT SHORT OUT 𝒗𝑺𝟏 DIRECTLY. Return 𝑣!! to the circuit.

5.3.4 Measure the voltage (v2) across resistor 𝑅! in Figure 3 with the polarities as specified and record it as 𝑣!!! in Section 6.2.1.

NOTE:

1. Before leaving the laboratory, have your experimental results for all sections of the lab, examined and signed by a TA. Also, the Prelab should have been signed at the start of the lab.

2. The lab report should include the cover page (pg. 8) and a fully completed Section 6 (pg. 9 – 14) showing the signature of a TA for both the Prelab and the experimental results. As well, Prelab calculations should be attached to the report.

3. Late submissions (after 9:00 am on Wednesday, Mar. 28) will be penalized and may not be accepted.

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Faculty of Engineering and Applied Science Memorial University of Newfoundland

 

 

 

 

 

 

 

 

ENGINEERING 1040: Electric Circuits Experiment 2 – Analysis and Measurement of Resistive Circuit Parameters

 

 

Report Due In-class on Wed., Mar. 28, 2018

All parts of the lab must be a collaborative effort of both students.

 

 

Name Student ID

Student # 1 Student # 2

 

 

Section  #:  ______________________       Day  of  Lab:  ________________________  

                  (Mon.,  Tue.,  Wed.,  Thu.)  

 

Date  of  Submission:  _______________________________________  

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6.0 OBSERVATIONS AND COMMENTS  

6.0 Prelab Results Summary

6.0.1 Complete the table below with the summary of your Prelab results. Also, be sure to include the calculations (stapled to the back of the lab) showing how the numbers are derived.

Table 1: Results from the analysis of Figure 3.

Variable

Calculated values with 𝑣!!  removed and replaced by a

short circuit

Calculated values with 𝑣!!  removed and replaced by a

short circuit

Calculated values with both 𝑣!! and 𝑣!! in the circuit (sum of column 2

and column 3)

𝑣!(V)

𝑣!(V)

𝑣!(V)

𝑣!(V)

𝑖!(mA)

𝑖!(mA)

𝑖!(mA)

𝑖!(mA)

𝑖!!(mA)

𝑖!!(mA)

6.0.2 Record the power calculations from the Prelab below. Also, be sure to include the

calculations (stapled to the back of the lab) showing how the numbers are derived.

Source 𝑣!!: p1 = ________________________

Power is ____________________ (delivered/absorbed)

Source 𝑣!!: p2 = ________________________

Power is ____________________ (delivered/absorbed)

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6.1 Resistance, Voltage and Current Measurements  

6.1.1 Measurements

Table 2: Measurements of circuit parameters

Variable Calculated/Standard Value* Measured Value

𝑣!(V)

𝑣!(V)

𝑣!(V)

𝑣!(V)

𝑣!!(V)  

𝑣!!(V)  

𝑖!(mA)

𝑖!(mA)

𝑖!(mA)

𝑖!(mA)

𝑖!!(mA)

𝑖!!(mA)

𝑅!(Ω)

𝑅!(Ω)

𝑅!(Ω)

𝑅!(Ω)

𝑅!"!(Ω)

𝑅!"!(Ω)

* Calculated values refer to the values of voltages and currents in column 4 of Table 1. The values of the resistances 𝑅!…𝑅! to be recorded in column 2 refer to the standard values of the resistors.

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6.1.2 Using the measured quantities, calculate the power dissipated by each resistor and the power supplied by each voltage source.

6.1.3 Does 𝑣!! absorb or deliver power? Explain your answer. 6.1.4 Verify that the power delivered by the voltage source 𝑣!! is equal to the total power

absorbed by the rest of the elements in the circuit. 6.1.5 Compare the calculated (or ‘standard’ in case of the resistors) and measured results of the

resistances, currents, voltages and power. Comment on the results.

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6.1.6 From the results for the measured voltages in Table 2 verify that (within expected errors) KVL has been satisfied for

i) closed path 𝑎 − 𝑑 − 𝑐 − 𝑐 − 𝑎,

ii) closed path𝑑 − 𝑏 − 𝑐 − 𝑐 − 𝑑

iii) closed path 𝑎 − 𝑎 − 𝑏 − 𝑏 − 𝑑 − 𝑎

iv) closed path 𝑎 − 𝑎 − 𝑏 − 𝑏 − 𝑐 − 𝑐 − 𝑐 − 𝑎.

6.1.7 Briefly discuss any disparities. 6.1.8 From the results for the measured currents in Table 2, verify that (within expected errors)

KCL has been satisfied for

i) node 𝑎

ii) node 𝑐

iii) node 𝑑

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6.1.9 Briefly discuss any discrepancy.

6.2 Principle of Superposition

6.2.1 Measurements

𝑣!!!   =  ___________________________

𝑣!!! =  ____________________________ 6.2.2 From the measurements recorded in Table 2 and Section 6.2.1, verify the principle of

superposition.

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6.3 Discussion 6.3.1 Discuss any technical difficulties encountered during the lab. 6.3.2 State and comment on the major learning outcomes of the experiment.

Hand in pages 8-14 of lab instructions and attach Prelab calculations.