# DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE

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1 DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE NAME. Section 1

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4 UNIVERSITY OF LAHORE Department of Computer engineering Linear Circuit Analysis Laboratory Manual 2 Compiled by Engr. Ahmad Bilal Name Section Roll Number Semester INDEX LAB EXPERIMENT DATE GRADE SIGNATURE Experiment 8 Experiment 9 Experiment 10 Experiment11 Experiment 12 Project 4

5 Contents Experiment 8 Kirchhoff s Voltage and Current Law:... 6 OBJECTIVE: To verify experimentally Kirchhoff s Voltage Law To verify experimentally Kirchhoff s Current Law... 6 Material Required:... 6 THEORY:... 6 TASK 1 : Experiment to verify that The algebraic sum of all voltages in a loop must equal zero... 7 TASK 2 : Experiment to verify that The algebraic sum of all currents entering and exiting a node must equal zero... 8 THEORY:... 8 Experiment 9 SUPERPOSITION PRINCIPLE IN DC CIRCUITS OBJECTIVE: To verify superposition principle in DC Circuits Material REQUIRED: THEORY: TASK 1 : Experiment to verify superposition Principal Experiment 10 Thevenin s Theorem OBJECTIVE: To determine by analysis the values VTH (Thevenin voltage) and RTH (Thevenin resistance) in a dc circuit containing a single voltage source Material REQUIRED: THEORY: Experiment 11 Norton Theorem and Theorem of Source Transformation OBJECTIVE: To verify Norton s Theorem and the theory of source transformation Material REQUIRED: THEORY: Experiment # 12 (a) Non-inverting amplifier (b)application Of non-inverting amplifier Experiment 12(b) Charging and Discharging of a Capacitor I C = I C = Project

6 Experiment 8 Kirchhoff s Voltage and Current Law: OBJECTIVE: 1.To verify experimentally Kirchhoff s Voltage Law 2. To verify experimentally Kirchhoff s Current Law Material Required: 1. Resistors, 2. DMM 3. DC power supply. THEORY: 1)KIRCHOFF S VOLTAGE LAW: Explanation: Consider the simple series circuit Fig.. Here we have numbered the points in the circuit for voltage reference. As we are dealing with dc circuits, therefore we should carefully connect the voltmeter while measuring voltage across supply or any of the resistances as shown in fig.5.2, keeping in mind the similarity of polarities of voltage across the element and that of the connected probes of meter. In such case, we will observe that, This principle is known as Kirchhoff's Voltage Law, and it can be stated as such: "The algebraic sum of all voltages in a loop must equal zero" 6

7 TASK 1 : Experiment to verify that The algebraic sum of all voltages in a loop must equal zero a)for KVL: 1. Construct circuit of fig. using the values R1, R2, R3 as shown in the figure 2. Adjust the output of the power supply so that Vs = 12V. Measure and record this voltage in table. also measure and record the voltages V1, V2, V3 and enter the sum in the same table. Table VT V 1 V 2 V 3 Sum (V 1 +V 2 +V 3 ) 7

8 KIRCHHOFF S CURRENT LAW: TASK 2 : Experiment to verify that The algebraic sum of all currents entering and exiting a node must equal zero THEORY: Then, according to Kirchhoff s Current Law: "The algebraic sum of all currents entering and exiting a node must equal zero" Mathematically, we can express this general relationship as such: That is, if we assign a mathematical sign (polarity) to each current, denoting whether they enter (+) or exit (-) a node, we can add them together to arrive at a total of zero, guaranteed. Note: Whether negative or positive denotes current entering or exiting is entirely arbitrary, so long as they are opposite signs for opposite directions and we stay consistent in our notation, KCL will work. PROCEDURE: b)for KCL: 1- Connect the circuit of Fig.5 with Vs =12 V. 2- Measure and record in Table 5 currents IR1, IR2, IR3 and Itotal. 8

9 OBSERVATIONS: Itotal IR1 IR2 IR3 Sum (I R1 +I R2 +I R3 ) 9

10 Experiment 9 SUPERPOSITION PRINCIPLE IN DC CIRCUITS. OBJECTIVE: 1. To verify superposition principle in DC Circuits. Material REQUIRED: 1. DMM, 2. 2 DC Power Supplies, 3. Resistances (1k Ω, 1.8k Ω, 470Ω ). THEORY: The superposition principle states that : The current through or voltage across, any resistive branch of a multisource network is the algebraic sum of the contribution due to each source acting independently. When the effects of one source are considered, the others are replaced by their internal resistances. This principle permits one to analyze circuits without restoring to simultaneous equations. Superposition is effective only for linear circuit relationship. Non-linear effects, such as power, which varies as the square of the current or voltage, cannot be analyzed using this principle. TASK 1 : Experiment to verify superposition Principal 1 - Construct the Network of where R1 = 1 k Ω, R2 = 470 Ω, R3 = 1.8 k Ω.Verify the resistances using DMM. 2 - Using superposition and measured resistance values, calculate the currents indicated in observation table (a), for the network of fig Next to each magnitude include a small arrow to indicate the current direction for each source and for the complete network. 3 - Energize the network of fig and measure the voltages indicated in observation table 10

11 B, calculate current in table (b) using Ohm s Law. Indicate the polarity of the voltages and direction of currents on below figure 11

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13 4 - Construct the network of fig. b. Note that source E 2 has been removed. 5 - Energize the network of fig7. 2 and measure the voltages indicated in table C. Calculate currents using Ohm s Law. 6 - Repeat steps # 4 & 5 for the network of fig.c. Note that E 1 has been removed. 7 - Using the results of steps # 3, 5 and 6, determine the power delivered to each resistor and insert in table (e). OBSERVATIONS: Resistors: Nominal Values (Ω) 1 1 KΩ 2 470Ω KΩ Measured Values (Ω) a) Calculated Values for the Network of Fig:1 Due to E 1 Due to E 2 Algebraic Sum I 1 = V 1 = I 1 = V 1 = I 1 = I 1 + I 1 = V 1 = V 1 + V 1 = I 2 = V 2 = I 2 = V 2 = I 2 = I 2 + I 2 = V 1 = V 1 + V 1 = I 3 = V 3 = I 3 = V 3 = I 3 = I 3 + I 3 = V 1 = V 1 + V 1 = b) Measured Values for the Network of Fig: 1 V 1 = V 2 = V 3 = I 1 = I 2 = I 3 = c) Measured Values for the Network of Fig:2 V 1 = V 2 = V 3 = I 1 = 13

14 I 2 = I 3 = d) Measured Values for the Network of Fig. 3 V 1 = V 2 = V 3 = I 1 = I 2 = I 3 = e) Power Absorbed ( use measured values of I and V) Sum of Columns E1 & E2 Acting Difference of Due to E 1 Due to E 2 1 & 2 Simultaneously Columns 3 & 4 14

15 OBJECTIVE: Experiment 10 Thevenin s Theorem To determine by analysis the values VTH (Thevenin voltage) and RTH (Thevenin resistance) in a dc circuit containing a single voltage source Material REQUIRED: 1. DMM, 2. 2 DC Power Supplies, 3. Resistances 47,220,330, 1K THEORY: Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. Thevenin's Theorem is especially useful in analyzing power systems and other circuits where one particular resistor in the circuit (called the "load" resistor) is subject to change, and recalculation of the circuit is necessary with each trial value of load resistance, to determine voltage across it and current through it. Thevenin's Theorem makes this easy by temporarily removing the load resistance from the original circuit and reducing what's left to an equivalent circuit composed of a single voltage source and series resistance. The load resistance can then be re-connected to this "Thevenin equivalent circuit" and calculations carried out as if the whole network were nothing but a simple series circuit..before Thevenin 15

16 After Thevenin conversion The "Thevenin Equivalent Circuit" is the electrical equivalent of B 1, R 1, R 3, and B 2 as seen from the two points where our load resistor (R 2 ) connects. The Thevenin equivalent circuit, if correctly derived, will behave exactly the same as the original circuit formed by B 1, R 1, R 3, and B 2. In other words, the load resistor (R 2 ) voltage and current should be exactly the same for the same value of load resistance in the two circuits. The load resistor R 2 cannot "tell the difference" between the original network of B 1, R 1, R 3, and B 2, and the Thevenin equivalent circuit of E Thevenin, and RThevenin, provided that the values for EThevenin and RThevenin have been calculated correctly. PROCEDURE: 1. Connect the circuit as 2. Remove the R L from the circuit across which the Thevinin equivalents have to be evaluated. 3. To find the R TH remove the voltage-source from the circuit and short circuit the terminals from which the supply was connected. Now place an ohmmeter across the terminals A and B. 4. Also confirm the value of the equivalent resistance from calculations and record it in the table. 5. To find the value of V TH place a voltmeter across the terminals A and B after retaining the voltage source in the circuit back. 6. Also confirm the value of the equivalent voltage from calculations and record it in the table. 7. Now construct the thevenin equivalent circuit and measure V AB and I L. Also calculate the se values by using methods other than thevenin theorem 16

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18 OBSERVATIONS: TABLE (a): Resistors S:No: Nominal Value( ) Measured Value( ) 1 R 1 =47 2 R 2 =330 3 R 3 = R L =220 TABLE (b): Thevenin s Theorem RL VTH (volts) RTH (ohms) I L (A) VAB (V) Measured Computed Measured Computed Measured Computed Measured Computed 18

19 OBJECTIVE: Experiment 11 Norton Theorem and Theorem of Source Transformation To verify Norton s Theorem and the theory of source transformation. Material REQUIRED: 1. DC power supply 2. Ohmmeter 3. DC ammeter 4. DC voltmeter 5. Resistances of values 47, , 1K THEORY: Norton's theorem states that any two terminal network may be replaced by a simple equivalent circuit consisting of a constant current source IN, shunted by an internal resistance RN, Figure 9-1a shows the original network as a block terminated by a load resistance RL. Figure 9-lb shows the Norton equivalent circuit. The Norton current IN is distributed between the shunt resistance RN and the load RL. The current IL in RL may be found from the equation IL = IN RN R N +R L The rules for determining the constants in the Norton equivalent circuit are as follows: 1. The constant current I N is the current that would flow in the short circuit between the load resistance terminals if the load resistance were replaced by a short circuit. 2. The Norton resistance R N is the resistance seen from the terminals of the open load, looking into the original network, when the voltage sources in the circuit are replaced by their internal resistance. Thus R N is defined in exactly the same manner as is R TH in Thevenin s theorem. The theory of source conversion says that the Norton and Thevenine circuits can be terminally equivalent and related as follows: 19

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22 PROCEDURE: (a) NORTON S THEOREM: 1. Connect the circuit as shown in figure 2 2. Remove the R L from the circuit across which Norton equivalents have to be found out. 3. For R N or R TH of the circuit, remove the voltage source and short circuit the open terminals. Now place an ohm meter across A and B. 4. Verify your observation, by calculating the R TH. 5. For I N, retain the source back into the circuit and place an ammeter connecting the terminals A and B. 6. The value of the current is the short circuit current i.e. I N. 7. Also compute the value of the Norton s equivalent current and record it in the table. 7. Now construct the Norton s equivalent circuit and measure the IL and VAB. (That is vary the supply voltage until DMM indicates the value IN )Also calculate the value of IL and VAB by using methods other than Norton s theorem. (b) Source Transformation: 1. Construct the Norton s equivalent circuit (That is vary the supply voltage until DMM indicates the value I N ). 2. Measure the supply voltage. Construct the thevinine equivalent circuit (d) from previous exp. 3. Measure V AB and I L. 4. Are these values the same as obtained in part (a)? 22

23 OBSERVATIONS: TABLE (a): Resistors S:No: Nominal Value(Ω) 1 R 1 = 2 R 2 = 3 R 3 = 4 R L = Measured Value(Ω) TABLE (b): Norton s Theorem IN (A) R N (Ω) I L (A) VAB (V) R L Ω Measured Computed Measured Computed Measured Computed Measured Computed 23

24 Experiment # 12 (a) Non-inverting amplifier Objective: To understand the behavior of opamp in the case of using non inverting pins.. Theory: The input signal is applied to the non-inverting (+) input. The output is applied back to the inverting (-) input through the feedback circuit (closed loop) formed by the input resistor R1 and the feedback resistor Rf. This creates ve feedback as follows. Resistors R1 and Rf form a voltage-divider circuit, which reduces VO and connects the reduced voltage Vf to the inverting input. The feedback is expressed as The difference of the input voltage, Vin and the feedback voltage, Vf is the differential input of the opamp. This differential voltage is amplified by the gain of the op-amp and produces an output voltage expressed as Circuit diagram: 24

25 Calculations: V IN (v) V OUT (v) 25

26 (b)application Of non-inverting amplifier Objective: To understand the application of non-inverting amplifier. Apparatus: 741 IC 10uf Potentiometer Red & green Led Resistors 10kohm, 330kohm Supply (9v) Theory: It is the simple circuit of non-inverting opamp. We apply the 9v across the 741 IC. The data sheet of the IC is given bellow. The pin 2 is connected with capacitor and then grounded it means that when the capacitor charge then red led is glow and when the capacitor is discharge then blue led is glow. We want to find out the charge and discharge voltage across the led. Circuit diagram: 26

27 Calculations: V in V Led1 V led2 27

28 Experiment 12(b) Charging and Discharging of a Capacitor Objective: The objective of this experiment is to verify the exponential behavior of capacitors during charging and discharging processes. Apparatus: A capacitor, a resistance box, 2 multi-meters, connecting wires, a watch, a dc power source, and a 2-way switch Theory: A capacitor is a passive electric device that stores electric energy. A parallel-plates capacitor is made of two parallel metallic surfaces, each of area A, separated by an insulation layer of thickness d, and it has a capacity of where C is the capacity in Farads, A the area of each plate in m 2, d the insulation (dielectric) thickness in (m), and ε o the permittivity of free space (vacuum) for electric field propagation expressed in F/m that reads Farads/meter. The factor, κ, pronounced "kappa" denotes the dielectric constant, and depends on the material of the insulation layer. The capacitance C does not depend on the material of the plates. The dielectric constant ε o is related to Coulomb's constant k by In Fig, at t = 0, the capacitor is uncharged. As soon as the key in the circuit is closed, electrons flow from the negative pole of the battery toward the lower plate of the capacitor. They distribute over the lower plate, making it negative. At the same time, the repelled free electrons of the upper plate flow toward the positive pole of the battery. This causes the upper plate to 28

29 become positively charged. This process does not happen suddenly. It takes some time. The current is greatest to begin with, and decreases as charges accumulate on the plates. At the beginning the capacitor is empty; therefore, the voltage across it is zero, but as more and more charges build up on its plates, its voltage keeps increasing. The voltage across the capacitor V C asymptotically approaches the battery voltage V Bat. During the charging and discharging processes, the voltage across the capacitor and the current through it follow the following exponential equations: (Charging) Battery in Circuit At t = 0, V C = 0 I C = V B / R As t V C = V Bat. I C = 0 (Discharging) With battery removed, the initial capacitor voltage is V o = Q o /C making the initial current I o = V o /R At t = 0, V C = Q o /C I C = Q o /(RC) As t V C = 0 I C = 0 It is a good idea to examine the values in the third and fourth columns by once setting t = 0 and once t in the appropriate equations. Note that the charge-voltage formula for a capacitor is Q = CV. These exponential variations will be observed in this experiment. 29

30 Procedure: Arrange a circuit as shown: If a computer is used to directly graph V C and I C versus time via an electronic interface, there is no need for using large capacitance C and a large resistance R in order to have a large value for the time constant τ = RC. If voltage, current, and time are measured by three different group members, then use of large capacitance and resistance is recommended in order to have a large value for τ so that relatively accurate measurements (readings) can be made. The two-way switch shown is first put in position 1 to start the charging process. In this case, the group member who keeps track of time must also close the circuit at the same time he/she starts the stop watch. He/she must also announce the time at equal intervals. When he/she announces the time, two other group members read the current and voltage values. A good value for τ is 20s, and intervals of 10s will give each experimenter enough time to read and record a value, and concentrate on the occurrence of the next value. Obtaining 10 to 15 points for each of current and voltage is sufficient. The data may be exchanged between the experimenters afterwards. Do not disconnect the circuit. This is because while preparation is underway for the discharging part of the experiment, the capacitor voltage keeps increasing asymptotically toward the battery voltage. When all members are ready for the second part of the experiment (the discharging of the capacitor), the timekeeper must be ready to announce the starting time and at the same time put the two-way switch in position 2 as shown in Fig below: Graphs: 30

31 Graph the following: For charging: V C versus t and I C versus t, and for discharging: V C versus t and I C versus t. of I C (t) for the charging process: If ln(i C ) is graphed versus t, obtained. To understand why, let us consider the equation a straight line will be Data: Given: V B = the battery voltage (to be read at the start of charging) V oc = the initial capacitor voltage (to be read at the start of discharging) Let R = 20kΩ and C = 1,000 μf such that τ = 20s. Use other values if suggested by your instructor. Measured: Capacitor Charging: Note: I C at t = 0 is Known. I C = V B /R. t (sec) V C (volts) 0 I C (Amps) V B /R Capacitor Discharging: 31

32 Note: I C at t = 0 is Known. I C = V oc /R. t (sec) V C (volts) V oc I C (Amps) V oc /R Calculations: For the charging part: I o = V B /R. For the discharging part I o = V oc /R. Conclusion: 32

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