LAB-CKRTS PDF - Thevenin's Theorem & Superposition Experiment

# Experiment No. 7 ## Thevenin's Theorem ### Objectives The activity aims to: 1. Construct a Thevenin equivalent circuit. 2. Determine the Thevenin's voltage and resistance condition experimentally. ### Discussion This theorem says that any circuit with a voltage source and a network of resistors...

# Experiment No. 7 ## Thevenin's Theorem ### Objectives The activity aims to: 1. Construct a Thevenin equivalent circuit. 2. Determine the Thevenin's voltage and resistance condition experimentally. ### Discussion This theorem says that any circuit with a voltage source and a network of resistors can be transformed into one with a voltage source and one resistor. Any two-port linear network may be replaced by a single voltage source with adequate internal resistance, according to Thevenin's Theorem for DC circuits. The original circuit's load current and voltage will be produced by the Thevenin equivalent for any load. Therefore, rather than "reinventing the wheel" each time, utilizing a Thevenin equivalent is proven to be a quicker analysis approach when taking into account a variety of different loads or sub-circuits. ### Materials - 24V DC Supply - 6.8k Ω Resistor - 1 kΩ Resistor - 10k Ω Resistor - 2.2 k Ω Resistor - DMM - 3.3 k Ω Resistor - DC Voltmeter - 4.7 k Ω Resistor - DC Ammeter - 5k Ω Resistor - Connecting Wires ### Procedures 1. Construct the given circuit in Figure 5.77. Set the value of the DC source by 24V. Set R1, R2, and R3 to 1000, 1.5kΩ, and 900Ω respectively. Set the R4 as the load resistance (Use 1k as the initial value of RL). 2. To connect the circuit, first connect the red terminal of the 24V DC source to the red terminal of R1. Connect the black terminal of R1 and the red terminal of R3 and R2 to the red terminal of common terminal 1. Connect the black terminal of R2 to the red terminal of RL. Lastly, connect the black terminal of the 24V DC source, R3 and R1 to the black terminal of common terminal 1. 3. Remove the load resistor and connect a voltmeter to read the open circuit voltage between A and B. To do this, remove the connection between the black terminal of R2 and the red terminal of RL, and between the black terminal of RL and the common terminal. This is VTH for this circuit between A and B. 4. Remove the 24V source. Replace it with a short circuit. To do this, remove the connection between the red terminal of the DC source and the red terminal of R1, as well as the connection between the black terminal of the DC source to the common terminal. Connect the red terminal of the R1 to the black terminal of common terminal 1. Connect a DMM between A and B. Record the value of the resistance (RTH in Figure 5.78) 5. Connect the equivalent Thevenin circuit; set R1 as RTH and R2 as RL. Set the measured value of VTH. 6. To create the circuit, first set the adjustable DC source supply to the value of VTH. Then connect the red terminal of the DC source to the red terminal of RTH. Connect the black terminal of the RTH to the red terminal of the RL. Lastly, connect the RL's black terminal to the DC source's black terminal. 7. Vary R1 between 1kΩ to 10kΩ. Measure the voltage between A and B VL in each case. To measure the voltage, connect the red terminal of the voltmeter to the red terminal of RL. Then, connect the black terminal of the voltmeter to the black terminal of the RL. Enter the results in the table below. 8. Also build and simulate the circuit in Multisim. Using the virtual DMM, determine the voltage and current across each component. Using the results, compare these to the theoretical and measured values recorded. Compute the % difference between the measured and calculated values. ### Data and Results | | VTH | RTH | |:-------- |:----------- |:---------- | | Measured | | | | Simulated | | | | Computed | | | | % Difference | | | ### Analysis 1. Compare the measured values obtained with the theoretical values obtained through manual computations. Comment on the accuracy of the methods. 2. What will happen to the value of V1 if you increase/decrease the value of RL? 3. How would the Thevenin equivalent computations change if the original circuit contained more than one voltage source? # Experiment No. 9 ## Superposition ### Objectives The activity aims: 1. To verify experimentally the Superposition theorem. 2. To give detailed instructions on how to use superposition when calculating voltages and currents in a circuit with two or more power sources. 3. To compare theoretical and experimental values. The Superposition Method must be used to compute the theoretical values. ### Discussion When two or more sources are present and connected, the network can be solved using the superposition theorem, a circuit analysis theorem. This theorem states that "in any linear and bilateral network or circuit having multiple independent sources, the response of an element will be equal to the algebraic sum of the responses of that element by considering one source at a time," and that "the other source may be replaced or removed without affecting the result." This is done by utilizing a short circuit instead of the voltage source. While removing a voltage source, its value is set to zero. When removing a current source, its value is set to infinite. This is done by replacing the current source with an open circuit. Because it reduces a complex circuit into a Norton or Thevenin equivalent circuit, the superposition theorem is particularly essential in circuit analysis. In applying the superposition principle, we must keep in mind the following things: 1. Circuit must contain only independent sources. 2. Consider only one source active at a time. 3. Remove all other ideal voltage sources by the circuit and all other ideal current sources by an open circuit. 4. Voltage source is replaced by a short circuit. 5. Current source is replaced by an open circuit. ### Materials - 15V DC Supply - 500 Ω Resistor - 1k ΚΩ Resistor - 5 ΚΩ Resistor - Voltmeter - Ammeter - Connecting Wires ### Procedures 1. Connect the circuit as shown in figure 5.84 below. 2. To begin, connect the red terminal of the 20 VDC source to the red terminal of the 5ΚΩ. Connect the black terminal of 5k and 1kΩ and the red terminal of 5000 to the red terminal of common terminal 1. Then, connect the red terminal of 1kΩ to the red terminal of 15 VDC source. Lastly, connect the black terminal of the 20 VDC source, 15 VDC source and the black terminal of the DC source and 5000 to the black terminal of common terminal 1. 3. Check the connection and then begin to turn on the main switch. To find the current, identify the points in the circuit where you want to measure current. Connect the ammeter in series with the circuit. Record the measured current. After that, turn off the power supply and return to the original connection. 4. Next, find the current flowing through each resistor by considering only the 5V voltage source. Remove the connection of the current source to the 2.2k and the black terminal of the common terminal 1, hence, the modified circuit diagram is shown in the following figure. Identify the points in the circuit where you want to measure current. Connect the ammeter in series with the circuit. Record the measured current. After that, turn off the power supply and return to the original connection. 5. Then, find the current flowing through each resistor by considering only the current source. Remove the connection of the 20 V voltage source to the red terminal of 5k and common terminal. Identify the points in the circuit where you want to measure current. Connect the ammeter in series with the circuit. Record the measured current. After that, turn off the power supply and return to the original connection. 6. Also build and simulate the circuit in Multisim. Using the virtual DMM, determine the current across each component. Using the results, compare these to the theoretical and measured values recorded. Compute the % difference between the measured and calculated values. ### Data and Results | | Measured Current (Only 20 V is connected) | % Difference | | Measured Current (Only 15 V is connected) | % Difference | |:------------ |:-------------------------------------------- |:-------------- |:------------ |:-------------------------------------------- |:-------------- | | R1 | Computed | | R1 | Computed | | | | Measured | | | Measured | | | | Simulated | | | Simulated | | | R2 | Computed | | R2 | Computed | | | | Measured | | | Measured | | | | Simulated | | | Simulated | | | R3 | Computed | | R3 | Computed | | | | Measured | | | Measured | | | | Simulated | | | Simulated | | ### Analysis 1. Compare the measured values obtained with the theoretical values obtained through manual computations. Comment on the accuracy of the methods. 2. Based on the data above, compare the algebraic summation of currents flowing through resistors when one source is connected to the current measured when both sources are connected in a circuit. 3. By doing this experiment, do you think, is the superposition theorem applicable to power? # CircuitDesign 1. Create a design with the given components present in the trainer. Make sure that the design can undergo a superposition method. The design must comply with the following: two power supply units and set of resistors. And must have ready equipment like Voltmeter, Ammeter for measuring the values. After creating the design of the circuit, apply the superposition theorem. The first step is to turn-off all sources except one by replacing a short-circuit for voltage sources and an open-circuit for current sources. Apply any convenient analysis method to solve for the currents and/or voltages with that one source acting alone. Repeat the process until all sources in the original circuit have been used. The actual current and/or voltage for any one resistor will be the algebraic sum of the currents and/or voltages found on each case for that particular resistor. Calculate theoretically using superposition theorem the voltage across each resistor and record your results. Compare between the practical and theoretical results. Note: Simulate the circuit first using Multisim. Remember not to exceed the power rating of the resistor. The power across the resistors should not exceed ½ watts. ### Problems 1. By using the superposition theorem, find I in the circuit shown in the figure below. 2. Using Superposition theorem, find the current through a link that is to be connected between terminals a-b. Assume the link resistance to be zero. 3. Find io and i from the circuit of figure below using Superposition Theorem.