Thevenin and Norton Theorem report, Lab Reports of Electrical Circuit Analysis

Download Thevenin and Norton Theorem report and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! Name: CHARDI MBAYO SHAHIYA Date performed: 30 December 2021 Student number:219009910 Date submitted: 11 January 2021 Group A Electrical circuit and Electronics ECE602S EXPERIMENT 1 and 2 Title: THEVENIN THEOREM AND NORTON THEOREM 1.1 Aim: To use the Thevenin’s and Norton’s theorems to find the current flowing in a resistor (variable load) in a network and also to verify the theorems by comparing the calculated values to those obtained by measurement. 2.1 Introduction: Thevenin’s Theorem: Thevenin’s theorem greatly simplifies analysis of complex circuits by allowing us to replace all of the elements with a combination of just one voltage source and one resistor. “A complex two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistor RTH.” In the new circuit: VTH is the open circuit voltage at the terminals. The Voltage between A and B. RTH is the input or equivalent resistance at the terminals when the sources are turned off. The equivalent resistance between A and B. Norton’s theorem: Norton’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN where IN is the short-circuit current through the terminals and RN is the input or equivalent resistance at the terminals when the independent sources are turned off. Figure 1: Linear resistor network 3.1 Apparatus • Adjustable DC power supply • Digital Multimeters = 5.61 KΩ % Error between measured and calculated RTh %Error= 100%| 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑙𝑢𝑒− 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 | = 100%| 5610− 5570 5610 | = 0.71% RThevenin Calculated 2 using Ohm’s Law and Rload RTh= voltage across rTh 𝐼𝑇ℎ = 𝑉𝑜𝑐−𝑉𝐿 𝑉𝐿 𝑅𝐿 ⁄ RTh= 9.1−4.6 4.6 4700⁄ =4597.83 Ω fav = ( 5610+4597.83 2 ) =5103.9 Ω %Diff= 100%| 𝑓− 𝑓𝑜𝑡ℎ𝑒𝑟 𝑓𝑎𝑣 | = 100%| 5610− 5346.25 5103.9 | =5.2% Vab Calculated Vab= VTh I1=I2 10−𝑉𝑇ℎ 1 = 𝑉𝑇ℎ−0 10 100-10𝑉𝑇ℎ =𝑉𝑇ℎ -11𝑉𝑇ℎ=-100 𝑉𝑇ℎ =9.09 V % Error Thévenin voltage measured and calculated %Error= 100%| 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑙𝑢𝑒− 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 | = 100%| 9.1− 8.5 9.1 | = 6.59% Norton’s theorem: Measured values Theoretical values Norton’s Resistance Norton’s current current in RL Norton’s resistance Norton’s current current in RL 5010 Ω 0.08 A 0.19 A 5610 Ω 1.62x10-3 A 0.882x10-3 A RN = ( 1 𝑅1 + 1 𝑅3 )-1 + R2 = ( 1 1 + 1 10 )-1 + 4.7 = 5.61 KΩ 10−𝑉𝑇ℎ 1 = 𝑉𝑇ℎ−0 10 100-10𝑉𝑇ℎ =𝑉𝑇ℎ -11𝑉𝑇ℎ=-100 𝑉𝑇ℎ =9.09 V IN= 𝑉𝑇ℎ 𝑅𝑁 = 9.09 5610 =1.62x10-3 A IL = IN ( 𝑅𝑁 𝑅𝑁+𝑅𝐿 ) =1.62x10-3 ( 5610 5610+4700 ) = 8.82x10-4 A %Error= 100%| 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑙𝑢𝑒− 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 | = 100%| 5610− 5010 5610 | =10.70% 5.1 Conclusion In these experiments, the Thevenin and Norton theorem were studied through calculations and experimentations. The experimental results were in close agreement with the theory only for some measurements. Thus, the experiment demonstrated the validity of both theorems. The percentage error remained below 2% between the measured and calculated Thevenin resistance. The things that we still concern is the difficulty in measuring the voltage and the current with the material provided. Thus, we noticed a percentage error above 2%.For the Thevenin's Theorem there were quite a huge error of percentage. It might be because of an inaccurate of the equipment. So, we got a percentage error of Vth equal to 6.59%. However, for Rth there was an error of 0.71%. For the Norton's Theorem in this experiment, we used the same equipment as for the previous experiments (same order and resistances) and also find some of the values in term of Norton’s Theorem because the rest of the values can transfer from Thevenin’s Theorem values. For the Thevenin's Theorem there were quite a huge error of percentage. It might be because of an inaccurate of the equipment. So, we got a percentage error of Rth equal to 10.70% 6.1 Post-lab questions 1. yes, the aim of the test has been achieved. 2. The experimental results were in close agreement with the theory. thus the experiment demonstrated the validity of validity of both theorems. 3.yes, This is because it provides a technique by which the input or output impedance of a complex circuit, where many components are connected together can be estimated. Usually, the application of the theorem is done visually, without doing explicit calculations if the circuit is relatively simple. But in some cases, some back-of-the-envelope calculations may be needed. 4. No, because Norton's theorem is converse of Thevenin's theorem in the respect that Norton's theorem uses a current source, whereas Thevenin's theorem uses a voltage source. Thevenin's theorem uses a resistor in series, while Norton's theorem uses a resister set in parallel with the source. Thus, in practice the Norton's equivalent circuit and Thevenin's equivalent circuit can be easily interchanged. 5. Both theorems are most applicable in case of changing a complex circuit into a simple equivalent circuit consisting of a single resistance in series with a source voltage 6.yes, because the only reasons when these theorems cannot be valid is if the circuit consists of nonlinear elements, Also to the unilateral networks. There should not be magnetic coupling between the load and circuit to be replaced with the Thevenin’s equivalent. There should not be controlled sources on the load side which care controlled from some other parts of the network. 7. yes, when there are only dependent sources, obviously VTH = 0 and IN = 0, but notice that RTh can be found by adding a source to the circuit.