1. Do the polarities of the sources in Figure 14.1 matter as to the resultingvol
ID: 2268775 • Letter: 1
Question
1. Do the polarities of the sources in Figure 14.1 matter as to the resultingvoltages? Will the magnitudes of the voltages be the same if one or both sources have an inverted polarity?2. In both circuits of this exercise the negative terminals of the sources are connected to ground. Is this a requirement for nodal analysis? What would happen to the node voltages if the positions of E1 and R1 in Figure 14.1 were swapped?
3. If mesh analysis was applied to the circuit of Figure 14.2, how many unknown currents would have to be analyzed and how many equations would be needed? How does this compare to nodal analysis?
4. The circuits of Figures 14.1 and 14.2 had been analyzed previously in the Superposition Theorem and Mesh Analysis exercises. How do the results of this exercise compare to the earlier results? Should the resulting currents and voltages be identical? If not, what sort of things might affect the outcome?
5. In general, compare and contrast the application of Superposition, Mesh and Nodal Analyses to multi- source DC circuits. What are the advantages and disadvantages of each? Are some circuits better approached with a particular technique? Will each technique enable any particular current or voltage to be found or are there limitations? 1. Do the polarities of the sources in Figure 14.1 matter as to the resultingvoltages? Will the magnitudes of the voltages be the same if one or both sources have an inverted polarity?
2. In both circuits of this exercise the negative terminals of the sources are connected to ground. Is this a requirement for nodal analysis? What would happen to the node voltages if the positions of E1 and R1 in Figure 14.1 were swapped?
3. If mesh analysis was applied to the circuit of Figure 14.2, how many unknown currents would have to be analyzed and how many equations would be needed? How does this compare to nodal analysis?
4. The circuits of Figures 14.1 and 14.2 had been analyzed previously in the Superposition Theorem and Mesh Analysis exercises. How do the results of this exercise compare to the earlier results? Should the resulting currents and voltages be identical? If not, what sort of things might affect the outcome?
5. In general, compare and contrast the application of Superposition, Mesh and Nodal Analyses to multi- source DC circuits. What are the advantages and disadvantages of each? Are some circuits better approached with a particular technique? Will each technique enable any particular current or voltage to be found or are there limitations? R1 R2 R3 E2 Figure 14.1 R4 R1 R2 R3 R5 Figure 14.2
Explanation / Answer
Answer1: Polarities of the voltage sources will definately attect the resulting voltages. No, magnitude will not be same as the polairity changes the current direction will change and hence the voltage.
Answer2: for nodal analysis one has to take any one of the node as a reference so in ideal practice, the negative terminal is kept as a reference node. if the position of E1 and R1 are swaped then the node voltage at A is E1 and the voltage across R1 will be E1(E1-0), where as in original position the voltage across R1 was Va - E1 (Va means voltage at node A).
Answer3: If mesh analysis is applied to this circuit there will be 3 currents in 3 loops and hence 3 Equations are required. Where as if you go for the Node analysis only 2 node equation are need to solve. nodal analysis is easy in this case compare to the mess analysis.
Answer4: results for the currents and node voltages are remain same irrespective of the method used for analysis the circuit. some times the polarity may be different for voltage and currents but the magnitude remains same.
Answer5: Superposition theorm is applied for the multi-source circuits but it is not prefered always, it may be time consuming for many of the cases. Also sometimes the simple mess analysis will solve the purpose. Superposition is not applicable for the non-linear networks. and the circuits where the total power is need to be calculated for perticular element there super position is avoided.
Mesh analysis is prefered to find the currents in the each loops. in a circuit if they are asked for the current through perticular element then mesh analysis is prefered. in many of the cases where there are more loops then the nodes then one should avoid the mesh analysis as it will increase the complexity as number of unknown is more in case of mesh analysis.
Nodal analysis is prefered incase of finding voltage at each node given in circuits.problems inwhich voltage is need to be calculated across any element then the nodal analysis is good. also some of the case like 14.2 where the number of nodes are less then the loop currents then one should go for nodal analysis. but in an example where currents are need to calculated the node analysis is bit lengthy process.
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