Chapter 3 Nodal and Mesh Equations - Circuit Theorems

1 Chapter 3 Nodal and mesh Equations - Circuit Theorems3-52 Circuit Analysis I with MATLAB ApplicationsOrchard ExercisesMultiple Choice1. The voltage across the resistor in the Circuit of Figure for Question 12. The current in the Circuit of Figure for Question 22 6 V16 V8 V32 Vnone of the above8 A6 V+ + 2 8 Ai2 A5 A3 A4 Anone of the above+ 2 + 2 2 2 4 V10 ViCircuit Analysis I with MATLAB Applications3-53 Orchard PublicationsExercises3. The node voltages shown in the partial network of Figure are relative to some referencenode which is not shown.

2 The current for Question 34. The value of the current for the Circuit of Figure for Question 4i4 A83 A5 A6 Anone of the above+ 2 + 2 2 8 V4 Vi+ 8 V8 V13 V6 V6 V12 Vi3 A8 A9 A6 Anone of the above+ 6 3 8 A12 V6 3 iChapter 3 Nodal and mesh Equations - Circuit Theorems3-54 Circuit Analysis I with MATLAB ApplicationsOrchard Publications5. The value of the voltage for the Circuit of Figure for Question 56. For the Circuit of Figure , the value of is dimensionless. For that Circuit , no solution is pos-sible if the value of for Question 6v4 V6 V8 V12 Vnone of the above2 A2 2 ++ + vvX2vXkk21 0none of the above2 A4 4 + + vkvCircuit Analysis I with MATLAB Applications3-55 Orchard PublicationsExercises7.

3 For the network of Figure , the Thevenin equivalent resistance to the right of terminalsa and b for Question 78. For the network of Figure , the Thevenin equivalent voltage across terminals a and b for Question 8 RTH12510none of the above2 3 abRTH2 2 2 2 4 VTH3 V 2 V 1 V5 Vnone of the above+ 2 2 A2 V2 abChapter 3 Nodal and mesh Equations - Circuit Theorems3-56 Circuit Analysis I with MATLAB ApplicationsOrchard Publications9. For the network of Figure , the Norton equivalent current source and equivalent parallelresistance across terminals a and b for Question 910.

4 In applying the superposition principle to the Circuit of Figure , the current due to the source acting alone is for Question 10 INRN1 A2 , A25 ,4 ,0 A5 ,none of the above2 A5 ab5 2 Ai4 V8 A1 A4 A2 Anone of the above8 A2 2 4 V+ i2 Circuit Analysis I with MATLAB Applications3-57 Orchard PublicationsExercisesProblems1. Use Nodal analysis to compute the voltage across the 18 A current source in the Circuit of Answer: Figure for Problem 12. Use Nodal analysis to compute the voltage in the Circuit of Figure Answer: Figure for Problem 23. Use Nodal analysis to compute the current through the resistor and the power supplied (orabsorbed) by the dependent source shown in Figure Answers: 4.

5 Use mesh analysis to compute the voltage in Figure Answer: 5. Use mesh analysis to compute the current through the resistor, and the power supplied (orabsorbed) by the dependent source shown in Figure Answers: 6. Use mesh analysis to compute the voltage in Figure Answer: V12 A24 A18 A+ 10 1 4 1 6 1 8 1 4 1 5 1 v18 Av6 V12 A24 A18 A4 6 12 15 + + 36 Vv6 6 w , v36 Vi6 w , v10 VChapter 3 Nodal and mesh Equations - Circuit Theorems3-58 Circuit Analysis I with MATLAB ApplicationsOrchard PublicationsFigure for Problem 3 Figure for Problem 4 Figure for Problem 512 A24 A4 6 12 15 36 V+ + iX5iXi6 18 A12 A240 V36 A4 6 8 12 + + + 120 V24 A4 3 v36 A12 A24 A18 A4 6 12 15 36 V+ + i6 iX5iXCircuit Analysis I with MATLAB Applications3-59 Orchard PublicationsExercisesFigure for Problem 67.

6 Compute the power absorbed by the resistor in the Circuit of Figure using any : Figure for Problem 78. Compute the power absorbed by the resistor in the Circuit of Figure using anymethod. Answer: Figure for Problem 89. In the Circuit of Figure :a. To what value should the load resistor should be adjusted to so that it will absorbmaximum power? Answer: 12 V4 6 12 15 + + + 24 V10 8 v10 iX10iX10 w12 V6 2 + + 24 V10 3 + 36 V20 w12 V2 + 6 A3 20 8 Chapter 3 Nodal and mesh Equations - Circuit Theorems3-60 Circuit Analysis I with MATLAB ApplicationsOrchard Publicationsb.

7 What would then the power absorbed by be? Answer: Figure for Problem 910. Replace the network shown in Figure by its Norton : Figure for Problem 1011. Use the superposition principle to compute the voltage in the Circuit of Figure : Figure for Problem 11 RLOAD135 w12 A18 A4 6 12 15 + 36 =,=iX4 5 15 5iXabv18 V12 A24 A18 A+ 10 1 4 1 6 1 8 1 4 1 5 1 v18 ACircuit Analysis I with MATLAB Applications3-61 Orchard PublicationsExercises12. Use the superposition principle to compute voltage in the Circuit of Figure : Figure for Problem the Circuit of Figure , and are adjustable voltage sources in the range V, and and represent their internal resistances.

8 Table shows the resultsof several measurements. In Measurement 3 the load resistance is adjusted to the same value asMeasurement 1, and in Measurement 4 the load resistance is adjusted to the same value as Mea-surement 2. For Measurements 5 and 6 the load resistance is adjusted to . Make the neces-sary computations to fill-in the blank cells of this : , , , TABLE Table for Problem 13 Measurement Switch Switch (V) (V) (A)1 ClosedOpen 480 162 OpenClosed 036 63 ClosedOpen0 54 OpenClosed 0 425 ClosedClosed15186 ClosedClosed240v6 V12 A24 A18 A4 6 12 15 + + 36 Vv6 vS1vS250V50 RS1RS21 S1S2vS1vS2iLOAD15 V 7 A 11 A24 V Chapter 3 Nodal and mesh Equations - Circuit Theorems3-62 Circuit Analysis I with MATLAB ApplicationsOrchard PublicationsFigure for Problem 1314.

9 Compute the efficiency of the electrical system of Figure Answer: Figure system for Problem 1415. Compute the regulation for the 2st floor load of the electrical system of Figure : Figure for Problem 15+ + + 1 1 + + 1st FloorLoad100 A2nd 80 + + 1st FloorLoad100 A2nd 80 AVSi1i2 Circuit Analysis I with MATLAB Applications3-63 Orchard PublicationsExercises16. Write a set of Nodal Equations and then use MATLAB to compute and for the cir-cuit of Example which is repeated as Figure for : Figure for Problem V , + 12 V+ + 3 3 5 6 10 7 8 RL+ 4 iLOADiX20iXvLOADC hapter 3 Nodal and mesh Equations - Circuit Theorems3-64 Circuit Analysis I with MATLAB ApplicationsOrchard Answers to ExercisesMultiple Choice1.

10 E The current entering Node A is equal to the current leaving that node. Therefore, there is nocurrent through the resistor and the voltage across it is C From the figure below, . Also, and . Then, and . Therefore,.3. A From the figure below we observe that the node voltage at A is relative to the referencenode which is not shown. Therefore, the node voltage at B is relative to thesame reference node. The voltage across the resistor is and the direc-tion of current through the resistor is opposite to that shown since Node B is at a higherpotential than Node C.