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. 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.

2 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. 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.

3 For the network of Figure , the Norton equivalent current source and equivalent parallelresistance across terminals a and b for Question 910. 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.

4 Use Nodal analysis to compute the current through the resistor and the power supplied (orabsorbed) by the dependent source shown in Figure Answers: 4. 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.

5 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. What would then the power absorbed by be? Answer: Figure for Problem 910.

6 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. 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.

7 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. Compute the efficiency of the electrical system of Figure Answer: Figure system for Problem 1415.

8 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. E The current entering Node A is equal to the current leaving that node.

9 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. Thus 2 8 A6 V+ + 2 8 AA8 A8 AVAC4 V=VABVBC2 V==VAD10 V=VBDVADVAB 102 8 V===VCDVBDVBC 82 6 V===i62 3 A==+ 2 + 2 2 2 4 V10 ViABCD6 V612+18 V=VBC18 6 12 V==3 i123 4 A ==+ 3 + 2 2 8 V4 Vi+ 8 V8 V13 V6 V6 V12 VABCC ircuit Analysis I with MATLAB Applications3-65 Orchard PublicationsAnswers to Exercises4.

10 E We assign node voltages at Nodes A and B as shown Node Aand at Node BThese simplify to andMultiplication of the last equation by 2 and addition with the first yields and E Application of KCL at Node A of the Circuit below yieldsorAlso by KVL+ 6 3 8 A12 V6 3 iABVA12 6------------------VA6------VAVB 3-------------------++0=VBVA 3-------------------VB3------+8=23---VA1 3---VB 2=13--- VA23---VB+8=VB18=i183 6 A ==2 A2 2 ++ + vvX2vXAv2---v2vX 2-----------------+2=vvX 2= Chapter 3 Nodal and mesh Equations - Circuit Theorems3-66 Circuit Analysis I with MATLAB ApplicationsOrchard Publicationsand by substitutionorand thus6. A Application of KCL at Node A of the Circuit below yieldsorand this relation is meaningless if.