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Chapter 5: Circuit Theorems Chapter 5 Circuit Theorems ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.1-1 Design problem involving a strain gauge bridge. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.2-1 Dynamo Room at the Pearl Street Station. This was Edison’s first central station for incandescent electric lighting. It began operation in New York City in 1882. Courtesy of General Electric Company. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.2-2 Baker electric car, 1910. Courtesy of Motor Vehicle Manufacturers Assoc. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.2-3 Bay Area Rapid Transit (BART) railway. Photograph copyright © by Ron May. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.2-4 Skyline of New York City at night. Photograph copyright © by Ron May. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.2-5 Chapter 5: Circuit Theorems Original tinfoil phonograph patented by Edison in 1877. Courtesy of Science Museum, London. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-1 Two equivalent circuits. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-2 (a) Voltage source with an external resistor R. (b) Current source with an external resistance R. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-3 Method of source transformations. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-4 The circuits of Example 5.3-1. All resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-5 The circuit of Example 5.3-2. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.3-6 Source transformation steps for Example 5.3-2. All resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.3-1 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.3-2 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.3-3 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.3-4 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.4-1 (a) A circuit containing two independent sources. (b) The circuit after the ideal ammeter has been replaced by the equivalent short circuit and a label has been added to indicate the current measured by the ammeter, im. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.4-2 (a) Circuit of Example 5.4-1 with the current source set equal to zero. (b) Circuit of Example 5.4-1 with the voltage source set equal to zero. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.4-1 (a) A circuit containing two independent sources. (b) The circuit after the ideal voltmeter has been replaced by the equivalent open circuit and a label has been added to indicate the voltage measured by the voltmeter, vm. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure E 5.4-2 Chapter 5: Circuit Theorems (a) A circuit containing two independent sources. (b) The circuit after the ideal ammeter has been replaced by the equivalent short circuit and a label has been added to indicate the current measured by the ammeter, im. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.4-3 (a) A circuit containing two independent sources. (b) The circuit after the ideal voltmeter has been replaced by the equivalent open circuit and a label has been added to indicate the voltage measured by the voltmeter, vm. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.4-3 Circuit for Example 5.4-2. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.4-4 Circuit with (a) the voltage source activated and the current source deactivated and (b) the current source activated and the voltage source deactivated. All resistances are in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-1 Hermann von Helmholtz (1821–1894), who is often credited with the basic work leading to Thévenin’s theorem. Courtesy of the New York Public Library. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-2 (a) Circuit and (b) a Thévenin circuit connected to a load resistor. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-3 Summary of Thévenin circuit approach. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-4 Circuit for Example 5.5-1. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.5-5 Chapter 5: Circuit Theorems Steps for determining the Thévenin equivalent circuit for the circuit left of the terminals of Figure 5.5-4. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-6 Circuit for Example 5.5-2. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-7 Circuit of Figure 5.5-6 with all the sources deactivated. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-8 Thévenin equivalent circuit for the circuit of Figure 5.5-6. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-9 Thévenin circuit with a short circuit at terminals a–b. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-10 Circuit of Example 5.5-3. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-11 Circuit of Figure 5.5-10 with output terminals a–b short-circuited. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-12 Circuit for Example 5.5-4. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-13 Circuit of Figure 5.5-12 with terminals a–b short-circuited. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-14 A circuit for which we seek its Thévenin equivalent. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-15 Circuit of Figure 5.5-14 with a 1-A source connected at terminals a–b. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-16 Thévenin equivalent circuit for the circuit of Figure 5.5-14. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.5-17 (a) Circuit under test with laboratory source vs, and resistor R. (b) Circuit of (a) with Thévenin equivalent circuit replacing test circuit. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.5-1 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.5-2 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.5-3 Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-1 Norton equivalent circuit for a linear circuit A. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-2 Circuit of Example 5.6-1. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-3 Short circuit connected to output terminals. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-4 Circuit of Example 5.6-2. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-5 Short circuit connected to terminals a–b of the circuit of Figure 5.6-5. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.6-6 Chapter 5: Circuit Theorems Circuit of Figure 5.6-5 with its sources deactivated. The voltage source becomes a short circuit, and the current source is replaced by an open circuit. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-7 Norton equivalent of the circuit of Figure 5.6-5. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-8 The circuit of Example 5.6-3. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-9 Circuit of Figure 5.6-8 with a short circuit at the terminals a–b. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.6-10 The Norton equivalent circuit for Example 5.6-3. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.6-1 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.6-2 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.6-3 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.7-1 Circuit A contains resistors and independent and dependent sources. The load is the resistor RL. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.7-2 The Thévenin equivalent is substituted for circuit A. Here we use vs for the Thévenin source voltage. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.7-3 Chapter 5: Circuit Theorems Power actually attained as RL varies in relation to Rt. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.7-4 Norton’s equivalent circuit representing the source circuit and a load resistor RL. Here we use is as the Norton source current. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.7-5 Circuit for Example 5.7-1. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.7-6 Thévenin equivalent circuit connected to RL for Example 5.7-1. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.7-7 Chapter 5: Circuit Theorems Determination of maximum power transfer to a load RL. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.7-1 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.7-2 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.7-3 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure E 5.7-4 ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.8-1 Chapter 5: Circuit Theorems A two-mesh circuit with a dependent source and a variable input source V1. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-2 The PSpice program for the circuit of Figure 5.8-1. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-3 Output for the PSpice program of Figure 5.8-2. The currents in R1 and R3 are provided for V1 equal to 10 V and 12 V. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-4 A circuit with an input source vs. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-5 The circuit of Example 5.5-3. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-6 The circuit of Figure 5.8-5 redrawn for PSpice. Resistances in ohms. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.8-7 Chapter 5: Circuit Theorems The PSpice program for Example 5.5-3. The dummy source VM1 generates the control current. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.8-8 Output of PSpice program for Example 5.5-3. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.9-1 The circuit in (b) is obtained by connecting a resistor, R, across the terminals of the circuit in (a). ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.9-2 MATLAB file used to solve the mesh equation representing the circuit shown in Figure 5.9-1b. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.9-3 Computer screen showing the use of MATLAB to analyze the circuit shown in Figure 5.9-1. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.9-4 The circuit obtained by connecting a resistor, R, across the terminals of a Thévenin equivalent circuit. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.9-5 MATLAB file used to calculate the opencircuit voltage and Thévenin resistance. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.10-1 Chapter 5: Circuit Theorems (a) A circuit with data obtained by measuring the voltage across the resistor R and (b) the circuit obtained by replacing the part of the circuit connected to R by its Thévenin equivalent circuit. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.11-1 Design problem involving a strain gauge bridge. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Figure 5.11-2 Chapter 5: Circuit Theorems Calculating (a) the open-circuit voltage and (b) the Thévenin resistance of the strain gauge bridge. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed Chapter 5: Circuit Theorems Figure 5.11-3 Solution to the design problem. ©2001, John Wiley & Sons, Inc. Introduction To Electric Circuits, 5th Ed