1 Chapter 3 Resistive Circuits

2 Figure The circuit being designed provides an adjustable voltage, v, to the load circuit. Figure (a) A proposed circuit for producing the variable voltage v (b) the equivalent circuit after the potentiometer is modeled Adjustable Voltage Source

3 Kirchhoff ’ s Law Figure (a) An electric circuit. (b) The same circuit, redrawn using straight lines and horizontal and vertical elements. (c) The circuit after labeling the nodes and elements. Example Figure Four circuit drawings.

4 Kirchhoff ’ s Law Kirchhoff ’ s Current Law (KCL) The algebraic sum of the currents into a node at any instant is zero Kirchhoff ’ s Voltage Law (KVL) The algebraic sum of the voltages around any loop in a circuit is identically zero for all time

5 Example Kirchhoff ’ s Law Figure (a) The circuit considered in Example and (b) the circuit redrawn to emphasize the nodes. Example Figure Circuit with two constant- voltage sources.

6 Figure (a)Circuit with dependent source and an ammeter (b)Equivalent circuit after replacing the ammeter by a short circuit Example Figure The circuit of Figure after labeling the nodes and some element currents and voltages. Kirchhoff ’ s Law

7 Figure (a)Circuit with dependent source and a voltmeter (b)Equivalent circuit after replacing the voltmeter by a open circuit. Figure The circuit of Figure b after labeling the nodes and some element currents and voltages. Example Kirchhoff ’ s Law

8 Exercise 3.3-1Exercise Exercise Kirchhoff ’ s Law Exercise 3.3-3

9 Figure Single loop circuit with a voltage source v s. - KCL - KVL A Single Loop Circuit – Voltage Divider

10 Figure Voltage divider circuit with R 1 =9Ω Figure Equivalent circuit for a series connection of resistors. Example A Single Loop Circuit – Voltage Divider

11 Figure (a) A circuit containing series resistors (b) The circuit after the ideal ammeter has been replaced by the equivalent short circuit and a label has been added to indicate the current measured by the ammeter, i m. Example A Single Loop Circuit – Voltage Divider

12 Exercise Exercise Exercise Exercise A Single Loop Circuit – Voltage Divider

13 Figure A circuit with a current wource. Figure Parallel circuit with a current source. Figure Equivalent circuit for a parallel circuit. Parallel Resistors and Current Division

14 Figure Set of N parallel conductances with a current source i s. Parallel Resistors and Current Division

15 Example Example Figure (a) A circuit containing parallel resistors (b) The circuit after the ideal voltmeter has been replaced by the equivalent open circuit and a label has been added to indicated the voltage measured by the voltmeter, vm. (c) The circuit after the parallel resistors have been replaced by an equivalent resistance. Parallel Resistors and Current Division

16 Parallel Resistors and Current Division Exercise Exercise Figure E3.5-2 (a) A current divider. (b) The current divider 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.

17 Figure (a) A circuit containing voltage sources connected in series (b) an equivalent circuit. Serious Voltage Source and Parallel Current Source Figure (a) A circuit containing parallel current sources (b) an equivalent circuit.

18 Table Parallel and Series Voltage and Current Sources. Serious Voltage Source and Parallel Current Source

19 Figure Circuit with a set of series resistors and a set of parallel resistors. Figure Equivalent circuit of Figure Circuit Analysis

20 Figure (a) Circuit for Example (b) Partially reduced circuit. Figure Equivalent circuit. Example Circuit Analysis

21 Example Figure Circuit Analysis

22 Figure The equivalent resistance looking into terminals c-d is denoted as R eqc-d. Circuit Analysis

23 Exercise Exercise Exercise Circuit Analysis

24 Figure (a) A resistive circuit and (b) an equivalent circuit. Circuit Analysis using MATLAB Figure Plot of I versus V s for the circuit shown in Figure

25 Figure (a) An example circuit and (b) computer analysis using Mathcad. Circuit Analysis using Mathcad

26 Figure The circuit being designed provides an adjustable voltage, v, to the load circuit. Adjustable Voltage Source Figure The circuit after setting R 1 =R 2 =R. Figure (a) A proposed circuit for producing the variable voltage, v, and (b) the equivalent circuit after the potentiometer is modeled.

27 Table Equivalent Circuits for Series and Parallel Elements. Equivalent Circuits

28 Problems 3.3 – 2, 4, 7, – 2, 4, – 2, 4, – 2, 4, 6, 10, 14 Homework #2