ETEC Chapter 2 Circuit Elements

Transcription

1 ETEC 3501 Chapter 2 Circuit Elements

2 Introduction Five basic circuit elements are: voltage sources, current sources, resistors, inductors, and capacitors. Voltage sources, current sources, and resistors will be discussed in this chapter. Electrical safety warning signs state Danger High Voltage. Not only is there a hazard associated with the voltage but with the current as well. The voltage of a system is normally held constant and is easier to measure than current. The hazards of current and an electrical model of the human body is reviewed at the end of the chapter.

3 2.1 Voltage and Current Sources Ideal voltage source an element that maintains a prescribed voltage across its terminals regardless of the current flow through those terminals. Ideal current source an element that maintains a prescribed current through its terminals regardless of the voltage across those terminals. Independent source a voltage or current source whose output does not rely on current or voltage elsewhere in the circuit. The symbols for independent voltage and current sources are shown in Figure 2.1.

4 Figure 2.1 The circuit symbols for (a) an ideal independent voltage source and (b) an ideal independent current source. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Copyright 2011, 2008, 2005 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

5 Dependent source a voltage or current source whose output depends on current or voltage elsewhere in the circuit. Both the dependent current source and the dependent voltage source may be controlled by either voltage or current elsewhere in the circuit. Therefore, there are a total of four variations of the dependent sources. The symbols for each of the dependent are shown in Figure 2.2. Note that the controlling current or voltage has a x subscript, i.e. v x or i x.

6 Figure 2.2 The circuit symbols for (a) an ideal dependent voltage-controlled voltage source, (b) an ideal dependent current-controlled voltage source, (c) an ideal dependent voltage-controlled current source, and (d) an ideal dependent current-controlled current source. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Copyright 2011, 2008, 2005 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

7 Note that is a multiplying constant that is dimensionless. Note that has the dimension of volts per ampere. Note that has the dimension of amperes per volt. Note that is a multiplying constant that is dimensionless. Ideal sources are examples of active circuit elements a device capable of generating electric energy. Resistors, capacitors, and inductors are examples of passive circuit elements a device that cannot generate electric energy.

8 Example 2.1 Testing Interconnections of Ideal Sources Using the definitions of the ideal independent voltage and current sources, state which of the circuits in Figure 2.3 are valid and which are invalid.

9 Example 2.2 Testing Interconnections of Ideal independent and Dependent Sources Using the definitions of the ideal independent dependent sources, state which of the circuits in Figure 2.3 are valid and which are invalid.

10 Assessment Problems

11 2.2 Electrical Resistance Resistance the capacity of a material to impede the flow of electrical current. Figure 2.5 shows the circuit symbol for the resistor, with R denoting resistance value of the resistor. Movement of electrons in the resistive material generates some amount of heat. Sometimes desirable sometimes not. Resistance is dependent on the type of material and the geometry of the resistor.

12 Voltage and current notation used in this text are shown in Figure 2.6. The relationship between resistance, current, and voltage (Ohm s law) is given in Equation 2.1

13 Conductance the reciprocal of resistance, represented by the letter G and the units of siemens (S) The older units of conductance was mho Power calculations for the resistor are as follows: Also, So, And, And for G,

14 Example 2.3 Calculating Voltage, Current, and Power for a Simple Resistive Circuit

15 2.3 Construction of a Circuit Model Review section 2.3 for homework.

16 2.4 Kirchhoff s Laws Kirchhoff s current law The algebraic sum of all currents at any node in a circuit equals zero. Example 2.6 Using Kirchhoff s Current Law

17 Kirchhoff s voltage law The algebraic sum of all voltages around a closed path in a circuit equals zero. Example 2.7 Using Kirchhoff s Voltage Law

18 Example 2.8 Applying Ohm s Law and Kirchhoff s Laws to Find an Unknown Current Writing the KCL equation for node b yields: Writing the KVL equation for the left-side loop yields: Solving the two equations for i o and i 1 yields:

19 Example 2.8 Cont.

20 Assessment Problems

21 2.5 Analysis of a Circuit Containing Dependent Sources Analyze a circuit that contains a dependent sources (Figure 2.22). There are two unknown values in the circuit: Using KVL to write the first equation yields: Using KCL to write the second equation yields: Solving the equations yields: and

22 Example 2.10 Applying Ohm s Law and Kirchhoff s Laws to Find an Unknown Voltage Writing two KVL equations yield: Solving the two KVL equations yield: and Total power delivered equals total power consumed (21.7 W each)

23 Assessment Problems

24 Figure 2.25 (a) A human body with a voltage difference between one arm and one leg. (b) A simplified model of the human body with a voltage difference between one arm and one leg. Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Copyright 2011, 2008, 2005 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

25 Electric Circuits, Ninth Edition James W. Nilsson Susan A. Riedel Copyright 2011, 2008, 2005 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.