Chapter4AllinEnglish学习教案

1、会计学1Chapter4AllinEnglish第一页，共23页。2022-6-252第1页/共23页第二页，共23页。2022-6-253第2页/共23页第三页，共23页。4.1 Element LawsThe elements in the electrical circuit are resistors, capacitors, inductors and sources.Passive elementsResistorCapacitorInductorBecause: cant introduce additional energySourceActive elementBecause

2、: can introduce energy into the circuit and serve as the inputMechanical systemDashpotMassSpringForceDisplacementElectrical system第3页/共23页第四页，共23页。4.1.1 ResistorA resistor is an element for which there is an algebraic relationship between the voltage across its terminals and the current through it-t

3、hat is, an element that can be described by a curve of UR versus i.A linear resistor is one for which the voltage and current are directly proportional to each other-that is, one described by Ohms law:RURi (4.1)1RiUR where R is the resistance in Ohms ()(4.2)Figure 4.2 A resistor and its variables.20

4、22-6-255第4页/共23页第五页，共23页。4.1.2 CapacitorA capacitor is an element that obeys an algebraic relationship between the voltage and the charge, where the charge is the integral of the current. For a linear capacitor, the current and voltage are related by,1CUidtC (4.3)Figure 4.3 A capacitor and its varia

5、bles.where C is the capacitance in Farads (F).CCtqCUidtCU 2022-6-256第5页/共23页第六页，共23页。4.1.3 InductorAn inductor is an element for which there is an algebraic relationship between the voltage across its terminals and the derivative of the flux linkageFor a fixed linear inductor, the current and voltag

6、e are related by,(4.5)LdiULdt where L is the inductance with units of Henries (H).Figure 4.4 An inductor and its variables.2022-6-257第6页/共23页第七页，共23页。2022-6-258RURi 1CUidtC LdiULdt 第7页/共23页第八页，共23页。2022-6-259第8页/共23页第九页，共23页。2022-6-2510第9页/共23页第十页，共23页。4.2 Interconnection LawsTwo interconnection law

7、s are used in conjunction with the appropriate element laws in modeling electrical circuits. These laws are known as Kirchhoffs Voltage Law and Kirchhoffs Current Law:(1) The algebraic sum of voltages around a closed-loop equals zero.(2)The algebraic sum of currents flowing into a circuit node equal

8、s zero.2022-6-2511第10页/共23页第十一页，共23页。4.2.1 Kirchhoffs Voltage LawWhen a closed path- that is, a loop - is traced through any part of a circuit, the algebraic sum of the voltages across the elements that make up the loop must equal zero.0jjU (4.7)around any loopwhere Uj denotes the voltage across the

9、 jth element in the loop.It follows that summing the voltages across individual elements in any two different paths from one point to another will give the same result.2022-6-2512第11页/共23页第十二页，共23页。Figure 4.5 Partial circuits to illustrate Kirchhoffs voltage law.Summing the voltages around the loop,

10、 going in a counterclockwise direction, and taking into account the polarities indicated on the diagram give,12340UUUUReversing the direction in which the loop is traversed yields,34120UUUULikewise, going from point B to point A by each of the two paths shown gives,1234UUUUwhich is equivalent to bot

11、h of the foregoing loop equations.2022-6-2513第12页/共23页第十三页，共23页。4.2.2 Kirchhoffs Current Law(4.8)When the terminals of two or more circuit elements are connected together, the common junction is referred to as a node.All the joined terminals are at the same voltage and can be considered part of the

12、node.The algebraic sum of the currents at any node must be zero at all times.0jji at any nodewhere the summation is over the currents through all elements joined to the node.a plus sign: a current arrow directed away from the node.a minus sign: a current arrow directed toward the node.Figure 4.6 Par

13、tial circuits to illustrate Kirchhoffs current law.Applying (4.8) at the node to which the three elements of the figure 4.5 are connected gives,1230iii2022-6-2514第13页/共23页第十四页，共23页。4.2.3 The Nodal Method of Electrical Network AnalysisIn the nodal method of electrical network analysis, one node in th

14、e network is usually chosen as the reference node and voltages between the reference node and other node are defined.The rules for writing the integro-differential equations for each node are summarized as follows:(1) The number of equations required equals the number of unknown node voltages.(2) On

15、e equation is written for each node.2022-6-2515第14页/共23页第十五页，共23页。Procedure to establish differential equation of a physical system is listed as follows:1.Analyze the principle of the practical system, make clear the relationships among all the parameters and the variables of the system, definite th

16、e system input and output variables.2.Start from the system input to express the dynamic equations of all the components in terms of the special physical laws.3.Eliminate the intermediate variables so as to derive the differential equation that describes the relationship between the system input and

17、 output.4.Normalize the differential equation. That is, to move all terms related to the input (output) to the right-hand (left-hand) side of the differential equation and arranged in descendent or ascendent order.2022-6-2516第15页/共23页第十六页，共23页。4.3 ExamplesApply Kirchhoffs law and Ohms law to write a

18、 modeling differential equation for the system shown in Figure 4.8. And ui (t) and uo (t) are the input voltage and output voltage, respectively. R1, R2 and C are the constants for every element of this system.EXAMPLE 4.1Figure 4.8 A circuit system.2022-6-2517第16页/共23页第十七页，共23页。SOLUTIONAccording to

19、the Kirchhoffs law and Ohms law, together with nodal method of electrical network analysis, we can get,)()()(21tititi 1 1o( )( )( )iu tRi tu t )()(1112tiRdttiC )()(2otiRtu Eliminating the variable i1(t), i2(t), i (t) yields the differential equation,)()()()(tudttduCRtuRRRdttduCRiioo 12211ABCAbout A

20、B to A to C B to A A to C 2022-6-2518第17页/共23页第十八页，共23页。Apply Kirchhoffs law and Ohms law to write a modeling equation for the system shown in Figure 4.9. ui (t) and uo (t) are the input voltage and output voltage, respectively. R1, R2, L and C are the constants for every element of this system.EXAM

21、PLE 4.2Figure 4.9 A circuit system.2022-6-2519第18页/共23页第十九页，共23页。SOLUTIONAccording to the Kirchhoffs law and Ohms law, together with nodal method of electrical network analysis, we can get,Eliminating the variable i1(t), i2(t), i 3(t) yields the differential equation,321iii dtiCRiui311122231RidtdiLdtiC 220Riu )()()()()()(22121221tuRtuRRdttduLCRRdttudLCRiooo ACBDEA to B to C “B to C” = “B to D to E ”About B D to E 2022-6-2520第19页/共23页第二十页，共23页。2022-6-2521第20页/共23页第二十一页，共23页。4.4 Analogue relation among different systemsp Dynamic characteristics