ENGR 2405 Class No Electric Circuits I

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1 ENGR 2405 Class No Electric Circuits I Dr. R. Williams Ph.D.

2 Electric Circuit An electric circuit is an interconnec9on of electrical elements

3 Charge Charge is an electrical property of the atomic and subatomic par9cles of which ma?er consists. The charge on an electron is nega9ve and has the magnitude of x C

4 CHARGE Points to be note about charge: 1. 1 C of charge accounts for 6.24 X electrons (i.e. 1 C / x C/electron) 2. The only (full) charges that occur in nature are integral mul9ples of the electron charge. 3. The Law of Conserva9on of Charge states that charges cannot be created or destroyed, only transferred. Laboratory measurements of charge are typically concerned with µc, pc, etc. Par9al charges in chemistry are superposi9ons of full charges The sum of electric charges in a system is constant

5 Electric Current Electric current is the flow of electronic charge in a conductor. Posi9ve charges move in one direc9on and nega9ve charges move in the opposite direc9on. We know that the charge carriers in metals are electrons, and that their charge is nega9ve, However, it is historical conven9on to define current flow as the movement of posi9ve charges.

6 Electric Current Current, i, is measured as charge moved per unit time through an element. Unit is Ampere (A), one Coulomb/second i dq dt Andre-Marie Ampere

7 Direct Current / Alternating A current that remains constant with time is called Direct Current (DC), represented by the capital I. Current Time varying current uses the lowercase, i. A current that varies sinusoidally with time is called Alternating Current (AC)

8 Direction of Current A positive current through a component is the same as a negative current flowing in the opposite direction. 8

9 Voltage It is equal to the energy needed to move a unit charge between the locations. Positive charge moving from a higher potential to a lower yields energy. Moving from negative to positive requires energy.

10 Power and Energy Voltage alone does not equal power. It requires the movement of charge, i.e. a current. Power is the product of voltage and current, measured in Watts (W) p = vi It is equal to the rate of energy provided or consumed per unit time. 10

11 Passive Sign Convention By convention, we say that an element being supplied power has positive power. A power source, such as a battery has negative power. Passive sign convention is satisfied if the direction of current is selected such that current enters through the terminal that is more positively biased. 11

12 Conservation of Energy In a circuit, energy cannot be created or destroyed. Thus power also must be conserved The sum of all power supplied must be absorbed by the other elements. Energy can be described as watts x time. Power companies usually measure energy in watthours Σp = 0 12

13 Two types: Active Passive Active elements can generate energy Generators Batteries Operational Amplifiers Circuit Elements 13

14 Circuit Elements Passives absorb energy Resistors Capacitors Inductors But it should be noted that only the resistor dissipates energy ideally. The inductor and capacitor do not. 14

15 Ideal Voltage Source An ideal voltage source has no internal resistance. It also is capable of producing any amount of current needed to establish the desired voltage at its terminals. Thus we can know the voltage at its terminals, but we don t know in advance the current. 15

16 Ideal Current Source Current sources are the opposite of the voltage source: They have infinite resistance They will generate any voltage to establish the desired current through them. We can know the current through them in advance, but not the voltage. 16

17 Ideal sources Both the voltage and current source ideally can generate infinite power. They are also capable of absorbing power from the circuit. It is important to remember that these sources do have limits in reality: Voltage sources have an upper current limit. Current sources have an upper voltage limit. 17

18 Dependent Sources A dependent source has its output controlled by an input value. Symbolically represented as a diamond Four types: A voltage-controlled voltage source (VCVS). A current-controlled voltage source (CCVS). A voltage-controlled current source (VCCS). A current-controlled current source (CCCS). 18

19 Dependent Source example The circuit shown below is an example of using a dependent source. The source on the right is controlled by the current passing through element C. 19

20 CHAPTER 2 BASIC LAWS

21 Resistivity Materials tend to resist the flow of electricity through them. This property is called resistance The resistance of an object is a function of its length, l, and cross sectional area, A, and the material s resistivity: R = ρ l A 21

22 Resistivity of Common Materials 22

23 Ohm s Law In a resistor, the voltage across a resistor is directly proportional to the current flowing through it. The resistance of an element is measured in units of Ohms, Ω, (V/A) V = IR The higher the resistance, the less current will flow through for a given voltage. 23

24 Short and Open Circuits A connection with almost zero resistance is called a short circuit. Ideally, any current may flow through the short. In practice this is a connecting wire. A connection with infinite resistance is called an open circuit. Here no matter the voltage, no current flows. 24

25 Linearity Not all materials obey Ohm s Law. Resistors that do are called linear resistors because their current voltage relationship is always linearly proportional. Diodes and light bulbs are examples of nonlinear elements 25

26 Power Dissipation Running current through a resistor dissipates power. 2 2 v p= vi= i R= R The power dissipated is a non-linear function of current or voltage Power dissipated is always positive A resistor can never generate power 26

27 Conductance A concept that is often convenient is Conductance, G, defined to be the reciprocal of resistance with units of mhos or siemens (S). G = 1 / R = i / v (mhos) 27

28 Nodes Branches and Loops Circuit elements can be interconnected in multiple ways. To understand this, we need to be familiar with some network topology concepts. A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches. A loop is any closed path in a circuit. 28

29 Nodes Branches and Loops

30 Network Topology A loop is independent if it contains at least one branch not shared by any other independent loops. Two or more elements are in series if they share a single node and thus carry the same current Two or more elements are in parallel if they are connected to the same two nodes and thus have the same voltage.

31 Kirchoff s Laws Ohm s law is not sufficient for circuit analysis Kirchoff s laws complete the needed tools There are two laws: Current law Voltage law 31

32 KCL Kirchoff s current law is based on conservation of charge It states that the algebraic sum of currents entering a node (or a closed boundary) is zero. It can be expressed as: N n= 1 i n = 0 32

33 KVL Kirchoff s voltage law is based on conservation of energy It states that the algebraic sum of voltages around a closed path (or loop) is zero. It can be expressed as: M m= 1 v m = 0 33

34 Series Resistors Two resistors are considered in series if the same current pass through them Take the circuit shown: Applying Ohm s law to both resistors v = ir v = ir If we apply KVL to the loop we have: v+ v1+ v2 = 0 34

35 Series Resistors Combining the two equations: v= v + v = i R + R ( ) From this we can see there is an equivalent resistance of the two resistors: R = R + R eq 1 2 For N resistors in series: R eq N = R n= 1 n 35

36 Voltage Division The voltage drop across any one resistor can be known. The current through all the resistors is the same, so using Ohm s law: R R v = v v = v R1+ R2 R1+ R2 This is the principle of voltage division 36

37 Parallel Resistors When resistors are in parallel, the voltage drop across them is the same v= ir 1 1 = i2r2 By KCL, the current at node a is i= i + i 1 2 The equivalent resistance is: R eq = RR 1 2 R + R

38 Current Division Given the current entering the node, the voltage drop across the equivalent resistance will be the same as that for the individual resistors v = ir = eq ir1r 2 R + R 1 2 This can be used in combination with Ohm s law to get the current through each resistor: i ir = i = ir R1+ R2 R1+ R2 38

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