Chapter 1

Chapter 1Circuit Elements and VariablesFor FunI really excited study electric circuit theoryWhat is Electric Circuit?An electric circuit is an interconnection of electrical elementsExample: Consists of 3 basic elements: battery, lamp, connecting wires.When the wires are connected properly, the circuit is said to be closed and the lamp will light. When the wires are disconnected, the circuit is said to be open.

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Circuit Diagram4

Basic Electric ConceptReview SI unit (International Systems of Unit)Know the definition of basic electrical quantities : charge, current, voltage, power & energyKnow the symbols and definition of the elements of the circuit: passive and active elements & independent and dependent sourcesTo understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohms Law, nodes, branches, loops & Kirchoffs Law

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Review SI Units (1) 6SI: International System of Unit is used by all the major engineering societies and most engineers throughout the world.

Review SI Units(2)7Standardized prefixes to signify powers of 10

Basic Electric ConceptReview SI unit (International Systems of Unit)Know the definition of basic electrical quantities : charge, current, voltage, power & energyKnow the symbols and definition of the elements of the circuit: passive and active elements & independent and dependent sourcesTo understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohms Law, nodes, branches, loops & Kirchoffs Law

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Unit, Symbol and DefinitionQuantityUnitSymbolCharge, QCoulombCCurrent, IAmpereAVoltage, VVoltVPower, PWattWEnergy, WJouleJ9QuantityDefinitionCharge, QElectric charge is a property of the atomic particles possessed by both electrons and protons.Current, ICurrent is the movement of charge in a specified direction.Voltage, VVoltage (or potential difference) is the energy required to move a unit charge through an elementPower, PPower is the time rate of expending or absorbing energy.Energy, WEnergy is the capacity to do workCharge, Q (C)The charge on one electron is called electronic charge and equivalent to Q of e = - 1.602 10-19 C How many electrons in 1 C? 1 C = 1 / 1.602 10-19 = 6.24 x 1018 electrons10Current, I (A)

11 Current = I (A) = Charge TimedQdt

Direct current (DC)Alternating current (AC) 2 common types of current:C/sCurrent is the movement of charge in a specified direction.Voltage, V (v) It is a potential energy difference between two points, a and b 12 Voltage = vab = EnergyChargedWdQ

Voltage (or potential difference) is the energy required to move a unit charge through an element12Power, P (W)13i+vi+vP = +vi P = viabsorbing power supplying power

Power =P = Energy TimedW dtPower is the time rate of expending or absorbing energy.Energy, W (J)14Energy is the capacity to do work, measured in joules (J).

Basic Electric ConceptReview SI unit (International Systems of Unit)Know the definition of basic electrical quantities : charge, current, voltage, power & energyKnow the symbols and definition of the elements of the circuit: passive and active elements & independent and dependent sourcesTo understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohms Law, nodes, branches, loops & Kirchoffs Law

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Active and Passive Elements16Circuit ElementsActive elementscapable of generating electric energyExample : generators, batteries, operational amplifier, voltage and current sources Passive elementsincapable of generating electric energyExample : resistor, inductor, capacitor

Independent Source17Voltage(+/- sign)Current(arrow)

ACDCDependent SourceA dependent source is an active element in which the source quantity is controlled by another voltage or current.

They have four different types: VCVS: Voltage-controlled voltage source CCVS: Current-controlled voltage sourceVCCS: Voltage-controlled current sourceCCCS: Current-controlled current source

18Dependent Source (Diamond shape)19Voltage (+/- sign)Current(arrow)

Example of sources

20Current controlled voltage source, V =10 iIndependent voltage sourceV =20 VCurrent controlled current source, Is =10.2 IBasic Electric ConceptReview SI unit (International Systems of Unit)Know the definition of basic electrical quantities : charge, current, voltage, power & energyKnow the symbols and definition of the elements of the circuit: passive and active elements & independent and dependent sourcesTo understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohms Law, nodes, branches, loops & Kirchoffs Law

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Ohms Law Ohms law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor.

Two extreme possible values of R: R = 0 : short circuit R = : open circuit.

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Short CircuitR = 0 , no voltage difference exists, thus V = 0 V, but current still can flow.23

Open circuitR = , no current flows .Voltage difference can exist, as determined by the circuit

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Conductance & PowerConductance is a measure of the ability of an element to conduct electric currentInverse of resistanceThe units is Siemens (S) or mhos

Power dissipated by resistor:

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Example 1In the circuit, calculate the current I, the conductance G, and the power P.26

Example 2In the circuit, calculate the voltage V, the conductance G, and the power P.

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BranchesA branch represents a single element such as a voltage source or a resistor. In other words, a branch represents any elements which has two terminals.281234Exercise

29Should we consider it as one branch or two branches?NodesA node is the point of connection between two or more branches. A node usually indicated by a dot in a circuit.If a short circuit (no element between dots), the multiple dots constitute as a single nodes.

How many branches connected to node a, b and c?

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LoopsA loop is any closed path in a circuit.

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Relation of branches, nodes and loopsA network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:

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Example 335How many branches, nodes and loops are there?Does it satisfy b = l + n -1?

Kirchhoff LawGustav Robert Kirchhoff (18241887)Models relationship between:circuit element currents (KCL)circuit element voltages (KVL)Introduce two laws:Kirchhoff Current Law (KCL)Kirchhoff Voltage Law (KVL)36

Kirchhoffs Current Laws (KCL)Kirchhoffs current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.37

Kirchhoffs Current Laws (KCL)Convention sign for current entering and leaving node: current entering node = + icurrent leaving node = - iAccording to KCL, for any node:

Without the sign (+Ve or -Ve), the formula of KCL can be written as:Current entering node = current leaving node(What goes in, must comes out)

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N = number of branches connected to the nodesin = nth current entering (+ i) or leaving (- i) the nodeExample of KCL (1)2 options:

Current entering = current leaving

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Current entering node, (+i)Current leaving node, (-i)Node A

Example of KCL (2)Node a

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IT : Leaving node a (-Ve)I1 : Entering node a (+Ve)I2: Leaving node a (-Ve)I3: Entering node a (+Ve)

Kirchhoffs Voltage Laws (KVL)Kirchhoffs voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. 41

Kirchhoffs Voltage Law (KVL)For any circuit loop:

Convention sign for voltage inside loop (clockwise or anticlockwise direction):If the positive terminal of voltage is met first: +VIf the negative terminal of voltage is met first: -V

Without the +/- sign, KVL formula can be written as Sum of voltage drops = sum of voltage rises

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M = number of voltages in the loopvm = mth voltageExample of KVL43

-VVoltage rise+VVoltage drop

-VVoltage rise+VVoltage drop+VVoltage drop44

Example 4Find v1 and v2 using KVL and Ohms Law. 45

Example 5Find v1, v2 and v3 using Ohms Law KCL and KVL.46

Example 6Determine vo and I in the circuit47