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UNIT-1- DC Circuits & AC Circuits Dr.Y.Rajendra Babu Professor in EEE department Sreenidhi University
Resistance(R) Def: Resistance is the opposition to the flow of electric current through a conductor. It determines how much current will flow in response to a given voltage. Unit: Ohm (Ω): Formula:Resistance 𝑅is calculated using Ohm's Law:𝑅=V/𝐼
Ohm’sLaw Example .1 An electriciron boxdraws2Aat 120V.Finditsresistance. Solution: FromOhm’slaw,
Ohm’sLaw Example -2
Ohm’sLaw Avoltagesourceof20sinπt Visconnectedacrossa 5-kΩresistor.Findthe currentthroughtheresistorandthepowerdissipated. Solution:
CircuitElements • WeclassifycircuitelementsasPassiveandActive. • Passiveelementscannotgenerateenergy.Commonexamples ofpassive elements areresistors,capacitorsandinductors.Wewillseelaterthat capacitorsandinductorscan storeenergybutcannotgenerateenergy. • Active elements can generate energy.Common examples of active elements arepowersupplies,batteries,operationalamplifiers.
CircuitElements • The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them. There are two kindsofsources:IndependentandDependentsources.
CircuitElements Therearefourpossibletypesofdependentsources,namely: Avoltage-controlledvoltagesource(VCVS). Acurrent-controlledvoltagesource(CCVS). Avoltage-controlledcurrentsource (VCCS). Acurrent-controlledcurrentsource (CCCS).
CircuitElements Acurrent-controlledvoltagesource(CCVS). Avoltage-controlledvoltagesource(VCVS).
CircuitElements voltage-controlledcurrentsource (VCCS). current-controlledcurrentsource (CCCS).
UNILATERAL & BILATERAL ELEMENTS Unilateral Elements
LINEAR & NON LINEAR ELEMENTS Linear Elements:
LINEAR & NON LINEAR ELEMENTS Non-Linear Elements:
Electric Circuit • AsimpleelectriccircuitisshowninFig below,Itconsistsofthreebasic elements:a battery, a lamp,andconnectingwires. • Analysisofthecircuits–Describingthebehaviorofthecircuit • How does itrespondtoagiveninput? • Howdo theinterconnectedelementsanddevicesinthecircuitinteract? Asimple electric circuit.
Nodes, Branches,andLoops In other words, a branch represents any two-terminal element. The circuit in Fig. has five branches, namely, the 10-V voltage source, the 2-A current source,andthethreeresistors. FigureNodes,branches,andloops.
Nodes, Branches,andLoops A node is usually indicated by a dot in a circuit. If a short circuit (a connecting wire) connects two nodes, the two nodes constitute a single node. The circuit in Fig.hasthreenodesa,b,andc. FigureNodes,branches,andloops.
Nodes, Branches,andLoops Thecircuitin Fig.ahas onlythreenodesby redrawing the circuit in Fig.b. The 2circuits are identical. Nodes b and c are spread out with perfectconductorsasin Fig.a. Figurea Nodes,branches,andloops. Figureb The three-nodecircuit of Fig. 2.10isredrawn.
Nodes, Branches,andLoops • A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node morethanonce. • A loop is said to be independent if it contains at least one branch which is not a part of any other independent loop. Independent loops or paths result in independentsetsofequations. • Anetworkwithbbranches,nnodes,andlindependentloopswillsatisfy thefundamentaltheoremofnetworktopology:
Nodes, Branches,andLoops DeterminethenumberofbranchesandnodesinthecircuitshowninFig.a.Identifywhichelements are in seriesandwhichareinparallel. • Solution: • Since there are four elements in the circuit, the circuit has four branches: 10 V,5 Ω, 6 Ω,and2A. • The circuit has three nodes as identified in Fig.b. • The 5-Ω resistor is in series with the 10-V voltagesourcebecause thesamecurrent wouldflowin both. • The 6-Ω resistor is in parallel with the 2-A currentsourcebecause both areconnected tothesamenodes2and3. Figurea Figureb
Kirchhoff’sLaws -KCL Mathematically,KCLimpliesthat whereNisthenumberofbranchesconnectedtothenodeandinisthenthcurrententering(orleaving)thenode. Consider the Node in Fig. applyingKCL Gives since currents i1,i3 and i4 are entering the node, while currents i2 and i5 are leaving it. Figure Currents at a node illustratingKCL.
Kirchhoff’sLaws -KCL consider the node in fig. Applying KCL gives since currents i1,i3 and i4 are entering the node while currents i2 and i5 are leaving it. Figure Currents at a node illustrating KCL.
Kirchhoff’sLaws -KCL Fig.(a)can be combinedas in Fig.8(b). FigureCurrentsources inparallel:(a)originalcircuit,(b)equivalentcircuit.
Kirchhoff’sLaws -KCL ExampleDetermine thecurrentI for the circuitshowninthefigure below. 63
Kirchhoff’s Laws -KVL FigureA single-loop circuit illustrating KVL.
Kirchhoff’s Laws -KVL Forexample,forthevoltagesourcesshowninFig.(a),thecombined orequivalentvoltagesourcein Fig.(b)is obtainedbyapplyingKVL. FigureVoltagesourcesinseries: originalcircuit, equivalentcircuit.
When resistors are connected in series, the total resistance of the circuit increases with the addition of each resistor. • For m resistors connected in series, the voltage drop across each resistor can be expressed as follows. • Applying KVL circuit • V𝑠=VR1+VR2+……VRm • IRs=IR1+IR2+…+IRm • Rs=R1+R2+......+Rm SERIES CONNECTION
When resistors are connected in parallel, the total resistance of the circuit decreases as the number of resistors increases. • For a configuration with m parallel branches, the current flowing through each branch can be described by the following equation. IT=I1+I2+ …….. +Im • Thesamevoltageisappliedacrosseachresistor.ByapplyingOhm’slaw,thecurrentineachbranchisgivenby PARALLEL CONNECTION
Applying KCL (Kirchoff’s Current Law), We have • From the above equation, We can have PARALLEL CONNECTION
Example 5.1: Given the circuit below. Find Req. Circuit for Example 5.1.
. Figure : Reduction steps for Example 5.1. Ans:
Example 5.2: Given the circuit shown below. Find Req. Figure: Diagram for Example 5.2.
Example 5.2: Continued. Reduction steps.
Example 5.2: Continued. 10 resistor shorted out Req Reduction steps.
