ECE 2006Fundamental Laws of CircuitsResistanceConductanceOpen/Short CircuitsCircuit TopologySeries and ParallelTypes of BranchesCounting Branches and NodesKirchhoff’s LawsKCLKVLSeries ResistorsVoltage DivisionResistors in ParallelCurrent DivisionDelta-Wye TransformWye-Delta TransformECE 2006Lecture for Chapter 2S.NorrFundamental Laws of Circuits•Ohm’s Law:–The voltage across a resistor is directly proportional to the current through it.–The constant of proportionality is called ResistanceResistance•The electrical resistance, R, of a material is dependent on its Resistivity, Length and Cross-Section.•Examples: Copper has a Resistivity of 1.7 x 10-8 Ohm-meters. Glass has a Resistivity of about 1012 Ohm-meters.Conductance•Conductance, G, is the inverse of Resistance•It is sometimes easier to consider the Conductance of a material instead of its Resistance. G = 1 / R = I / VOpen/Short Circuits•A circuit element having no resistance is considered to be a Short Circuit (infinite conductance)•A circuit element having infinite resistance is considered an Open Circuit (zero conductance)Circuit Topology•Branch – Part of a circuit containing only one element, such as a resistor or a source.•Node – A point of connection between to or more Branches•Loop – Any closed path contained within the circuit of interestSeries and Parallel•Two (or more) branches are in Series if the share a single node exclusively.–Branches in Series carry identical current•Two (or more) branches are in Parallel if they connect to the same two nodes–Branches in Parallel have identical voltageTypes of Branches•Branches that are a Source of Energy:•Branches that are a Load (Dissipate Energy): ResistorCounting Branches and Nodes•The number of Branches in a circuit is the same as the number of circuit elements•The number of nodes is representative of all places in the circuit where branches connectKirchhoff’s Laws•Based of the Law of Conservation of Charge (conservation of energy): The algebraic sum of charges within a closed system cannot change.•KCL – Kirchhoff’s Current Law: The algebraic sum of currents entering a node (or any closed boundary) is Zero.•KVL – Kirchhoff’s Voltage Law: The algebraic sum of voltages around a Loop (or any closed path) is Zero/KCL•Application of KCL is straightforwardKVL•Use care in assessing each voltage as a drop or rise:Series Resistors•Elements in series each see the same current•Resistors in series add directly:•Rac = Rab + Rbc•Conductances in series add as the inverse of the sum of their inversesVoltage DivisionVR = Vs*Same/SumResistors in Parallel•Elements in parallel are each impressed with the same voltage•Resistors in parallel add as the inverse of the sum of their inverses•Conductances in parallel add directlyCurrent Division•IR = IS*Opp/SumDelta-Wye Transform•Resistors in a delta shaped arrangement can be transformed into the corresponding wye shaped circuit:Rx = Adj*Adj/SumWye-Delta Transform•Resistors in a wye shaped arrangement can be transformed into the corresponding delta shaped circuit: Rx = Sum of Product
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