Series/Parallel Combination CircuitsSeries and Parallel ElementsEquivalent ResistanceSeries and Parallel EquivalentsSeries and Parallel SourcesExamplesSlide 7Single Loop Circuits with Dependent SourcesSingle Node-Pair Circuits with Dependent SourcesKevin D. Donohue, University of Kentucky1Series/Parallel Combination CircuitsSeries and Parallel Elements, Simplification, and Problem Solving Strategies.Kevin D. Donohue, University of Kentucky2Series and Parallel ElementsTwo elements are connected in series if and only if they have a common node to which no other elements are attached.Two elements are connected in parallel if and only if they have common nodes at both terminals. R1R2R3Is R1R2 R3VsKevin D. Donohue, University of Kentucky3Equivalent ResistanceSeries and parallel resistors can be combined into one element with an equivalent resistance.Equivalent resistance refers to a single resistance replacing a multiple resistor subcircuit such that it draws the same current and produces the same voltage drop. Apply Ohm’s law to derived formula for finding equivalent resistance.Kevin D. Donohue, University of Kentucky4Series and Parallel Equivalents R1R2RNReqRN ReqR1R2NeqRRRR  21NeqRRRR111121Kevin D. Donohue, University of Kentucky5Series and Parallel SourcesVoltage sources in series can be combined into a single voltage source:Current sources in parallel can be combined into a single current source:Ia + Ib + IcVa+Vb+Vc VaVbVcIa Ib IcKevin D. Donohue, University of Kentucky6ExamplesSimplify complex circuits containing independent sources and resistors to a minimum number of equivalent elements.Kevin D. Donohue, University of Kentucky7ExamplesFind voltages and currents in all branches of circuits containing resistors and independent sources through simplifying and expanding the circuitVoltages and currents in the original circuit can be determined byFinding currents and voltages of the simplified circuitExpanding back to the original configuration while applying current and voltage division to determine their current and voltage values.Kevin D. Donohue, University of Kentucky8 Single Loop Circuits with Dependent SourcesSince current is the the same throughout the entire loop, express all unknowns in terms of the loop current. Find Vo in circuit below:6 V+Vo-2  120  3  + Vd -100VdKevin D. Donohue, University of Kentucky9Single Node-Pair Circuits with Dependent SourcesSince voltage is the the same across every element, express all unknowns in terms of the node voltage difference. Find Io in circuit below:6 AIo2  3 