Critically evaluate different techniques used to solve problems on series-parallel R, L, C circuits using A.C....

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Electrical Engineering

Critically evaluate different techniques used to solve problems onseries-parallel R, L, C circuits using A.C. theory.

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Series circuitFigure 1 RLCseries circuitV the voltage source powering the circuitI the current admitted through the circuitR the effective resistance of the combined load source andcomponentsL the inductance of the inductor componentC the capacitance of the capacitor componentIn this circuit the three components are all in series with thevoltage source The governing differential equation can be found bysubstituting into Kirchhoffs voltage law KVL the constitutiveequation for each of the three elements From the KVLwhere VR VL and VC are thevoltages across R L and C respectively and Vtis the timevarying voltage from the sourceSubstitutinginto the equation above yieldsFor the case where the source is an unchanging voltage takingthe time derivative and dividing by L leads to the following secondorder differential equationThis can usefully be expressed in a more generally applicableform and 0 are both in units of angularfrequency is called the neper frequency orattenuation and is a measure of how fast the transientresponse of the circuit will die away after the stimulus has beenremoved Neper occurs in the name because the units can also beconsidered to be nepers per second neper being a unit ofattenuation 0 is the angular resonancefrequencyFor the case of the series RLC See Answer

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