L-10(GDR)(ET) ((EE)NPTEL) - Module 3 R-L & R-C...

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Module 3 R-L & R-C Transients Version 2 EE IIT, Kharagpur
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Lesson 10 Study of DC transients in R-L and R-C circuits Version 2 EE IIT, Kharagpur
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Objectives Definition of inductance and continuity condition for inductors. To understand the rise or fall of current in a simple series R L circuit excited with dc source. Meaning of '( ) ' τ for R L Time Constamt circuit and explain its relationship to the performance of the circuit. Energy stored in an inductor Definition of capacitance and Continuity condition for capacitors. To understand the rise or fall voltage across the capacitor in a simple series RC circuit excited with dc source. Meaning of ) ' for Time Constamt circuit and explain its relationship to the performance of the circuit. Energy stored in a capacitor L.10.1 Introduction So far we have considered dc resistive network in which currents and voltages were independent of time. More specifically, Voltage (cause input) and current (effect output) responses displayed simultaneously except for a constant multiplicative factor ( VR ). Two basic passive elements namely, inductor R I () L and capacitor ( ) are introduced in the dc network. Automatically, the question will arise whether or not the methods developed in lesson-3 to lesson-8 for resistive circuit analysis are still valid. The voltage/current relationship for these two passive elements are defined by the derivative (voltage across the inductor C L L di t vt L dt = , where =current flowing through the inductor ; current through the capacitor L it C C dv t it C dt = , = voltage across the capacitor) or in integral form as ( ) C vt 00 11 (0 ) ) tt LL L C vtd ti o rvt i td tv LC =+ = + ∫∫ C rather than the algebraic equation ( VI R = ) for all resistors. One can still apply the KCL, KVL, Mesh-current method, Node-voltage method and all network theorems but they result in differential equations rather than the algebraic equations that we have considered in resistive networks (see Lession-3 to lesson-8). An electric switch is turned on or off in some circuit (for example in a circuit consisting of resistance and inductance), transient currents or voltages (quickly changing current or voltage) will occur for a short period after these switching actions. After the transient has ended, the current or voltage in question returns to its steady state situation (or normal steady value). Duration of transient phenomena are over after only a few micro or milliseconds, or few seconds or more depending on the values of circuit parameters (like ,, R L and C ).The situation relating to the sudden application of dc voltage to circuits possessing resistance ( R ), inductance ( L ), and capacitance ( C ) will Version 2 EE IIT, Kharagpur
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now be investigated in this lesson. We will continue our discussion on transients occurring in a dc circuit. It is needless to mention that transients also occur in ac circuit but they are not included in this lesson.
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L-10(GDR)(ET) ((EE)NPTEL) - Module 3 R-L & R-C...

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