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Unformatted text preview: ents are referenced in to (or both are referenced out of) the dotted terminals, then the mutual term is positive. If one current is referenced into and the other is referenced out of the dotted terminal then the mutual term carries a negative sign as: di1
di
M 2
dt
dt di2
di1
M
v2 L2
dt
dt
v1 L1 Comparison of capacitor and inductor dvc (t ) dt
di (t )
For an inductor vL (t ) L L dt For a capacitor ic (t ) C It can be seen that the roles of voltage and current are reversed in the two elements but both are described by a differential equation of the same form. There is a duality between inductor and capacitor. We can make important observations from the differential relationship between voltage and current. For capacitor, the voltage must be continuous as otherwise the current has to be infinity which is not possible. For inductor, the current must be continuous as otherwise the voltage has to be infinity which is not possible. These properties of inductor and capacitor give rise to many useful circuits. 69 EE1002 Introduction to Circuits and Systems DC Transients Learning objectives: 1)
2)
3)
4) Understand the meaning of transients. Write differential equations for circuits containing inductors and capacitors. Determine the DC steady‐state solution of circuits containing inductors and capacitors. Write differential equation of first‐order circuits in standard form, and determine the complete solution of fir...
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This document was uploaded on 01/20/2014.
 Winter '14

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