3-Lesson_Notes_Lectu - EE 204 Lecture 16 The Inductor The Inductor Symbol of the inductor is shown in the diagram The unit of the inductance L is

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EE 204 Lecture 16 The Inductor The Inductor: Symbol of the inductor is shown in the diagram The unit of the inductance L is the Henry (H) L Figure 1 Current-Voltage Relationship in the Inductor: 1- Differential Relation: The current-voltage relation in an inductor is: () L L di t vt L dt = This differential relation is valid only if L i enters the (+) side of L v . A minus sign must be inserted in the above relation if L i enters the (-) side of L v [According to the passive sign convention]. i L (t) + V L (t) L Figure 2 L L di vL dt = L L di v dt [The voltage across an inductor is proportional to the rate of change of the current through the inductor].
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Example 1: The time variation of the current source is shown graphically. Find the voltage () L vt across the 2[ ] H inductor. Figure 3 Solution: First, express L i analytically: 0, 0 3, 0 2 6, 2 4 31 8 ,4 6 6 Ls t tt it it t t < ≤< == −+ L L di vL dt = 0 0 2 () 2 2 4 8 6 6 L t d t dt t < < < 0 0 2 2 4 4 6 6 L t t t t t < −≤ < 0 0 2 2 4 4 6 6 L t t t t t < < = < The graphs of () L it & L are shown: Comments: 1- In the three time intervals 0 t < & 24 t
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This note was uploaded on 01/16/2010 for the course EE ee204 taught by Professor Profosama during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lectu - EE 204 Lecture 16 The Inductor The Inductor Symbol of the inductor is shown in the diagram The unit of the inductance L is

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