3-Lesson_Notes_Lecture_15 - EE 204 Lecture 15 The Capacitor...

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EE 204 Lecture 15 The Capacitor Energy Storage Elements: Some electric circuit elements can store electric energy. These include the capacitor and the inductor . A resistor clearly is not an energy storage element, because the electric energy it absorbs is converted to heat energy and thus it is lost. Ideal voltage sources and ideal current sources are not considered energy storage elements. Energy storage elements (ESE) can absorb electric energy. This energy remains in electric form (stored). ESE can also deliver electric energy, but they can only deliver the energy that has been previously absorbed (stored energy). In this lecture we will study the capacitor. The inductor will be considered in the next lecture. The Capacitor: Symbol of the capacitor is shown in the diagram The unit of the capacitance C is in Farads (F) The charge q stored in the capacitor is proportional to the voltage c v across the capacitor. The constant of proportionality is the capacitance C . c qC v = Figure 1 Voltage-Current Relationship in the Capacitor: 1- Differential Relation:
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In general , () qq t = & cc vv t = c qt Cv t = c dv t dq t C dt dt = c c dv t it C dt = c c dv iC dt = [ Explicit time dependence is not shown for simplicity] This is a differential relation between the voltage and current in a capacitor It is valid only if c i enters the (+) side of c v [Recall the passive sign convention] C i c (t) + v c (t) Figure 2 If c i enters the (-) side of c v c c dv dt =− [passive sign convention] Figure 3 c c dv dt = c c dv i dt [Compare thus relation with Ohm’s law vi R = iv ] Example 1: 5 () 3 [ ] t s vt e V = for 0 t a) Find () c it for 0 t b) Plot the voltage across and the current through the capacitor for 0 t Figure 4 Solution:
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a) s vC cs vv = c c dv iC dt = 55 5 2 (3 ) 2( 15 ) 30 [ ] tt t c d ie ee A dt −− == = Figure 5 b) The graphs of () c vt & () c it for 0 t are shown. c enters the capacitor from the (+) side of () c c c dv t it C dt = sign of ( ) c = sign of the slope of ( ) c decreasing c ( negative slope) ( ) 0 c < ( negative current) increasing c ( positive slope) ( ) 0 c > ( positive current) In the graph ( ) c decreases with time ( ) 0 c <
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3-Lesson_Notes_Lecture_15 - EE 204 Lecture 15 The Capacitor...

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