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CBSE Class 12-science Answered

A capacitor made of 2 parallel Plate area A and separation D being Charged by Ac Show that the displacement current inside capacitor is same as the current charging the capacitor
 
Asked by Anshul | 08 Sep, 2017, 06:28: PM
answered-by-expert Expert Answer
Alternating space emf space charging space the space plates space of space capacitor space be space straight E space equals space straight E subscript straight o space sinωt
Charge space in space the space capaictor comma space straight q space equals space EC space equals space straight C space space straight E subscript straight o space sinωt
Instantaneous space current space is space straight I space equals space dq over dt space
Substituting space and space differentiating comma space we space get
straight I space equals space Io space cosωt space space left parenthesis where space space straight I subscript straight o space equals space straight omega space CE subscript straight o space right parenthesis
Displacement space current comma space straight I subscript straight D space equals space straight epsilon subscript straight o space dφ subscript straight E over dt space
Substitute space the space value space of space straight phi subscript straight E space equals space EA space equals straight A space open parentheses fraction numerator straight q over denominator straight epsilon subscript straight o straight A end fraction close parentheses space equals straight A space open parentheses fraction numerator space straight C space space straight E subscript straight o space sinωt over denominator straight epsilon subscript straight o straight A end fraction close parentheses space and space different.
We space get space space straight I subscript straight D space equals space straight I subscript straight o space cosωt
Thus comma space the space displacement space current space inside space the space capacitor space is space the space same space as space the space current space charging space the space capacitor. space
Answered by Yashvanti Jain | 11 Sep, 2017, 04:23: PM
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