Charged Capacitor: Opposing Emf Battery Series

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A charged capacitor can be mathematically represented as an uncharged capacitor in series with a battery of opposing EMF. The relationship between the charge stored in a capacitor and the voltage across it is fundamental and inseparable. Analyzing a simple linear circuit with a resistor connected to two configurations—one with a charged capacitor and the other with a capacitor in series with a voltage source—can yield similar step current responses. If both configurations produce the same response, they can be considered equivalent under all conditions. This illustrates the theoretical interchangeability of these components in circuit analysis.
vijayramakrishnan
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can a charged capacitor mathematically be represented as uncharged capacitor connected in series with battery of opposing emf ?
 
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Charge stored by a capacitor and teh voltage across it are two inseparable concepts. They exist together physically how mathematically things could be different then. Draw a diagram to show what you wish to propose.
 
Whenever analysing a simple linear circuit, see what it does to a resistor. Here, think of connecting a resistor across 2 black boxes, one of them has a charged capacitor, and the other one has a capacitor in series with a voltage source. Now you connect the switch on them both at the same time.
This is akin to a step current response. If you would get the same step current response on both the black boxes, both these black boxes would behave the same way for all conditions.
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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