Charged Capacitor: Opposing Emf Battery Series

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SUMMARY

A charged capacitor can be mathematically represented as an uncharged capacitor in series with a battery of opposing electromotive force (emf). The relationship between charge stored in a capacitor and the voltage across it is fundamental, and both concepts must be analyzed together. When examining a simple linear circuit, connecting a resistor across two configurations—a charged capacitor and an uncharged capacitor with an opposing emf—yields identical step current responses, indicating that both configurations behave equivalently under the same conditions.

PREREQUISITES
  • Understanding of capacitor charge-voltage relationships
  • Familiarity with linear circuit analysis
  • Knowledge of electromotive force (emf) concepts
  • Basic principles of step current response in circuits
NEXT STEPS
  • Explore the mathematical modeling of capacitors in series with opposing emf sources
  • Study the effects of step current response in linear circuits
  • Investigate the behavior of resistors in circuits with capacitors and emf sources
  • Learn about the implications of charge and voltage relationships in circuit design
USEFUL FOR

Electrical engineers, physics students, and circuit designers interested in advanced capacitor behavior and circuit analysis techniques.

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 the 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.
 

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