Capacitor and Time Varying Potential

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SUMMARY

The discussion focuses on the behavior of a capacitor when subjected to a time-varying potential, specifically when one side (Vb) changes sinusoidally while the other side (Va) remains constant. It is established that the charge on the capacitor will vary in response to the sinusoidal changes in Vb, leading to an out-of-phase relationship between Vb and the capacitor charge. The sinusoidal nature of Vb results in a corresponding sinusoidal behavior in current and voltage across the capacitor, while Va remains constant, affecting the net voltage across the capacitor.

PREREQUISITES
  • Understanding of capacitor behavior in AC circuits
  • Knowledge of sinusoidal functions and their properties
  • Familiarity with voltage and current relationships in electrical systems
  • Basic concepts of electric potential and charge
NEXT STEPS
  • Study the principles of AC circuit analysis
  • Learn about phasors and their application in sinusoidal steady-state analysis
  • Explore the relationship between voltage, current, and charge in capacitors
  • Investigate the effects of phase differences in AC signals
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Electrical engineers, physics students, and anyone interested in understanding the dynamics of capacitors in time-varying electric potential scenarios.

Apteronotus
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Hi

Suppose you have two regions of electric potential Va and Vb separated by a capacitor.
If Va remains constant and we change Vb according to some time varying formula, a sinusoid say, then
1. How does the charge on the capacitor charge?
2. How does Va change with time?Va ------||-------Vb
 
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I forgot a bit about AC systems, but Vb and the capacitor charge are probably out phase by some value. Something to note is that if the source of the change is sinusoidal, then so is the behavior of the respective values (at least for current, voltage, inductance, and capacitance). If Va is a constant source, then the voltage of that source remains the same; you could take into account the net voltage, in which the change (which is due to a sinusoidally changing Vb) is sinusoidal.
 
Thank you for your reply.
 

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