RC circuit - Capacitor discharge

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Discussion Overview

The discussion revolves around the mathematical modeling of capacitor discharge in an RC circuit, focusing on the correct formulation of the governing equations and the implications of the signs in those equations.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents an equation for capacitor discharge but notes a missing minus sign, questioning its necessity.
  • Another participant references Kirchoff's Second Law to derive the correct relationship between voltage and charge, indicating that the negative sign is required for consistency.
  • A third participant expresses a lack of familiarity with the laws being discussed, suggesting a potential gap in understanding among participants.
  • Another participant points out that if dq/dt is negative during discharge, it leads to a contradiction in the original equation presented, highlighting the importance of sign conventions in the equations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formulation of the equations, and there are competing views regarding the necessity and implications of the negative sign in the equations.

Contextual Notes

The discussion reveals potential limitations in understanding the application of Kirchoff's laws and the implications of charge flow direction on the equations used.

jpas
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When a capacitor discharges, the potential difference between its plates and the resistor's terminals is the same. Hence,

[tex]\frac{Q}{C}=R \frac{dq}{dt}[/tex]
Solving this equation we get

[tex]q(t)= Q_{0} exp \frac{t}{RC}[/tex]

Obviously, this isn't the solution. It is actually [tex]q(t)= Q_0 exp \frac{-t}{RC}[/tex]. So, I'm missing a minus sign on the original equation.

But why should it be there?
 
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According to Kirchoff's Second Law, the sum of the voltages is equal to zero. R(dQ/dt) + (Q/C) = 0, therefore you need -R(dQ/dt) = (Q/C). I apologize for the lack of proper script.
 
Thank you.
Didn't know such laws.
 
If the capacitor discharges, then dq/dt is negative, so according toyour originial equation, Q/C which is positive equals something negative
 

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