First order circuits. Solving for v(t)

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Discussion Overview

The discussion revolves around solving for v(t) in first order circuits, particularly focusing on the mathematical manipulation required to express the voltage in a specific form. Participants explore concepts related to derivatives and the behavior of circuit components in steady-state conditions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in transforming the equation for v(t) into the form presented by their lecturer, indicating a need for mathematical assistance.
  • Another participant suggests that the lecturer may be using the property of derivatives that allows for the addition or subtraction of a constant without affecting the derivative, which could simplify the derivation of v(t).
  • A participant questions the behavior of capacitors and inductors in steady-state DC conditions, specifically why a capacitor is not treated as an open circuit when the source voltage is constant.
  • In response, another participant confirms that replacing the capacitor with an open circuit is valid, noting that it leads to a steady-state current of zero.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical properties of derivatives and the behavior of circuit components in steady-state conditions, but there is some uncertainty regarding the specific application of these concepts to the problem at hand.

Contextual Notes

The discussion includes assumptions about the behavior of circuit components under steady-state conditions and the implications of mathematical transformations on the equations involved. There are unresolved questions about the specific application of these principles to the circuit in question.

CoolDude420
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Homework Statement


So our lecture introduced first order circuits to us.
We are trying to solve for v(t) in the following circuit. However in the notes he gets it into a form in which we can solve for v(t). However I can't seem to get it into the same form he has. This is more of a maths question rather than a circuits question.

The purpose of writing it in the form that he has is to solve for v(t). Any ideas how I can get it into that form?

054f0907b2.jpg

Homework Equations


[/B]
i(t) = C dv(t)/dt

The Attempt at a Solution


[/B]
In Pic above
 
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Presumably E is a constant here?

The derivative of a function is unaffected if you first add (or subtract) a constant value∆[/size] to the function,
so it follows that d(v(t))/dt is identical to d(v(t)–E)/dt

It looks like your lecturer might be finding it convenient to use this fact in his derivation of v(t)?

∆ the derivative of a sum is equal to the sum of the individual derivatives
 
NascentOxygen said:
Presumably E is a constant here?

The derivative of a function is unaffected if you first add (or subtract) a constant value∆ to the function,
so it follows that d(v(t))/dt is identical to d(v(t)–E)/dt

It looks like your lecturer might be finding it convenient to use this fact in his derivation of v(t)?

∆ the derivative of a sum is equal to the sum of the individual derivatives

Ah. That makes much more sense. I've been trying to figure this out for a while now. Thank you very much,
 
Hi,

I've just come back to revise this after properly I think understanding dynamic circuits. I am told that in the DC steady state(i.e when the source is providing a steady voltage), capacitors behave as open circuits and inductors behave as short circuits. So why doesn't that happen in this case(where E is constant).? I mean the circuit is providing a constant V and so the time derivative in i = C dv/dt should evaluate to 0 thus giving us i=0 which is an open circuit. Why don't we just replace the capacitor with a open circuit here?
 
CoolDude420 said:
Why don't we just replace the capacitor with a open circuit here?
You can. If you do that it will tell you that the steady-state current is zero, which is true.
 

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