Time Constant RC circuit with dependent source

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Discussion Overview

The discussion revolves around determining the time constant of an RC circuit that includes a dependent voltage source. Participants explore the implications of the dependent source on the time constant and how to approach solving the problem using differential equations and equivalent resistance concepts.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants note that the time constant T = R*C is applicable in standard RC circuits with constant voltage sources, but question its validity in circuits with dependent sources.
  • One participant suggests starting with a loop equation and using the differential equation relating voltage across the capacitor (Vc) and current through the capacitor (Ic) to explore the time constant.
  • Another participant mentions the need for an initial condition to solve the problem, asserting that the choice of initial condition should not affect the time constant in a linear circuit.
  • There is a proposal to model the combination of the resistor and the dependent source as an equivalent resistance, suggesting that this can be calculated by replacing the capacitor with a test current and multiplying the equivalent resistance by the capacitance to find the time constant.
  • One participant expresses appreciation for the method of finding equivalent resistance and encourages the original poster (OP) to verify results by trying multiple approaches.
  • A participant shares their calculations, indicating a potential misunderstanding of the equivalent resistance and time constant, suggesting they may be missing something in their analysis.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, particularly regarding the impact of the dependent source on the time constant. There is no consensus on the best method to solve the problem or the implications of the dependent source.

Contextual Notes

Participants highlight the importance of initial conditions and the potential for different approaches to yield varying results. The discussion does not resolve the mathematical steps or assumptions involved in calculating the time constant with a dependent source.

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Homework Statement


ecequ.jpg



Homework Equations


T = R*C


The Attempt at a Solution


I have no idea how to go about this. I know that T=R*C in a RC circuit
 
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teh_cookie said:

Homework Statement


ecequ.jpg



Homework Equations


T = R*C


The Attempt at a Solution


I have no idea how to go about this. I know that T=R*C in a RC circuit

That time constant is true when you have a constant voltage source and you close a switch into the RC portion of the circuit (or similar setup). This problem looks different, since voltge source is depentent on the voltage drop through the resistor (and hence dependent on the current in the circuit).

I'd start with a loop equation for the loop, using the differential equation relating Vc and Ic. Then see if solving it gives an exponential relation still, and if it does, finding the time constant that results.
 
BTW, you're going to have to assume some initial condition to solve the problem, but since it's a linear circuit, the initial condition you choose shouldn't affect the time constant (at least I don't think it will).
 
The combination of the resistor and the dependent source can be modeled as a resistance. Find this equivalent resistance by considering the capacitor replaced by a test current. Multiply the equivalent resistance by the capacitance of C to get the time constant.
 
Adjuster said:
The combination of the resistor and the dependent source can be modeled as a resistance. Find this equivalent resistance by considering the capacitor replaced by a test current. Multiply the equivalent resistance by the capacitance of C to get the time constant.

Hah! Neat trick, and very logical. I hadn't seen that before.

But the OP should do it both ways, to check his answers...:wink:
 
Trying Adjuster's trick I basically get v_in=5*v_1, My guess is that I can translate that to a R_eq of 5. But 5*0.01 = 0.05s (an order of magnitude too small).

My guess is that I'm missing something here

edit: v_1 = 10 Ohms * i_in

v_in = 5 * (10 * i_in)

R_eq = 50 Ohms

50 Ohm * 0.01 F = 0.5 s
 
Last edited:

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