Find Currents I1 and I2 in an Electric Circuit

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Discussion Overview

The discussion revolves around finding the currents I1 and I2 in an electric circuit, specifically using differential equations as mandated by the lecturer. Participants are exploring the application of Kirchhoff’s laws and the use of differential equations versus phasor algebra in solving the problem.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in grasping the concepts needed to find the currents I1 and I2, mentioning the given voltage function E(t) and the circuit parameters R, L, and C.
  • Another participant questions the correctness of the equations provided for I1 and I2 and suggests that differential equations may not be necessary for a steady-state solution, proposing the use of phasor algebra instead.
  • A participant provides the values for R, L, and C but indicates that the lecturer insists on using differential equations, which they find challenging.
  • There is a suggestion that using differential equations will lead to complicated second-order equations with two variables, while the phasor approach could yield results more efficiently.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether differential equations are necessary for solving the problem. Some advocate for the use of phasor methods, while others adhere to the requirement of using differential equations as stated by the lecturer.

Contextual Notes

The discussion highlights the potential complexity of using differential equations in this context and the uncertainty regarding the necessity of such methods versus simpler approaches like phasor algebra.

Harshna
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Homework Statement


I need to find the currents I1 and I2 in the attached image, but am having some difficulties grasping the concepts. I am given E(t) = 338sin(t) as well as values for R, L and C. I think I know what I need to use but I am not sure how to put it all together

Homework Equations


Kirchhoff’s Voltage Law
Kirchhoff's Current Law
I1 = L d2I/dt2 + R dI/dt + I/c = E(t)
I2 = R dI/dt + I/C

The Attempt at a Solution


I have tried a bunch of things but I don't think any of them are right
 

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What are the values of R, L and C?
Harshna said:
I1 = L d2I/dt2 + R dI/dt + I/c = E(t)
I2 = R dI/dt + I/C
These equations are incorrect.
But, you don't have use DEs unless you want a complete time-domain solution (transient+steady state). You only need steady state currents here, so use phasor algebra.
Harshna said:
I have tried a bunch of things but I don't think any of them are right
You need to show what you've tried.
 
Hi cnh1995,

R = 5 Ohms, L = 1 Henry, C = 0.02 Farad

Thanks - unfortunately Lecturer said that we have to use differential equations.

I have tried solving with differential equations to find I(t) - but this doesn't really find the answer
 
Which course is this assignment from? If it is from ac circuits course, I am sure you don't need DEs at all.
Harshna said:
Hi cnh1995,

R = 5 Ohms, L = 1 Henry, C = 0.02 Farad

Thanks - unfortunately Lecturer said that we have to use differential equations.

I have tried solving with differential equations to find I(t) - but this doesn't really find the answer
You'll have second order DEs with two variables. It would get very complicated.
The phasor approach will take less than five steps to find the (steady state) currents.
 

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