Finding i(t) Across R3 & R2 After Switch Closure at t=0

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Homework Help Overview

The problem involves analyzing a circuit with a switch that has been closed for a long time before opening at t = 0. Participants are tasked with finding the current i(t) across resistors R3 and R2 for t > 0, focusing on the behavior of the circuit immediately after the switch opens.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the behavior of inductors in circuits when a switch changes state, with one noting that an inductor acts like a wire when closed and has infinite resistance when the state changes. Others question the understanding of the time variable in the context of the problem and seek clarification on relevant equations.

Discussion Status

The discussion is ongoing, with participants sharing their attempts to apply Kirchhoff's Voltage Law (KVL) and expressing uncertainty about their approaches. Some guidance has been offered regarding the need for specific formulas related to RL circuits, but there is no clear consensus on the next steps or methods to be used.

Contextual Notes

Participants indicate a lack of examples from lectures and express concern about missing relevant equations, which may impact their ability to solve the problem effectively.

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Homework Statement


The switch in the circuit has been closed for a long time before opening at t = 0
a. Find i(t) across R3 for t>0.
b. Find i(t) across R2 for t>0.

I have attached the circuit.

Homework Equations





The Attempt at a Solution


The only thing I know for this problem is that when a switch has been in a certain state for a long time an inductor acts essentially like a wire (no resistance) and when the state changes the inductor has infinite resistance.
 

Attachments

  • HW7-1.jpg
    HW7-1.jpg
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To solve this you need to know the formula for di/dt for RL circuits. Isn't this in your textbook or covered by lecture?
 
I apologize...I thought that I included the relevant equations...but this is what I know:

hw7-eq.jpg


What I don't understand is what the change in time is...I really don't know how to go about solving this problem...and I have no examples from lecture...all I have from lecture is basically the 2 equations I have included. Any help would be greatly appreciated...Thanks.
 
So I've done some work and this is what I've came up with...I'm not sure if this is even remotely close:

I applied KVL's around each loop

HW7-KVL.jpg


HW7-KVLeq-1.jpg


Am I even on the right track with this?
 

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