What is the current in these 3 circuits right after the switches are opened?

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Homework Help Overview

The discussion revolves around determining the current through a resistor labeled 'R' in three different circuits immediately after switches in those circuits are opened. The context involves analyzing the behavior of inductors in electrical circuits, particularly how they influence current flow when the circuit configuration changes.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of opening the switch after it has been closed for a long time, questioning how current behaves in the presence of an ideal inductor. There are differing interpretations regarding the initial current through the resistor and the role of the inductor in maintaining current flow.

Discussion Status

Participants are actively engaging with each other's reasoning, with some suggesting that the inductor maintains the initial current while others question the labeling of resistors and the assumptions about their values. There is a recognition of the need for clarity regarding the circuit configuration and the definitions of the resistors involved.

Contextual Notes

There is uncertainty regarding the labeling of the resistors, particularly which one is designated as 'R', and whether all resistors are identical. Participants express confusion about how current can flow through components when the circuit is open, highlighting the need for a clear understanding of circuit principles.

L_landau
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Homework Statement


What is the current through the resistor marked 'R' in all three circuits just after the switch is reopened after being closed for a long time?

The Attempt at a Solution


The explanation that we were given for (1) is that I = V/2R and (2) I = V/3R and (3) I = V/(R/2) but I don't understand how this makes sense because when the circuit is opened, current shouldn't flow in unclosed parts. As I understand it the inductor should act as an energy source and form a closed loop with the resistors so that in (1) I = V/R and (2) I = V/2R and (3) I = V/(R/2). What am I missing here??
 

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Well, I disagree with both of you. In all three cases, the current through the inductor when the switch has been closed for a long time is I = V/R. Remember that an ideal inductor has zero resistance, so the resistors in parallel with the inductor are effectively shorted out. When you open the switch, the current through the inductor cannot change instantaneously, so it is still I = V/R. What current goes through the resistor R in the three cases?
 
phyzguy said:
Well, I disagree with both of you.
Yeah, and the "R" we need to define the initial current is not labeled (it is the resistor in the upper left). The resistor labeled "R" is shorted by the inductor out while the switch is closed...
 
Okay so after the switch has been closed a long time, since ideal inductors have zero resistance, then I = V/R because all the current goes through the inductor.
Once the switch is opened, the current through the inductor is still V/R, so for (1) and (2) the current is V/R and for (3) the current just gets split between the two resistors? That seems right.
 
L_landau said:
Okay so after the switch has been closed a long time, since ideal inductors have zero resistance, then I = V/R because all the current goes through the inductor.
Once the switch is opened, the current through the inductor is still V/R, so for (1) and (2) the current is V/R and for (3) the current just gets split between the two resistors? That seems right.
That would be right if the upper left resistor were labeled "R", but it's blank. Are you told that all of the resistors are identical?
 
No we are just told that the labeled R is what we are trying to find the current through. How could current flow through the other resistor once the circuit is open? I thought a circuit had to be closed for current to run through it.
 
L_landau said:
No we are just told that the labeled R is what we are trying to find the current through. How could current flow through the other resistor once the circuit is open? I thought a circuit had to be closed for current to run through it.
It doesn't. When the switch is closed for a long time, the current flows from the voltage source through the upper left resistor (call it Rul) and through the inductor (which has V=0 across it since it's ideal). That defines the initial current through the inductor, Ii = V / Rul. That is the same current that flows in the right-hand circuits right after the switch is opened.
 
Yes, I just assumed they were all R. You can't do the problem otherwise, but you need to ask.
 
Okay. Thanks for the help everyone!
 

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