Circuit Question Involving Resistors and Inductors

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Homework Help Overview

The discussion revolves around a circuit problem involving resistors and an inductor, specifically focusing on the behavior of current at different time intervals after a switch is closed and reopened. The components include an inductor with a value of 2.0 H, an emf of 10 V, and two resistors with values of 10 ohms and 20 ohms.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equivalent resistance of resistors in series and the initial current calculation using Ohm's law. There is also exploration of the inductor's behavior over time, particularly its impedance at DC and its effect on current through the resistors. Questions arise regarding the time constant when the switch is reopened and the implications of the inductor's characteristics on the circuit.

Discussion Status

Some participants have confirmed the correctness of initial calculations and are engaging in further exploration of the circuit's behavior over time. There is a recognition of the inductor acting as a wire after a long time, and discussions are ongoing about the time constant and the current decay when the switch is reopened.

Contextual Notes

Participants note the lack of explicit values for certain parts of the problem, particularly regarding the time constant when the switch is reopened, and the implications of the inductor's behavior in the circuit setup.

Jordan1361
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Homework Statement



For the circuit below, if L=2.0 H, emf=10 V, R1=10 ohms, R2= 20 ohms, what is the current through each component

a) at the instant the switch is closed
b)a long time after the switch is closed
c) If after a long time the switch is reopened, what is the time constant for the current?

Homework Equations



V=IR

The Attempt at a Solution



For a) I think the resistors are in series so equivalent resistance would be 30 ohms. Then I used V=IR to find a current of 0.33 A.

Could someone please check if a) is right and show me the steps to do the other parts. Thanks!
 

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Jordan1361 said:

Homework Statement



For the circuit below, if L=2.0 H, emf=10 V, R1=10 ohms, R2= 20 ohms, what is the current through each component

a) at the instant the switch is closed
b)a long time after the switch is closed
c) If after a long time the switch is reopened, what is the time constant for the current?




Homework Equations



V=IR

The Attempt at a Solution



For a) I think the resistors are in series so equivalent resistance would be 30 ohms. Then I used V=IR to find a current of 0.33 A.

Could someone please check if a) is right and show me the steps to do the other parts. Thanks!

The current you calculated for right after the switch is closed is correct. What about the current a long time after the switch is closed? What is an inductor's impedance at DC?
 
After a long time, the inductor will act like a piece of wire with no resistance so current would still be flowing through R1 but zero current would be in R2. The current in R1 would be I=10/10=1 A. Am I correct?

For part c, I know that the time constant is tau=L/R so do I just use L=2.0 H and R=0 ohms?
 
Jordan1361 said:
After a long time, the inductor will act like a piece of wire with no resistance so current would still be flowing through R1 but zero current would be in R2. The current in R1 would be I=10/10=1 A. Am I correct?

Yes, very good. :smile:

For part c, I know that the time constant is tau=L/R so do I just use L=2.0 H and R=0 ohms?

When the switch is opened, what is in parallel with the inductor? The inductor current cannot change instantly, so it will decay with what time constant?
 
R2 is in parallel with the inductor. I know that current decrease is represented by
I(final)=I(initial)*e^(-t/τ).
 
Jordan1361 said:
R2 is in parallel with the inductor. I know that current decrease is represented by
I(final)=I(initial)*e^(-t/τ).

Looks good!
 
So the time constant is τ=-t/ln(Ifinal/Iinitial)
There is no value for part c?
 

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