RL circuit with three resistors

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SUMMARY

The forum discussion centers on an RL circuit involving three identical resistors, a battery, an inductor, and a switch. The correct answers identified include that the voltage across the inductor immediately after closing the switch is 6 V, and the energy stored in the inductor after a long time is 3.30 × 10-6 J. Additionally, after reopening the switch, the fraction of current remaining after 3 μsec is 0.236. Key concepts discussed include Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL).

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  • Understanding of RL circuits and their components
  • Familiarity with Kirchhoff's Voltage Law (KVL)
  • Knowledge of Kirchhoff's Current Law (KCL)
  • Basic principles of inductance and energy storage in inductors
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  • Explore the impact of switch operations on RL circuits
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Homework Statement



http://i.imgur.com/22jq3.png

22jq3.png


Three identical resistors are connected to a battery, an inductor, and a switch as shown in the figure. (The values of all circuit elements are given below the figure.) The switch has been open for a very long time, and then it is closed at time t = 0.

Part A

Immediately after the switch is closed, the voltage VL across the inductor is
(a) VL = 0 V
(b) VL = 6 V Correct
(c) Neither of the above answers is correct.

Part B

After the switch has been closed for a very long time, how much energy EL is stored in the inductor?
(a) EL = 3.30 × 10-6 J Correct
(b) EL = 5.62 × 10-6 J
(c) EL = 8.63 × 10-6 J
(d) EL = 1.07 × 10-5 J
(e) EL = 1.12 × 10-5 J

Part C
After the switch has been closed for a very long time, a steady current has been established through the inductor. The switch is then reopened. What fraction of this current, fI, remains after a time interval of Δt = 3 μsec has elapsed?
(a) fI = 0.0521
(b) fI = 0.0926
(c) fI = 0.158
(d) fI = 0.201
(e) fI = 0.236 Correct




Homework Equations




KVL, KCL

The Attempt at a Solution



Part A,
can i just say regardless of any situation, VL is equal to Vbattery immdiately after switch is closed?

Part B,
I can't find the current across L. in this case.

Part C,

I am not sure how to start with this question.

Thx
 
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You need the relation between voltage and current across the inductor.

ehild
 
A: When you first try to push current through an inductor, does it act like a short circuit, an open circuit, or a resistive circuit?

"current across L" is an odd statement, since current is never "across" anything. Current flows THROUGH things due to voltage ACROSS things. This is NOT semantics, it is integral to how electricity works.
 
phinds said:
A: When you first try to push current through an inductor, does it act like a short circuit, an open circuit, or a resistive circuit?

"current across L" is an odd statement, since current is never "across" anything. Current flows THROUGH things due to voltage ACROSS things. This is NOT semantics, it is integral to how electricity works.

No current? I think...
 
Yes. Your answer to Part A is correct.

ehild
 

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