Rate of change of current in an R-L Circuit

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Discussion Overview

The discussion revolves around the rate of change of current in an R-L circuit, particularly focusing on the behavior of the current at the moment a DC voltage source is applied. Participants explore concepts related to inductors, the implications of applying a DC source, and the use of Laplace transforms and source transformations in analyzing the circuit.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that since the input is a DC source, the current at t=0+ equals the current at t=0-, leading to the conclusion that di/dt at t=0+ is zero.
  • Another participant questions the book's answer, suggesting it may be a typo, and proposes using source transformation to clarify the circuit's behavior.
  • A different participant agrees that the current across an inductor cannot change suddenly unless the input is an impulse voltage source, referencing the equation V = L di/dt.
  • One participant describes using Laplace transforms to arrive at a solution, while also expressing confusion about the expected behavior of the current.
  • Another participant argues that at t=0+, no current flows through the inductor, meaning the entire source voltage appears across it, leading to a non-zero di/dt.
  • There is a contention regarding whether di/dt can be considered zero at t=0+ due to the inductor not being excited prior to that moment.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of the current at the moment a DC voltage is applied, with no consensus reached on whether di/dt at t=0+ is zero or not. The discussion remains unresolved as participants explore various interpretations and methods of analysis.

Contextual Notes

There are limitations regarding assumptions about the circuit's initial conditions and the definitions of terms used, particularly concerning the behavior of inductors in response to DC sources versus impulse sources.

jaus tail
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Homework Statement


upload_2018-5-18_12-18-4.png


Homework Equations


Current cannot change suddenly through inductor unless input is impulse voltage source.

The Attempt at a Solution


since input is DC source we have i(0+) = i(0-) so we have di/dt at t = 0+ is 0.
Is it correct? Book has mentioned answer as B which is weird cause there is no Ls in circuit.
 

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jaus tail said:
Book has mentioned answer as B which is weird cause there is no Ls in circuit.
It's probably a typo. They meant Is instead of Ls.

jaus tail said:
since input is DC source we have i(0+) = i(0-) so we have di/dt at t = 0+ is 0.
No.
How about using source transformation? It will make the circuit look more familiar.
 
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Wow... I used laplace and then got the answer. You're right.
upload_2018-5-18_16-41-37.png

But shouldn't it be zero as per concept? Unless the input is an impulse voltage source the current across inductor cannot change so quickly. V = L di/dt. So unless V is an impulse, di/dt has to be zero.
 

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jaus tail said:
Wow... I used laplace and then got the answer. You're right.
Well, if you use source transformation, you end up with a series RL circuit with Rtotal=Rs+R and inductance L, excited by a voltage source of emf IsRs.
At t=0+, no current flows through the inductor, which means the entire source voltage appears across the inductor.
So, IsRs=Ldi/dt, which gives di/dt=IsRs/L.
jaus tail said:
the current across inductor cannot change so quickly. V = L di/dt. So unless V is an impulse, di/dt has to be zero.
No, here VL at t=0 is not zero, hence di/dt is also not zero. You can't compare the currents at t=0- and t=0+ to find di/dt at t=0+ because at t=0-, the inductor was not excited.
 
Well you're method is way quicker than mine.
Thanks a lot. Learnt new thing today.
 

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