Rate of change of current in an R-L Circuit

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SUMMARY

The discussion centers on the behavior of current in an R-L circuit when subjected to a DC voltage source. It is established that the current cannot change instantaneously through an inductor unless an impulse voltage source is applied. The participants clarify that at time t=0+, the rate of change of current (di/dt) is not zero due to the presence of voltage across the inductor, which contradicts the initial assumption. The use of Laplace transforms and source transformation techniques is highlighted as effective methods for analyzing the circuit's behavior.

PREREQUISITES
  • Understanding of R-L circuit dynamics
  • Familiarity with Laplace transforms
  • Knowledge of source transformation techniques
  • Concept of inductance and its role in current change
NEXT STEPS
  • Study R-L circuit analysis using Laplace transforms
  • Learn about source transformation in electrical circuits
  • Explore the concept of impulse voltage sources and their effects on inductors
  • Investigate the mathematical relationship V = L di/dt in detail
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding transient responses in R-L circuits.

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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