Find current through inductor after many time constants.

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SUMMARY

The discussion centers on calculating the current through an inductor after many time constants in an RL circuit with a resistor of 1.9 kΩ and a voltage source of 60 V. Initially, the user incorrectly calculated the current as 31.5789 A due to a unit conversion error, using ohms instead of kilo-ohms. After correcting the resistance to 1.9 kΩ, the user confirmed that the correct current is 10 mA after the switch is closed for a sufficient duration, aligning with the behavior of inductors in steady-state conditions.

PREREQUISITES
  • Understanding of RL circuit behavior and time constants
  • Knowledge of Ohm's Law (I = V/R)
  • Familiarity with the concept of steady-state current in inductors
  • Ability to perform unit conversions (Ω to kΩ)
NEXT STEPS
  • Study the concept of time constants in RL circuits
  • Learn about the transient response of inductors
  • Explore advanced circuit analysis techniques using Kirchhoff's laws
  • Review practical applications of inductors in electronic circuits
USEFUL FOR

Students studying electrical engineering, educators teaching circuit analysis, and anyone interested in understanding inductor behavior in RL circuits.

jlmccart03
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Homework Statement


In the figure, R = 1.9 kΩ and ε0 = 60 V . When the switch is closed, the current through the inductor rises to 10 mA in 30 μs .

What will the current in the circuit be after many time constants?

Homework Equations


I = V/R or I = ε/R if current is constant which after many time constants it should be correct?

The Attempt at a Solution


So I attempted to use I = ε/R, but that presented the wrong answer. So then I thought about the question and I remembered that after many time constants that is essentially saying a τ→∞ which would make ε = IR and again I = ε/R so I am not lost on where my thinking was going and if I was even correct in the initial process?
 

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What, precisely, was the value that you calculated and entered?
 
gneill said:
What, precisely, was the value that you calculated and entered?
I got 31.5789 A, which is taking ε = 60V and R = 1.9 Ω. EDIT: The Ω where in kΩ. I just needed to convert it and got the correct answer.
 

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