Finding the time constant of an inductor

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SUMMARY

The time constant τ for the first-order response of the given inductor circuit can be calculated using the formula τ = L/R. In this case, the inductor L is 6 H, and the effective resistance R, after analyzing the circuit with the switch open, is the parallel combination of R1 (8 Ω) and R2 (6 Ω). The equivalent resistance is 4.8 Ω, leading to a time constant τ of 1.25 seconds. This calculation is crucial for understanding the transient response of inductive circuits.

PREREQUISITES
  • Understanding of inductors and their behavior in circuits
  • Knowledge of Ohm's Law and resistance calculations
  • Familiarity with circuit analysis techniques, including series and parallel combinations
  • Basic concepts of time constants in electrical circuits
NEXT STEPS
  • Study the effects of different resistor values on the time constant in RL circuits
  • Learn about the transient response of RL circuits using differential equations
  • Explore the use of simulation tools like LTspice for circuit analysis
  • Investigate the impact of varying inductance on circuit behavior over time
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in analyzing the transient response of inductive circuits will benefit from this discussion.

Jd303
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Find the time constant τ for the first order response of the circuit below at t > 0 s.
L = 6 H
R1 = 8 Ω : R2 = 6 Ω
Give your answer to at least two decimal places, in s.

I am really struggling on where even to begin with this question.

I know that for a simplified circuit t = L/R

And that you are meant to analyse the circuit just before and after the switch is closed or something along those lines, but I can't seem to apply it.

Any help to allow me to understand this type of question better would be greatly appreciated. Thanks!
 

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Yes, you break the problem up into two parts. First, start with the switch closed (when t<0). Remember, an inductor supplied by a direct current acts just like a wire. Start by finding the current through the various circuit elements at that time.
 
The question just wants you to find the time constant for the circuit for t > 0. So draw the circuit that remains when the switch is open. Trim off any components where current cannot flow. What's the time constant for what remains?
 

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