Find current through inductor after many time constants.

In summary, the current in the circuit after many time constants is 31.5789 A, calculated using the equation I = ε/R with ε = 60 V and R = 1.9 kΩ. The initial thought of using I = V/R was incorrect, but after remembering that τ→∞ makes ε = IR, the correct approach was used.
  • #1
jlmccart03
175
9

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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  • #2
What, precisely, was the value that you calculated and entered?
 
  • #3
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.
 

FAQ: Find current through inductor after many time constants.

1. What is an inductor?

An inductor is an electrical component that stores energy in the form of a magnetic field. It is typically made of a coil of wire and is used in electronic circuits for its ability to resist changes in current.

2. What is meant by "time constant" in relation to an inductor?

Time constant refers to the amount of time it takes for an inductor to reach a steady state current when an external voltage is applied. It is determined by the inductance and resistance of the circuit.

3. How is the current through an inductor calculated after many time constants have passed?

The current through an inductor after many time constants can be calculated using the formula I=I0(1-e^(-t/τ)), where I0 is the initial current, t is the time passed, and τ is the time constant.

4. Why is it important to know the current through an inductor after many time constants?

Understanding the current through an inductor after many time constants can help in predicting the behavior of the circuit and determining its stability. It can also be useful in designing circuits for specific purposes.

5. Are there any practical applications of this concept?

Yes, the concept of finding current through an inductor after many time constants is used in various fields such as power distribution, telecommunications, and electronics. It is also important in designing filters, transformers, and other electrical components.

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