Simple initial conditions problem

In summary: Then solve for v.In summary, when the switch is opened, the current through the inductor will change and the voltage across the inductor will also change.
  • #1
Learnphysics
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Homework Statement


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Homework Equations





The Attempt at a Solution



This is a fairly simple problem. My issue is that I can't identify the second initial condition. The first one is simple. At t=0, the voltage on the capacitor is 10V.

The second condition I feel should be related to the inductor. Perhaps to the current at 0 seconds. Not sure how to find out what the current through that inductor would be the moment the switch opens.

Anyone lend a hand?
 
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  • #2
What is the inductor current after the switch has been closed for hours?

As for what happens when the switch opens... remember that inductors resist changes to the current flowing in them.
 
  • #3
CWatters said:
What is the inductor current after the switch has been closed for hours?

As for what happens when the switch opens... remember that inductors resist changes to the current flowing in them.

Would it simply be the current running through the 0.5 Ohm resistor?

I'm not sure what exactly would happen with the inductor resisting changes to the current flowing through it. Would there even be a sudden change?

The capacitor will charge to 10V. So that when the switch opens, there will still be 10volts on one side of the inductor, with the same resistance. There should be no change. It's just that when the capacitor starts decaying out that the changing voltage will cause a current across the inductor to happen as per 1/L intergal(vdt) = I(t).Am I correct with that idea?
 
  • #4
Learnphysics said:
Would it simply be the current running through the 0.5 Ohm resistor?
Yes.

I'm not sure what exactly would happen with the inductor resisting changes to the current flowing through it. Would there even be a sudden change?
There is never a "sudden" (as in instantaneous) change in current in an inductor, not without fireworks anyway.
 
  • #5
Learnphysics said:
Would it simply be the current running through the 0.5 Ohm resistor?

I'm not sure what exactly would happen with the inductor resisting changes to the current flowing through it. Would there even be a sudden change?

The capacitor will charge to 10V. So that when the switch opens, there will still be 10volts on one side of the inductor, with the same resistance. There should be no change. It's just that when the capacitor starts decaying out that the changing voltage will cause a current across the inductor to happen as per 1/L intergal(vdt) = I(t).


Am I correct with that idea?

Yes. The current i thru the inductor, which had been coming from the supply before t = 0, now has to come from the capacitor. So the capacitor voltage drops, V across the inductor begins to change and therefore so does its current since for the inductorr di/dt = V/L.

Now, to answer the question you should write the differential equation in i and v, wit v replaced by a function of i. Or you can get 2 equations in v and i & solve them simultaneously. Same difference.

After you get v(t), let t = 2.5πe-6 s.
 

FAQ: Simple initial conditions problem

What is the Simple Initial Conditions Problem?

The Simple Initial Conditions Problem is a concept in physics that relates to the fundamental question of why the universe has the specific initial conditions that it does. It seeks to understand why the universe began with a certain set of physical laws and parameters, and how these conditions have led to the state of the universe today.

Why is the Simple Initial Conditions Problem important?

The Simple Initial Conditions Problem is important because it helps us to understand the underlying principles and laws that govern the universe. By studying the initial conditions of the universe, we can gain insight into the fundamental nature of reality and potentially uncover new scientific discoveries.

What are some proposed solutions to the Simple Initial Conditions Problem?

There are several proposed solutions to the Simple Initial Conditions Problem, including the idea of a multiverse, where our universe is just one of many existing universes with different initial conditions. Another proposed solution is the anthropic principle, which suggests that the universe has the specific initial conditions that it does because they are necessary for the existence of intelligent life.

What challenges does the Simple Initial Conditions Problem present for scientists?

The Simple Initial Conditions Problem presents many challenges for scientists, including the fact that we have limited data and understanding of the early universe. It also raises questions about the role of randomness and determinism in the universe, and how these factors may have influenced the initial conditions.

How does the Simple Initial Conditions Problem relate to the Big Bang Theory?

The Big Bang Theory is one of the most widely accepted explanations for the origin of the universe and is closely related to the Simple Initial Conditions Problem. The theory suggests that the universe began as a singularity with extremely high density and temperature, and has been expanding and cooling ever since. Understanding the initial conditions of the Big Bang is key to solving the Simple Initial Conditions Problem.

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