Source free RL circuit confusion When this switch closes, does the current end?

In summary, when the switch is closed for a long time, the current is DC. The current through the other two resistors is still 100V/30 ohms, but the current through the inductor is not affected.
  • #1
mr_coffee
1,629
1
Hello everyone. I'm getting confused on what my professor did. Everything else makes sense to me but this one part. THe directions say:
Aftering having been closed for a long time, the switch in the circuit is opened at t= 0. (a) find IL(t) for t>0, (b) Evaluate IL(10ms).

I got both parts right. Here is my work and the circuit:
http://img119.imageshack.us/img119/7361/lastscan2at.jpg [Broken]


Okay if you look at t<0, you assume the inductor is short circuit, that's what those 2 little dots mean instead of the curly inductor symbol. THe current Io = IL. So when the switch is closed, if you notice the circuit is redrawn, with the 20 and 10 resistors in series not even in the circuit. When that switch is closed for along time, its DC current. But wouldn't the current branch off into 2 parts? 1 going into the 20 + 10 resistors on the left and another current going to the right through the 50 ohm resistor and then going into where the inductor was?

What I'm confused on is why U can just say screw those other resistors, Io isn't affected by them. Any explanation? Thanks!
 
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  • #2
mr_coffee said:
Hello everyone. I'm getting confused on what my professor did. Everything else makes sense to me but this one part. THe directions say:
Aftering having been closed for a long time, the switch in the circuit is opened at t= 0. (a) find IL(t) for t>0, (b) Evaluate IL(10ms).

I got both parts right. Here is my work and the circuit:
http://img119.imageshack.us/img119/7361/lastscan2at.jpg [Broken]


Okay if you look at t<0, you assume the inductor is short circuit, that's what those 2 little dots mean instead of the curly inductor symbol. THe current Io = IL. So when the switch is closed, if you notice the circuit is redrawn, with the 20 and 10 resistors in series not even in the circuit. When that switch is closed for along time, its DC current. But wouldn't the current branch off into 2 parts? 1 going into the 20 + 10 resistors on the left and another current going to the right through the 50 ohm resistor and then going into where the inductor was?

What I'm confused on is why U can just say screw those other resistors, Io isn't affected by them. Any explanation? Thanks!

It`s not that the 10 and 20 ohms disappear. It is simply that the potential difference across the 50 ohms is 100 V (and the potential difference across the 10 and 20 ohms combined is also 100 volts). Do you see this? (it`s clear since the terminals of the battery are directly connected across the 50 ohms). So if you only want the current across the 50 ohms, you simply divide 100V by 50 ohms. However, at the same time, the current through the other two resistors is 100V/30 ohms = 3.33 A. But you did not need that information to proceed so there was no need to calculate it.

Hope this helps

Pat
 
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  • #3
ahhh i c now! thanks Pat, helped alot!
 

1. What is a source free RL circuit?

A source free RL circuit is an electrical circuit that does not have an external voltage or current source connected to it. In other words, there is no battery or power supply providing a constant flow of electrons to the circuit.

2. What is the purpose of a source free RL circuit?

The purpose of a source free RL circuit is to study the behavior of inductors and resistors in an isolated system. It allows us to understand the effects of self-inductance and resistance in a circuit without the influence of an external source.

3. What happens when a switch in a source free RL circuit is closed?

When a switch in a source free RL circuit is closed, the circuit becomes a closed loop and current begins to flow through the inductor and resistor. The inductor will initially resist the change in current, causing it to build up gradually. This results in a voltage drop across the inductor and a corresponding current flow in the circuit.

4. Does the current ever end in a source free RL circuit when the switch is closed?

No, the current does not end in a source free RL circuit when the switch is closed. The inductor will continue to resist the change in current and maintain a steady flow of electrons in the circuit. However, the rate of change in current will decrease over time as the inductor reaches its maximum current capacity.

5. How does the current in a source free RL circuit behave over time?

The current in a source free RL circuit will behave in an exponential manner over time. When the switch is first closed, the current will increase rapidly, but as the inductor reaches its maximum current capacity, the rate of change in current will decrease. Eventually, the current will reach a steady state where it remains constant until the switch is opened or the circuit is disturbed in some way.

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