What is the maximum current in a RL circuit using V=IR?

[skibidi]

Homework Statement

The switch in a series RL circuit with a resistance of 5.8 Ω , inductance of 3.6 H, and
voltage of 23.7 V is closed at t = 0.5 s.
What is the maximum current in the circuit?
Answer in units of A.

Relevant Equations

I(f) = I(1-e^(-t/T))

I found the time constant using L/R and got 0.62s (3.6H/5.8ohms)
I found the initial current V/R and got 4.086A (23.7V/5.8ohms)

I(f) = 4.086A(1-e^(-0.5s/0.62s))
Then I plugged it into the equation and got 2.26A and it was wrong

 

[DaveE]

The exponential current response starts when the switch is closed at t=0.5 sec. That piece of information doesn't appear in your equation. Would you expect the same equation if it closed at t=1 sec, t= 100sec?

I suggest you draw a graph of that equation and compare it to your intuition about how the circuit will work.

 

[Gordianus]

Homework Statement: The switch in a series RL circuit with a resistance of 5.8 Ω , inductance of 3.6 H, and
voltage of 23.7 V is closed at t = 0.5 s.
What is the maximum current in the circuit?
Answer in units of A.
Relevant Equations: I(f) = I(1-e^(-t/T))

I found the initial current V/R and got 4.086A (23.7V/5.8ohms)

4.086 A isn't the initial current

 

[skibidi]

I found that to be the maximum current

 

[skibidi]

Would I use the equation I used to solve for the current at a given time such as 1s.

 

[Gordianus]

The equation you wrote assumes the switch closes at t=?

 

[skibidi]

0.5

 

[skibidi]

So would t be the duration since 0.5s, Some t value - 0.5s

Let's say that I had to find the current at 1.1s, so would use the equation and substitute t for 0.6s.

Would it be either
I = 4.09A(1-e^(-1.1s/(L/R))
or I = 4.09A(1-e^(-0.6s/(L/R))

The second one was correct

 

[skibidi]

I hate this so much...

 

[DaveE]

Sketch a graph of the waveform $v(t)=1-e^\frac{-t}{T}$ versus $t$ where $T$ is a constant, like 0.6 sec. What (where) is it's maximum value?

 

[DaveE]

here are some good online explanations about transient response in simple circuits:

https://www.khanacademy.org/science...xt=Transient period,response of the ‍ circuit.

https://eng.libretexts.org/Bookshel...uctors/9.5:_Transient_Response_of_RL_Circuits

https://ocw.mit.edu/courses/6-071j-...26d65de20ceb97d8d23f38a4_transient1_rl_rc.pdf

 

[Steve4Physics]

I hate this so much...

1. Don't give up! You are making a very simple mistake.

Relevant Equations: I(f) = I(1-e^(-t/T))

2. How's your maths? Suppose the switch is closed at t=0. Can you look at this equation and say how big the current is at t=0? And can you say how big the current is a long time later (when t is very large)?

I found the time constant using L/R and got 0.62s (3.6H/5.8ohms)

Ok. But the irony is that you don't need the time constant to answer the question! (You don't even need the value of L or the time at the switch is closed! They are 'red herrings'.)

I found the initial current V/R and got 4.086A (23.7V/5.8ohms)

3. The initial current is not 4.086A. (If you were using a capacitor rather than an inductor, you would be correct. Maybe that was in the back of your mind.) With the inductor, what is the current the moment the switch is closed? (Hint - see item 2 above).

I(f) = 4.086A(1-e^(-0.5s/0.62s))
Then I plugged it into the equation and got 2.26A and it was wrong

4. It should have been obvious that something was wrong!. 2.26A is smaller tha 4.086A. So 2.26A could not be the maximum (biggest) current!

5. Go back and read through the replies. @DaveE and @Gordianus were giving big hints. The question is really easy (no complicated maths) once you understand what's going on. Let us know if you're still stuck.

 

[Mister T]

I hate this so much...

Why are you focused on the time constant? That's just a value of $t$ for a particular value of $I$.

I suspect you are attempting success in the course using an answer-making strategy. But the entire purpose of the course is to get you to develop sense-making strategies.

This is the disconnect that's the cause of your frustration. Try to make sense of what's happening in that circuit, then the answer will come to you easily.

Develop that skill and you'll be successful in the course without those negative emotions like frustration and hate.

 

[dfghjkl]

For max current you literally only have to use the V=IR formula.