Calculating time constant of a circuit?

[rjackson]

Homework Statement

Here's a link to the circuit:
http://tinypic.com/view.php?pic=30js0wp&s=6
Initial current, t, and final current are given. Seeking time constant.

Homework Equations

I=Io (1-e^(-t/T)) where Io is initial current and T is the time constant. This is an RL circuit right?

The Attempt at a Solution

I used the equation above to calculate time constant, is that correct?

 

[gneill]

Homework Statement

Here's a link to the circuit:
http://tinypic.com/view.php?pic=30js0wp&s=6
Initial current, t, and final current are given. Seeking time constant.

Homework Equations

I=Io (1-e^(-t/T)) where Io is initial current and T is the time constant. This is an RL circuit right?

The Attempt at a Solution

I used the equation above to calculate time constant, is that correct?

Can you expand on the question statement? It's not clear what circuit conditions are implied... does the switch position change? What is meant by the "final current"? Is it the current at time t, or the eventual current after a very long time (t → ∞)? Are any component values specified?

 

[rjackson]

Sorry about that, here's the question:
An inductor, two resistors, a make-before-break switch an a battery are connected
as shown. The switch throw has been at contact e for a long time and the current in the inductor
is 2.5 A. Then, at t = 0, the throw is quickly moved to contact f. During the next 45 ms the
current in the inductor drops to 1.5 A. What is the time resistance for this circuit?

 

[gneill]

Sorry about that, here's the question:
An inductor, two resistors, a make-before-break switch an a battery are connected
as shown. The switch throw has been at contact e for a long time and the current in the inductor
is 2.5 A. Then, at t = 0, the throw is quickly moved to contact f. During the next 45 ms the
current in the inductor drops to 1.5 A. What is the time [STRIKE]resistance[/STRIKE] constant for this circuit?

Okay, that makes more sense. When the switch is thrown, will the current I increase to some new value, or decrease? What's the eventual value that it will approach? Given the answer to that query, does your choice of equation to describe the evolution of the current fit?

You have the right idea about using the given information in the appropriate equation to find the time constant; it's just a matter of making sure that your choice of equation is correct.

 

[rjackson]

Okay, that makes more sense. When the switch is thrown, will the current I increase to some new value, or decrease? What's the eventual value that it will approach? Given the answer to that query, does your choice of equation to describe the evolution of the current fit?

You have the right idea about using the given information in the appropriate equation to find the time constant; it's just a matter of making sure that your choice of equation is correct.

I was thinking that the current I would decrease after the throw and approach 1.5 A, so I used 2.5 as my Io and 1.5 as I or I(t). I used that equation because it's an RL circuit, and it gave me a positive value for the time constant so I believe it's correct. The other option I was considering was using I = Io(e^(-t/T)) because that also indicates decay, I'm just not sure which one is correct, because in my book it says to use the first equation if there is a battery in series.

 

[mukundpa]

I think when the switch is thrown from e to f the battery and R1 are out of circuit and only the L and R in the circuit. The current in the inductor decreases not growing. Thus the equation is not appropriate. Please go through the equation for the decreasing current.

 

[rjackson]

I think when the switch is thrown from e to f the battery and R1 are out of circuit and only the L and R in the circuit. The current in the inductor decreases not growing. Thus the equation is not appropriate. Please go through the equation for the decreasing current.

That makes sense. So in that case the proper equation is I = Io(e^(-t/T)), correct?

 

[gneill]

I was thinking that the current I would decrease after the throw and approach 1.5 A, so I used 2.5 as my Io and 1.5 as I or I(t). I used that equation because it's an RL circuit, and it gave me a positive value for the time constant so I believe it's correct. The other option I was considering was using I = Io(e^(-t/T)) because that also indicates decay, I'm just not sure which one is correct, because in my book it says to use the first equation if there is a battery in series.

Yes, the current will definitely decrease, since there's no source in the sub-circuit of interest once the switch is thrown, and the resistance R in it will dissipate energy. But there's more than one form of exponential function to describe the activity in an RL or RC circuit. One describes decay from a starting value to some ending value (often zero), while the other describes growth from a starting value (often zero) to some final nonzero value. Be sure to choose the correct form for the given case.