Urgent first order RL circuit problem

Favour

Joined Jul 15, 2008
10
Hello
Kindly assist me with a solution to the attached first order RL problem. Looking forward to your response.

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thingmaker3

Joined May 16, 2005
5,083
My apologies for having prematurely closed this thread. The second file was similar enough to the first I thought it was the same one. Comparing them side by side, they are obviously different. I have re-opened this thread.

Ratch

Joined Mar 20, 2007
1,070
Favour,

Possible error. A resistor connected to the 2A source is valued at 2K ohms. Is that correct, given that all the other resistors are much, much smaller? Ratch

theamber

Joined Jun 13, 2008
325
To analyze this is a complex calculation with differential equations. First you need to simplify the circuit with one resistance and one impedance with the Thevenim equivalent.
Also note that after the switch is closed at t>infinity the inductance is equivalent to a short circuit. And the current through the inductance prior to closing the circuit was 0.
The natural response of t=0 is exactly equal to the steady state response with the switch closed, but should be oposite in sign.
The time constant with any resistor in series with an inductor is t=L/R or in general t=1/|s|.

Ratch

Joined Mar 20, 2007
1,070
Favour,

Well, lets see. Since I did not get any feedback from you on whether that 2k ohm resistor is correct, I am going to assume that the resistance is really 2 ohms. The inductor shorts everything east of its position. This means that it forms a current divider with 4 ohms and 2 ohms. Therefore at t=0 the steady state current through the inductor is 2/3 A, and Vo is zero. At t=infinity, the inductor will again short out Vo to zero.

Now that we know the initial conditions at t=0, we can calculate the transient starting from t=0. The best way to do this is a loop equation using Laplace transforms. It is easy to learn to apply them compared to learning to solve differential equations. Ratch

Favour

Joined Jul 15, 2008
10
Ratch,

Sorry, I was offline. You are correct, it is 2 ohms and not kilo ohms as indicated.
How did you arrive at current through the inductor to be 2/3A? Made several attempt without success.
Guys,

Ratch

Joined Mar 20, 2007
1,070
Favour,

How did you arrive at current through the inductor to be 2/3A?
By using the current division formula. See http://www.tpub.com/content/doe/h1011v1/css/h1011v1_134.htm

While the switch is open, we have two branches across the current source. One branch is 4 ohms and the other which includes the inductor is 2 ohms. Therefore the current through the inductor branch is 2*(4/(4+2)) = 4/3 . As you can see, I made an arithmetic error in my previous post. Ratch

Favour

Joined Jul 15, 2008
10
Looking at the problem, at what time does Vo reduce to 50% of its value at t=0? Please help!

Favour

JoeJester

Joined Apr 26, 2005
4,390
Looking at the problem, at what time does Vo reduce to 50% of its value at t=0? Please help!
Show us your attempts at solving the problem.