Find Vx: Inductor Assumed to Have No Energy Stored

[tritium_3]

Homework Statement

find Vx for all t
inductor assumed to have no energy stored

[PLAIN]http://img651.imageshack.us/img651/773/circuitgt.jpg

Homework Equations

inductor v = L di/dt

unit step = 1 for t>0,
= 0 for t<=0

The Attempt at a Solution

using node voltage method, ground at the bottom, and "v1" for the top node

v1 = Ldi/dt ?
(v1 - .8 vx)/40 - 100u(t) + v1/60 = 0

2.5 v1 - 1.2Vx = 6000 u(t)

i fail.

Help anyone?

 

[Phrak]

"RL circuit with dependent voltage source and indep. current source with unit step"

Do you know what this shorthand means?

And do you know what the shorthand "inductor assumed to have no energy stored" means?

This looks like hasty notes scibbled in class, as the professor talks to fast. But it's important to know what these mean.

 

[tritium_3]

"RL circuit with dependent voltage source and indep. current source with unit step"

Do you know what this shorthand means?

And do you know what the shorthand "inductor assumed to have no energy stored" means?

This looks like hasty notes scibbled in class, as the professor talks to fast. But it's important to know what these mean.

OK, maybe the title isn't accurate of the circuit, but i listed everything in the circuit. excuse me if it has some other meaning.

and also I was trying to add addtional details, saying that there was no mention of stored charge in the inductor. But this problem isn't a tranisent problem anyway, so that has no relevance..

these are not scribbled notes, this is a homework assignment, on a printed piece of paper. It seems the instructor wrote this up too fast.

But If you cannot help me, just say nothing at all. I am no closer to finding the solution if you simply just question my methods of describing the problem.

 

[Phrak]

OK, maybe the title isn't accurate of the circuit, but i listed everything in the circuit. excuse me if it has some other meaning.

and also I was trying to add addtional details, saying that there was no mention of stored charge in the inductor. But this problem isn't a tranisent problem anyway, so that has no relevance..

these are not scribbled notes, this is a homework assignment, on a printed piece of paper. It seems the instructor wrote this up too fast.

But If you cannot help me, just say nothing at all. I am no closer to finding the solution if you simply just question my methods of describing the problem.

No, no. The idea on this forum is that you show some work to get help. "Dependent" in this case means time dependent. The voltage of the voltage source is a function of time; it's time dependent. The current source is constant.

"Inductor assumed to have no energy stored" can't mean anything except that at some initial time there is no current flowing in the inductor. An inductor with current has stored energy, W=(1/2)Li². So when you set up your problem, at time t₀, set the current in the branch containing the inductor to zero.

You've been handed a lousy problem set-up. "unit step" is the function u(t) so it seems, so the current steps from zero to 100 amps at time t=t₀.

 

[tritium_3]

right. I was just using the notion commonly used in my textbook. The voltage source is dependent because it depends on the value of Vx. The current source is independent since it provides 100Amps constantly no matter what, after time 0. Using circle as independent, and diamond as dependent. that's all i meant.


thanks for the hint. i see that from -infinity to 0 the current hasn't changed, so the V in inductor is 0.
this makes the inductor a short circuit.
[PLAIN]http://img7.imageshack.us/img7/8251/circuit2b.jpg



this is at time 0-
from -infinity to right before current source turns on.
[PLAIN]http://img695.imageshack.us/img695/8900/circuit2.jpg

 

[Phrak]

right. I was just using the notion commonly used in my textbook. The voltage source is dependent because it depends on the value of Vx. The current source is independent since it provides 100Amps constantly no matter what, after time 0. Using circle as independent, and diamond as dependent. that's all i meant.


thanks for the hint. i see that from -infinity to 0 the current hasn't changed, so the V in inductor is 0.

You have everything right, but backwards. It's the language that is confusing you.

The voltage source is said to be indepentent of time, because it doesn't change over time. It's constant.

The current source changes at the time, t₀, so it is said to be dependent upon time.

Initially, at time, t₀ there is no current flowing in the capacitor so it looks like an open circuit. It looks like an infinite valued restistor for just a moment.

At time t₀ the current suddenly changes from zero to 100 amps. This places a voltage across the 40 ohm resistor. This places a voltage across the inductor. When a step change in voltage is placed across the inductor, the current will initially increase at a constant rate. But it starts at zero.

I have to go; it's 3:30 AM here.