Transient responses

Thread Starter

KevinEamon

Joined Apr 9, 2017
284
Ok so here's the new thread as advised by Wbahm. A sensible suggestion if I've ever heard one.
There's a few pics on this, so I uploaded it on pdf.

Fig.1
Is one of the easier ones. Now I just want to know if I'm doing that correctly? as seen in Fig.2.a-b

And lastly fig 3. what the heck is that thing? Ha joking, I can see it's some sort of function of t
but how to implement that? I've seen the deferential proofs of these things, so pleaseee if you can resist. My lil brain is running near to empty, at this present moment and definitely well above room temperature, in like an abnormal way.

Anyways yeh is there like a proper name for these topics? So I an investigate it further. I heard the lecturer mention a few. I seem to be studying - discharging capacitors and inductors. Then Charging the same elements, and possibly complete responses as well, though that may be the same thing.... sooo confused lul :confused:
 

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RBR1317

Joined Nov 13, 2010
713
Anyways yeh is there like a proper name for these topics?
These sort of problems are generally known as the first-order transient response to a step function. There will be a resistor network with a single capacitor or inductor, and a switch. In order to find the transient response you need to calculate the initial (t=0) and final (t=∞) values of the inductor/capacitor voltage/current. The path from the initial to final value will always be a rising or falling exponential function with a time constant determined by the circuit. In order to find the time constant you may need to calculate the Thevenin equivalent resistance as seen by the inductor/capacitor. Of course, it can become a little more interesting when there are multiple switches opened/closed at different times. Just focus on finding the initial value, final value, and time constant at each switch point.
 

MrAl

Joined Jun 17, 2014
11,389
Haha doh. Assuming that calculation was true; though it's not. Would the overall structure be correct?
Hello there,

The circuit you've drawn looks correct although a little hard to read, but the solution you assume is not correct.

When you apply a step change to an energy free RL series circuit, the inductor initial current is ZERO.
The form is A*(1-e^(-a*t)) not A*e^(-a*t). That's because the current starts out at zero and then builds up, just like how a voltage builts up in a capacitor in a series RC circuit.

The two forms are:
Xo=Xs*(1-e^(-a*t))

and:
Xo=Xi*e^(-a*t)

The first is when the quantity is increasing, the second when it is decreasing.
Xo is the response, Xs is a source, Xi is an initial value.

There is a third form for when the quantity is increasing and there is also some initial energy in the storage element. This is:
Xo=(Xs-Xi)*(1-e^(-a*t))+Xi
 
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Thread Starter

KevinEamon

Joined Apr 9, 2017
284
No it's definitely a discharge for that question. I came across it in my notes and the curve is decreasing exponentially. Perhaps I should have included the question. It says : In the following circuits find the response of the capacitor at t>=0.

The topic is called transient responses of RC circuits.

But the notes definitely show a decreasing curve.
 

MrAl

Joined Jun 17, 2014
11,389
No it's definitely a discharge for that question. I came across it in my notes and the curve is decreasing exponentially. Perhaps I should have included the question. It says : In the following circuits find the response of the capacitor at t>=0.

The topic is called transient responses of RC circuits.

But the notes definitely show a decreasing curve.
Hi,

Are we looking at different circuits? The circuit i saw definitely had an inductor in it.
Post another pic of your circuit and i'll be happy to take another look.
Those equations still apply however, and you do have to pick the right one.
 

Thread Starter

KevinEamon

Joined Apr 9, 2017
284
Oh doh. Sorry I was looking at tutorial 4, which I was working on, at the time. So basically swap - capacitor with inductor and rc with rl and that's what the question asks.

what I'm most concerned about is this amp source that says 10 u(-t) A.
shown in fig 3.

I don't know how to deal with it
 

RBR1317

Joined Nov 13, 2010
713
...this amp source that says 10 u(-t) A.
shown in fig 3. I don't know how to deal with it
"The Heaviside step function, or the unit step function, sometimes denoted by u(t), is a discontinuous function whose value is zero for negative argument and one for positive argument." https://en.wikipedia.org/wiki/Heaviside_step_function

The unit step function can be used to model the closing of a switch at t=0, or the opening of a switch at t=0.
 
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