- Joined Oct 2, 2009
This is like asking what the voltage is across two ideal voltage sources in parallel -- the solution is indeterminate.Here is an interesting problem posted by @MrAl in another thread.
View attachment 172577
Two ideal current sources set for different current values are in series in a circuit.
What is the total current in the circuit?
I will provide an answer after you have had a chance to think about it.
So where is the answer that you said you would provide?All good answers.
But if you have an answer to the original question, what need is there to make it more manageable? In particular, what is it that is in need of managing?Let us see if we can make the problem more manageable.
Modeling a Norton source (an ideal current source in parallel with an equivalent resistance) as a Thevinen source (an ideal voltage source in series with an equivalent resistance) only works for finite-valued parameters.We will model a constant current source as capable of having an infinite voltage source and infinite series resistance.
If you are going to do this, you don't need to go through the break in the first place. Simply place a 1 TV limit on the voltage of your current sources and restrict the output resistance to be any nonnegative finite value. You can always then examine the behavior in the limit that the resistance becomes arbitrarily large.Now let us impose some real-world limitations. We will set a limit on the voltage to 1TV.
The series resistance can be any positive value from 0 to ∞ ohm.
To what end? What is the point of the exercise?Have a go again.
Hi,Here are my answers I wish to offer.
1) As many members have said, the current is indeterminate. This is a theoretical problem with an obvious paradox.
2) If we were to model an ideal current source as an infinite voltage source with infinite impedance, we can still apply Ohm's Law,
I = V / R
where we apply limits to infinity
I = (V → ∞) / (R → ∞)
For every large value of V, there is a value of R which will result in a finite value of I, and vice versa. This is still solvable.
There are two possible cases, (a) where the current source is bipolar, i.e. the direction of the current can be reversed, and (b) where the current source is unipolar, i.e. the direction of the current cannot be reversed.
Let us consider the limitation of (b) where the current source cannot change polarity.
The second limitation I wish to impose is that the maximum voltage is limited.
View attachment 172655
Using the above model of infinite voltage V and infinite resistance R for each current source, I will assume that source A is set for a higher source current than B.
As source A attempts to increase the current through the loop, VA will reach its maximum value and RA will be forced to zero.
Simultaneously, source B will attempt to reduce the loop current by setting VB to zero and RB in response to VA.
Thus the current I in the loop is VA / RB.
The lower current setting wins.
According to my analysis, @mvas takes home the prize.
Hi,I am saying that there is no solution for "ideal" current sources.
If you impose "real-world" limitations then there is a solution.
P.S. This is the difference between science and engineering.
In science, you work with ideal hypothetical concepts.
In engineering, you have to look outside the box, be pragmatic and ask "what if" questions. What if this is not an ideal case? What if we impose real world limitations?
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