# voltage\current sources

I read in a book that image-1 is not a valid connection since you apply on the same two terminals a and b different voltages however image -2 is said to be a valid connection and I don't understand why since even if i have the 5A current source it supplies current and does not effect on the voltages across it's terminals so the circuit remains with different voltages across it's terminals.

Thanks.

• Image 1 isn't valid because infinite current flows Sep 28, 2015 at 22:36

Pretend, for a moment, that there is a resistor between the positive terminals of the 10v and 5v supplies. Then the voltage across the resistor is 5 volts. So the current through the resistor is $$i = \frac{5}{R} amps$$ Since the two supplies are connected by a short circuit, with zero resistance, what do you think the current across point a is?

First thing first:

Ideal voltage source acts as a short circuit and sets voltage across its terminals. It is a mathematical construct that does not exist in real life. Its operation does not depend on current flowing through it.

Ideal current source acts as an open circuit and sets current flowing through its terminals. It is a mathematical construct that does not exist in real life. It's operation does not depend on voltage across its terminals.

Keeping that in mind, let's analyze picture one. Here we have two points, a and b, that are connected together. The voltage sources are here in parallel, meaning that one voltage source sets voltage of 10 V between a and b and the other sets voltage of 5 V between a and b. Here our mathematical model breaks down, since the voltage cannot at the same time be both 5 V and 10 V.
My advice here is not to think too much about current or anything else. As I mentioned before, ideal voltage source is there to help with modeling of a real-life circuit and in this case, the model breaks down. If you had say two batteries with shown voltages connected like that, you'd need more components to represent what is happening in real life.

Let's take a look at image 2. We have a simple circuit with a current source. Current source acts as a open circuit, so the voltage sources shown are not connected in parallel. Instead, the sources are connected in series. This way, the model doesn't break down, because we can have any voltage across the terminals of a current source and the voltage doesn't affect its operation.

The circuit from image-1 admits no solution. It's like trying to satisfy (solve) a systems of two constraints (equations) in one variable: x=10 and x=5, corresponding to the voltage from a to b. So what's the value of x that satisfies both of these simultaneously? The answer is none. As an aside, in a real circuit that is similar, but not identical to that from image-1, there will be a small (internal) resistance in series with both sources, which will lead to a solution because there's no single point where both voltage sources try to "win" (the series resistor separates them.) So you will have a point $a_1$ at 10V, a point $a_2$ at 5V and a non-zero resistance between them, though which a finite current will flow, such as illustrated below:

simulate this circuit – Schematic created using CircuitLab

Now regarding the circuit from your "image-2", note that the two voltage sources are separated, but by the current source. So there's no point at which they both try to win. I've redrawn the schematic:

simulate this circuit

There's also a 5V drop from $a_1$ to $a_2$ and a 5A current... which is numerically the same as saying there's a one ohm resistor between $a_1$ and $a_2$.