I often see the same method for computing voltage distribution in electronic circuits implying components whose V-I curves are not trivial.
For example, in a circuit implying a resistor and a LED having 2V / 20mA caracteristics, we substract 2V from the supply voltage to determine the remaining resistor's voltage, and we assume current in the whole circuit is 20mA to determine resistor's value using Ohm's law. But what about a direct computation? If the resistor's value is too low, the LED voltage would be higher than this ; on the other way, if the resistor's value is too high, the LED voltage will be lower.
Is there a standard way to compute voltage distribution directly, based on chosen components (i.e. the inverse of the method that determines other components)? And more generally, is the voltage distribution always unique?
Best Answer
Yes there is a general method, but its generally not useful.
If you go back to first principles, there is a equation for each component relating voltage and current. Let's simplify the problem to where one is a direct function of the other, like with your LED and resistor example. Put another way, there is only one degree of freedom to decide what each component is doing.
The problem then is a set of simultaneous equations. The general answer is to solve these simultaneous equations. Usually this is rather complicated and the extra level of accuracy is not necessary and even misleading because it exceeds the tolerance to which other values can be known.
In your specific LED and resistor example, you could solve this simple set of simultaneous equations visually with a graph. Plot the resistor and LED current separately, each as a function of the voltage of the node between them. You know one additional constraint, which is that the current thru both is the same. Visually, this means you look for the place the two curves intersect, because that is the point at which both have the same current.
Hopefully you can see that it gets a lot more complicated for anything but a simple contrived example.