Kirchoffs First and Second Law in this basic circuit:

[TheaterofHope]

Suppose I had this circuit:

I believe there are 3 different loops that current travels. I just don't know what they are (possibly one is ABCD)

Suppose I wanted to verify Kirchoffs first law:

That the sum of the EMF (voltage supply) and the "voltage drops" = 0.

How would I do this? I don't even know where the current is going. For one loop where will be the direction of current and what will be the voltage drops there? (specific values). Its just that there is a second voltage source and that confuses me where the voltage gets added and how is it negated.

Can you help me verify the first law. Once I get the voltage values I can calculate the current values and prove the second law as well.

 

[(*steve*)]

There is another very similar thread in this section. I recommend you read it.

https://www.electronicspoint.com/kirchhoffs-law-t264749.html

In general, if you have n unknowns, you need n equations. Each equation (for voltage) describes 1 loop. you only need to describe as many as you have variables (ensuring the variables are represented)

Yes, there are three possible loops. How many unknowns do you have? Which loops are easier to describe (and sometimes, which are relevant to describe)?

 

[(*steve*)]

Oh, you can't identify other loops? Are there any that contain XY?

 

[Laplace]

Suppose I wanted to verify Kirchoffs first law:

That the sum of the EMF (voltage supply) and the "voltage drops" = 0.

First, realize that you are not going to 'verify' Kirchoff's law by finding the answer. Rather you will be using Kirchoff's law in order to find the answer. For instance, when you assume the presence of a loop current, the voltage drops are expressed as IR drops - the product of the loop current times the component resistance. Write the loop equation as the sum of the voltage drops and voltage sources, then set it equal to zero (according to Kirchoff's law). If you find a solution to the equation, it will automatically 'verify' Kirchoff's law because the equation itself is the statement of Kirchoff's law. Second, in all but the simplest of circuits, assumed current loops will partially overlap - this is necessary to obtain a system of equations in a circuit where every part of the circuit affects every other part of the circuit. Again, when you solve the system of equations Kirchoff's law is 'verified' because each equation is a statement of Kirchoff's law.

 

[foTONICS]

I think mesh analysis may be of help here?

read up on this: http://en.wikipedia.org/wiki/Mesh_analysis


edit: sorry, superposition not mesh