I've been studying about circuits lately and I have a difficulty when applying Kirchhoff's rules. My question has to do with how can I find how many currents are in a circuit. I know about junctions etc and how it splits. But for example, when you have 2 or 3 batteries how many currents are there and which current runs through each resistor? I've been trying to practice online and I came accross this circuit: And I dont understand why there are 3 currents when there are 4 batteries. Can anyone help me please?
How many currents there are has nothing to do with how many batteries there are. Each uninterrupted part of the circuit will have its own amount of current going through it. If two batteries are in that same part, they will carry the same current ($E_3$ and $E_4$ in your case).
An uninterrupted part in this case means any stretch of circuit that does not have any way for current to leave (like a junction).
Instead of current, you can also think of it as a liquid going through pipes to make the intuition easier.