I want to find the current through the 20Ohm resistor in the following diagram, but am stuck with four equations and five unknown currents.
I can apply Kirchoff's current law to each of the nodes either side of 20Ohm resistor, which gives me two equations. Applying Kirchoff's voltage law to the left and right loops yields another two equations. However, I need another relation in order to be able to solve them simultaneously.
Can I assume two "Virtual Earths", so that the bottom rails are both at 0V? That would allow me to make another large loop around the entire circuit to apply Kirchoff's Voltage Law again. However, if this works, I'm not sure why it's a valid approach.
Does anybody have some ideas about how to solve this? Thanks!