The same network, driven by a 1 V test source

This is the circuit from the lecture, running. Change it and the answer changes with it:

• Click any component value to edit it, or drag components to rearrange.
• The wrench opens a step-by-step analysis — it chooses a reference node and writes the node equations. Leave its Domain on the DC operating point for this deck.
• The crosshairs probe reads a node voltage or a branch current, so you can check any intermediate result rather than only the final answer.

The 12 V source is gone and a 1 V test source has taken the load's place. It draws 0.4 A, so the network looks like $1/0.4 = 2.5\ \Omega$. Change the test source to 2 V: the current doubles and the ratio does not move.