How Kirchoffs voltage law can be a consequence of conservation of energy?
Electrical energy (flow of current) reaching a point in a circuit must equal the flow of energy away from the point (conservation of energy) provided no energy is lost as heat (wires are not red hot, etc.), regardless of the number of wires attached to the point. That would be similar to a river where all the water reaching a point (plane) equals all the water leaving the point regardless of tributaries or distributaries (ignoring evaporation, etc.). The current flows only under electrical pressure (voltage) much as water flows only under hydraulic pressure.