Hello, I was reading the article given in this link http://www2.ignatius.edu/faculty/decarlo/kirchhoff.htm, of which pertains to Kirchhoff's Rules. In this article, these claims are made: "1. Voltage Rule. This is based on the conservation of energy: 'the sum of voltages around a closed conducting loop (that is, a circuit) must be zero' In other words, since voltage and work are related, we are saying the net work done must be zero." I understand that the battery provides the electrons with energy, that they may traverse the circuit; in addition, I understand that when the electrons (which make up the electric current) flow through the resistor collisions between the electrons and the resistor occur, which results in the electrons losing energy, corresponding to the electric potential drop. However, I don't understand why it's necessary that all of the energy is used up as the electrons flow through the circuit, isn't it possible that some (perhaps even all of them) have some remaining energy when they come to the threshold of the positive terminal? As I attempted to answer this question, I came across this article: http://farside.ph.utexas.edu/teaching/302l/lectures/node59.html They, too, make a claim that I am unsure of: "This rule [voltage rule] is also easy to understand...zero net work is done in slowly moving a charge around some closed loop in an electrostatic field." Why is zero net work done? I'd massively appreciate it if someone could help me resolve these questions. Thank you for your time.