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Krichhoff's voltage law as conservation of energy

  1. Jul 18, 2015 #1
    Krichhoff's voltage law (kvl) is said to be conservation of energy but i couldn't get a satisfactory explanation for that,
    hence i tried of thinking one but i doubt its validity, my instructors at collage thought of it as something useless , i couldn't understand them !!
    I think somebody here can help me
    this is what i want to say -
    say, we have a simple circuit consisting of a battery(of emf E) and a resistor(of resistance R), so having connected them by ideal wires, we have electrons in the wire which sense the potential difference of the battery, and hence get some sort of energy
    then they move in the wire till they encounter the resistor,and then as krichhoff's law says the formerly energized electrons experience equal and -ve potential drop due to resistor so that net potential drop/ gain in the loop is zero.
    so i think this can be interpreted as - the resistor consumes all of the energy of the electrons provided to them by the battery and converts that to heat !!!!
    but the pitfall here in this logic is what happens to those electrons then , after they leave the resistor ??
    i couldn't think of that
    so is it correct or no ??
    i would like to have the answer on microscopic understanding , a classical point of view. i don't understand quantum mechanics
    But please keep the explanation simple i am in high school !!!
  2. jcsd
  3. Jul 18, 2015 #2
    Voltage (a.k.a electromotive force) is not energy. It's not even force. Instead it is the potential for force.

    When a charge, let's say an electron, is in a voltage field, it has a force exerted on it. But without the electron, there's no force. So voltage is kind of like half a force, or maybe ¾ths of a force.

    Consider gravity (often called a force depending on your model). Gravity only acts if there's a mass to act on. But gravity is itself caused by a mass somewhere. (The Earth perhaps?) So it's always a force, at least to itself.

    While voltage is often caused by a charge somewhere, it can also be caused by a magnetic field. So voltage is almost, but not quite a force. But when combined with magnetism, it becomes the electromagnetic force.

    Energy is (or is closely related to) force times distance. Thus an electron which moves up or down voltage changes its potential (electrical potential) energy. A resistor changes it to heat. An electron in free space would accelerate, changing it to kinetic energy. With some cleverness (an antenna, some circuitry) the potential can be converted to photons, and so forth.

    Clearly an electron at a certain voltage level has a fixed potential energy. If it leaves a fixed level, then comes back it will gain then lose (or lose then gain) the same amount of energy, coming back to the same potential. The path doesn't matter.
  4. Jul 18, 2015 #3


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    They are right: Useless.

    Kirchhoff says that the sum of voltage changes ( signs, directions included ) through a closed loop in a circuit = 0.

    Now, say that in your simple circuit, you call the nodes A and B. The battery is connected from A to B and the resistor is connected from B to A.
    You measure by a volt meter the voltage change ( through the battery ) from A to B and will read E. Now you include the voltage change through the resistor by moving the one probe from B to A. So now you are actually measuring the voltage change from A to A, and that must of course be zero ( ideal conductors ).
    ( As the sum of changes = 0, the voltage change across the resistor must be -E. )

    Kirchhoff never intended to make a new discovery, he just made systematic rules for electric circuits, which today especially are used by computers, analyzing complex circuits. Thanks to Kirchhoff for that. :smile:

    Ohm just said: V = R*I. No signs, no directions, no paths.
    Last edited: Jul 18, 2015
  5. Jul 19, 2015 #4
    Kirchoff's laws can be derived from Maxwell's equations, which in turn depend on the conservation of energy (and other things of course). The conservation of energy exists because certain universal laws (like Maxwell's equations) are unchanging in time. (See Noether's theorem.)

    Proving Kirchoff's laws from conservation of energy is a way to move from the simple to the complex. Mostly engineers try to move the other way, making complex rules simpler so they can be applied. So from an engineering point of view, it is useless.

    But from an artistic point of view it shows the elegance of the standard model. There is a great deal of awe in seeing how a complex system like the standard model (and presumably the universe from which it is drawn) all fits together. Is art useless? I don't think so. But don't expect to make much money this way.
  6. Jul 19, 2015 #5


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    According to my understanding, electrons in the resistor need more energy to maintain the current flow. So, inside resistor, their individual energy level is high. Once they come out in the conducting wire, the individual energy level drops. Heat is a part of their kinetic energy. I don't think "all" the energy is lost in the form of heat. For a given resistance and time, the energy lost as heat is proportional to the square of current.
  7. Jul 19, 2015 #6


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    The electrons will successively loose their energy, passing the electric field inside the resistor (counter-emf).
    Electrons have no significant kinetic energy, but have potential energy due to treir position in the field ( due to the electric potential at the location in the field ).

    Typically the speed of electrons in some conductor/resistor is measured in millimeters per minute: Not much kinetic energy in that.
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