Hi guys, I've realised that to truly, deeply, and fully understand something it often helps if you think about the conservation of energy, and then just build up from that.
So here I have tried to explain why a battery has a voltage, and why there are voltage drops across resistances, capacitances, and inductances, using the law of conservation of energy. This explanation should also help see the reasoning behind kirchhoff's voltage law.
However I'm very unsure if everything I have said is true, so it would help if someone could read it, and say if everything I have said is correct. Please be very critical, I want to fully understand this seemingly but not actually simple subject. One of the main uncertainties I have is when I say an electron has a kinetic energy. An electron does have a kinetic energy but i'm not sure if this is how the energy is transmitted along the circuit. Anyway, here is my explanation.
Applying the conservation of energy law to electrical circuits
A voltage is just a difference in electrical potential energy (EPE) between two places, per unit charge, where the electrical potential energy arises because of the forces between charges. If there is more electrical potential energy at one place than there is another, then a current will flow between these places until it causes the difference in electrical potential energy to equal zero. e.g in a wire with the electrons all bunched up at one end, the EPE here will be higher than at the other end, so electrons will flow until the difference in EPE at all places along the wire equals zero
In an electrical circuit a battery ensures that there is always more electrical potential energy at one side than there is the other (by using a chemical reaction to send electrons to the cathode), so a current constantly flows.
A voltage drop across a resistance occurs because some of the kinetic energy that the moving electrons have is transferred to the molecules inside the resistance (hence ohmic heating). For this situation, if we again consider the wire with a different EPE at each side, but this time with a resistor in the middle, then it will take longer for the flowing current to cause the difference in EPE to equal zero, as now each electron has less energy.(because some was lost due to ohmic heating)
A voltage drop across a capacitance is caused by the electrons building up on one side of the capacitor, and leaving the other side of the capacitor, causing an electrical potential energy difference between the two plates of the capacitor. In this case the energy of the electrons is being transferred back into electrical potential energy. The electrons will flow until the EPE per unit charge across the capacitor equals the EPE per unit charge from the source. In this case the energy is not transferred out of the circuit like it is with the resistance, it is just stored in the electrical field between the capacitor plates. If the source is removed, the EPE will be converted back into the kinetic energies of the electrons as they flow from the charged capacitor plate, and distribute themselves along the wire so that the electric fields created by each cancel each other out. If there was no resistance in the wire the kinetic energies of the charges could not be transferred, so the charges would forever oscillate between having maximum potential energy (when the capacitor plate is full) to having maximum kinetic energy (when the rate of discharge/charge is at its maximum). However this is not the case as a wire has a resistance, and the energies will be transferred out of the circuit as heat.
A voltage drop across an inductance is caused by a changing current, which creates a changing magnetic field, which induces an opposing voltage. In this case the energy from the electrons is being taken and stored in the magnetic field around the inductance. More specifically, the kinetic energies of the electrons are being transferred to magnetic potential energy, as the magnetic field opposes the acceleration of the electrons, and this causes them to have less kinetic energy, but energy is conserved because it is stored in the magnetic field around the inductance. (I'm very unsure about this one, it still doesn't make full sense to me)
So here I have tried to explain why a battery has a voltage, and why there are voltage drops across resistances, capacitances, and inductances, using the law of conservation of energy. This explanation should also help see the reasoning behind kirchhoff's voltage law.
However I'm very unsure if everything I have said is true, so it would help if someone could read it, and say if everything I have said is correct. Please be very critical, I want to fully understand this seemingly but not actually simple subject. One of the main uncertainties I have is when I say an electron has a kinetic energy. An electron does have a kinetic energy but i'm not sure if this is how the energy is transmitted along the circuit. Anyway, here is my explanation.
Applying the conservation of energy law to electrical circuits
A voltage is just a difference in electrical potential energy (EPE) between two places, per unit charge, where the electrical potential energy arises because of the forces between charges. If there is more electrical potential energy at one place than there is another, then a current will flow between these places until it causes the difference in electrical potential energy to equal zero. e.g in a wire with the electrons all bunched up at one end, the EPE here will be higher than at the other end, so electrons will flow until the difference in EPE at all places along the wire equals zero
In an electrical circuit a battery ensures that there is always more electrical potential energy at one side than there is the other (by using a chemical reaction to send electrons to the cathode), so a current constantly flows.
A voltage drop across a resistance occurs because some of the kinetic energy that the moving electrons have is transferred to the molecules inside the resistance (hence ohmic heating). For this situation, if we again consider the wire with a different EPE at each side, but this time with a resistor in the middle, then it will take longer for the flowing current to cause the difference in EPE to equal zero, as now each electron has less energy.(because some was lost due to ohmic heating)
A voltage drop across a capacitance is caused by the electrons building up on one side of the capacitor, and leaving the other side of the capacitor, causing an electrical potential energy difference between the two plates of the capacitor. In this case the energy of the electrons is being transferred back into electrical potential energy. The electrons will flow until the EPE per unit charge across the capacitor equals the EPE per unit charge from the source. In this case the energy is not transferred out of the circuit like it is with the resistance, it is just stored in the electrical field between the capacitor plates. If the source is removed, the EPE will be converted back into the kinetic energies of the electrons as they flow from the charged capacitor plate, and distribute themselves along the wire so that the electric fields created by each cancel each other out. If there was no resistance in the wire the kinetic energies of the charges could not be transferred, so the charges would forever oscillate between having maximum potential energy (when the capacitor plate is full) to having maximum kinetic energy (when the rate of discharge/charge is at its maximum). However this is not the case as a wire has a resistance, and the energies will be transferred out of the circuit as heat.
A voltage drop across an inductance is caused by a changing current, which creates a changing magnetic field, which induces an opposing voltage. In this case the energy from the electrons is being taken and stored in the magnetic field around the inductance. More specifically, the kinetic energies of the electrons are being transferred to magnetic potential energy, as the magnetic field opposes the acceleration of the electrons, and this causes them to have less kinetic energy, but energy is conserved because it is stored in the magnetic field around the inductance. (I'm very unsure about this one, it still doesn't make full sense to me)