# Voltage drop and potential energy

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1. Jul 21, 2015

### r731

Hi!

What is the potential energy of electrons converted to, in a circuit? I'm asking this question because I don't really understand the concept of voltage drop across some element.

If I have a series circuit with a 10V battery and two equal-in-magnitude resistors, then the potential difference across one resistor is 5V. The battery gives each coulomb of charge 10 joules of potential energy. The current is constant across all the circuit.

So, as an electron passes the first resistor, some of its potential energy is converted into heat. But, before the electron reaches the resistor, why doesn't the potential energy convert to e.g. kinetic energy?
If the pulse pushing the electrons is a consequence of applied voltage, then what prevents the potential energy to be converted to kinetic energy, instead of heat?

I need to understand basics of electricity for my computer-related course.

2. Jul 21, 2015

### DEvens

Think of potential energy like a hill. An electron wants to slide down the hill.

Think of a resistor like a very rough surface on the hill. The roughness uses up the kinetic energy. The faster the electron slides the more the roughness works to slow it.

3. Jul 21, 2015

### r731

As far as I know, if voltage is applied, then electrons will move from lower potential to higher potential. A test charge is accelerated when in an electric field. But in circuits, electrons do not accelerate, why? And as they give up potential energy in the circuit, electrons do not decelerate, why?

4. Jul 21, 2015

### nasu

They do accelerate, between any two successive interactions with the lattice. Their energy (gained from the electric field) is transferred to the lattice during these interaction.
Typically in a metal there are 10^16-10^17 interactions per second, so it is not the same thing as an electron in empty space even though these conduction electrons are called "free electrons".

5. Jul 21, 2015

### sophiecentaur

The basics of EE do not include how electrons behave in metals and you really don't need that for the EE needed for a "computer related course", imo; it is a very sophisticated process to analyse fully. Once you realise that the way electrons behave in a metal is very different from the intuitive model that is so often bandied about, then you start to realise why EE discusses Charge and Current and ignores electrons in pretty well every situation.
The conduction electrons in a metal (about one for every atom) are in constant thermal motion with a whole range of velocities. They behave very much like a gas and move very freely through the lattice. This accounts for the good thermal conductivity because the fast electrons travel quickly, carrying heat easily from a cold region to a hot region. But the speed of the thermal conduction is actually pretty slow - just hold a copper rod in a flame and you can count several seconds before it's too hot to hold. Applying a voltage (a few millivolts, probably) across the wire will produce an (almost) instantly measurable current. The average drift velocity is only a few mm per second for a current of several Amps. The voltage drop corresponds to the amount of work done on moving the charge through the metal (A Volt is one Joule of Work per Coulomb of charge passed). But very little energy is used up as the charge passes through the connecting wire, it's only when there is a resistive element / light bulb or Motor etc that much energy is transferred (i.e.many volts may be involved so there will be a lot of energy transferred for every Coulomb of charge that flows.

Incidentally, the very same model which describes Thermal and Electrical conduction, also accounts for the physical nature of metals (metallic bonding) which makes metals very strong yet able to be bent, stretched and squashed without fracturing. The metal is held together by each of these dissociated electrons hanging on to many of the positive ion cores in its vicinity. 'Push' on the electrons at one end of a wire and a load of them will be pushed out of the other end. The resistance of the wire is the ratio of the volts you have to apply across it for a given amount of current to flow.

6. Jul 21, 2015

### cpsinkule

Heat is kinetic energy. Temperature is a sort of average of the kinetic energy of the ensemble of particles. The electrons do accelerate, but they bump into other "things" which generates heat.
I agree with sophiecentaur. Conductivity and the flow of electrons in a conductor at the level you are talking about is the realm of quantum mechanics and condensed matter physics and you won't learn it in detail for a standard engineering or E&M course.

7. Jul 22, 2015

### sophiecentaur

Perhaps that could be put in a better way. A simple electron beam, in a vacuum, would gain all the KE that the power supply could give it. Collisions / interactions every time an electron traverses a lattice space will randomise the velocities and the KE is distributed in a random way, corresponding to an actual 'temperature' increase. You can't really assign a temperature value to a beam of electrons but the majority of the internal energy in a metal is carried by the KE of the electrons (plus the vibrational energy of the metal ions). Being so much lighter, the electrons won't transfer much KE to much more massive ions but share it out amongst themselves. (That's a very crude, mechanical way of looking at it)