# Confusion about relationship between energy per coulomb, and the amount of coulombs in current

I am trying to understand how a power supply works and working from the ground up I am learning about electricity, voltage, current, amps, and wattage. I am new to this stuff so I apologize if this is an easy or already answered question.

From what I have read so far, here is my understanding:

• electricity in a current is the movement of free electrons through a conductive material. The free electrons "hop" from one atom to the next.

• a coulomb is a unit of charge.

• Charge by itself is just a property of an object, number of electrons or lack thereof. When charges are separated, they create an electric field, which then allows you to define potential energy that an object in the field would have, depending on its location in that field, regardless of its charge. The potential energy is the Joules/Coloumb at that specific point in the e-field, which is volts. If you take volts * charge of object in the field at that point, you get the electric potential energy that the charge would carry.

• That electric potential energy is converted to some other energy for useful work as the charge moves through the current - light, heat, or power for a component. This is analogous to how potential energy of a falling object in a gravitational field is converted to kinetic energy.

• The AMOUNT of charge, moving past a specific point, is the Amperes. This is a rate measurement in coulomb's per second.

• Voltage and Amps are directly proportional. If you take voltage, which is joules per coulomb, and you take amps, which is coloumbs / s, and you multiply them, you get joules / s. This intuitively to me, means the amount of energy that can be provided to some component in a circuit, per second. This is Watts.

My confusion is that I don't understand the relationship between "amount of charge" and "energy of charge". A common analogy used here is water and water pressure. If I have a tank filled with water, and I attach a hose at the bottom, and I apply X amount of pressure, a certain amount of water (measured volume of water) will move past a certain point in the hose at a rate of Y. If I increase X, then the water molecules move more quickly through the hose, meaning numerically more water molecules move past the certain point, so Y (flow rate volume / second) increases. So, more pressure causes water molecules to move faster, meaning more water gets through the hose - i.e more volume of water per second.

With voltage and charges, voltage is supposed to represent pressure. If I increase the voltage, the numerically more electrons - more units of charge - flow through the circuit. But due to what? In other words, my question is:

Which of the following is correct?

1. More couloumbs AND more energy per coulomb: When voltage increases, amount of energy per unit of charge increases. This means each unit of charge is more "energized", and BECAUSE of that, moves faster through the circuit. Faster charges means MORE charges move through the circuit per second, and because each charge is MORE energized, there is more joules per second at any given point in the circuit (more work).

2. More coulombs BUT same energy per coulomb: When voltage increases, more units of charge flow through the circuit. But each unit of charge still has the same amount of energy as before the voltage increase. The increase in potential energy is spread across more coulombs of charge.

3. Same number of coulombs BUT more energy per coulomb: When voltage increases, the number of coulombs flowing through the circuit remains the same, but the energy per coulomb increases.

I know 3 will not be true because of V = IR, but I want to understand this on an intuitive level. Does the increase in voltage equate to increase in energy per unit of charge, or does an increase in voltage keep energy per charge equal but forces more charges to flow through the circuit?

• Thinking about it further, I think the answer is 1. Given a certain voltage, n electrons are displaced, and each of those electrons moves at a certain speed through the circuit. When the voltage increases, the pressure increases. If there was only 1 free electron, it would move faster, have higher speed. With n electrons, all n electrons move faster. If all electrons are moving faster, then there is higher throughput of electrons, more electrons moving past a point per second. Thus, current increases. Furthermore, for an electron to move "faster", it probably needs to be more "energized". Dec 30, 2020 at 0:03
• "Voltage and Amps are directly proportional." No, not always. This is true for resistors, and the constant of proportionality is the resistance. Dec 30, 2020 at 0:31

electricity in a current is the movement of free electrons through a conductive material.

This is one kind of current. But it's also possible to have positive current carriers. Batteries and many kinds of transistors would not work if electrons were the only kind of current carrier.

Voltage and Amps are directly proportional.

This is true in a linearly resistive material. For example in a copper wire or a resistor.

In other components, there will be a different relationship. For example, in a (junction) diode the current goes up exponentially with increased voltage across the device. In a transistor the current through one branch of the device may depend on the voltage across a different branch of the device.

Which of the following is correct?

Again, it depends what kind of device you are investigating.

More couloumbs AND more energy per coulomb:

This is the behavior of a resistor. If you increase the voltage across the resistor, by definition, you've increased the energy per coulomb lost as charge flows through the device. And, because of the nature of the resistor, you will also increase the current (rate of charge flowing through).

More coulombs BUT same energy per coulomb:

This would be the behavior of a voltage source when you change its load. You can increase or decrease the current you draw from it, but it will always (to the extent it's an ideal voltage source) produce the same potential across its terminals.

Same number of coulombs BUT more energy per coulomb

This is the behavior of a current source. You can apply whatever potential you want across it, and it will always (again, in the ideal case) produce the same current.

• Wait, i thought conventional current was just a convention. So there are actual positive charge carriers through a battery? Dec 30, 2020 at 1:11
• There are positive carriers in batteries, other ionic conductors, plasmas, p-type semiconductors, ... Dec 30, 2020 at 1:11
• Ok, to be honest this is still over my head. If I plug a device like a powersupply into a wall outlet of 110V, the power supply will receive some current. If I plug the same power supply into a wall with 220V, will I get more coulombs but same energy per coulomb since its a voltage source with a new load? Dec 30, 2020 at 1:22
• My main point is that whether a device draws more, less, or the same current depends on the design of that device. There is no universal law of nature that says it is always more. Dec 30, 2020 at 1:34
• It will depend what load is connected to the output of the power supplpy. Dec 30, 2020 at 2:06