Question

The voltage of a circuit is the difference in each Coulombs potential energy at the negative pole, compared to the positive pole. At the negative pole, there's a whole wire for the electrons to pass through under the influence of the Coulombic forces; a whole wire with atoms between which they can accelerate, before transmitting their kinetic energy into the atoms.

The longer the wire, the more durations of acceleration (thus, the more kinetic energy is produced). But, the longer the wire, the more resistance there is, thus, the lower the amperage. A lower amperage means less acceleration between each collision (assuming constant wire diameter). So, as the wire gets longer, there's more durations of acceleration, but the acceleration is lower. The accepted answer to this Q claims that this is the explanation.

But I doubt these two factors cancel each other out such as to leave the voltage unchanged with change in wire length. That is, despite this, I still think a longer wire would mean more kinetic energy is produced. More kinetic energy means there must have been more potential energy that was transmitted into it; thus, the voltage must have been higher. But it isn't, so what gives?

There's the distance factor; the longer the wire, the further away from the charged poles of the battery the electrons get. However, this would then make the voltage dependent on how close you lay the wire to the poles, which is again contrary to the assertion that the voltage only depends on the battery.

Answer 1

Voltage is a characteristic of the energy source and remains unchanged with wire length. It is the electrical potential energy per unit charge, and a battery's voltage does not increase with longer wires; instead, increased wire length introduces more resistance and decreases current, thereby affecting power delivery.

Step-by-step explanation:

The crucial aspect to understand when considering how voltage is affected by wire length is that voltage is defined as the electrical potential energy per unit charge and is a characteristic of the power source, such as a battery, not the conducting wire. The confusion may stem from equating the voltage with the total energy transferred, but this is not correct. Instead, one should view voltage as an intrinsic property of the energy source that does not change with wire length or resistance.

When discussing kinetic energy and potential energy, it is essential to recognize that voltage is not the same as energy. Voltage is the energy per unit charge. Hence, longer wires do not lead to an increase in voltage; they introduce more resistance, which indeed causes lesser current to flow (according to Ohm's law) and hence lower overall power delivery, as power is the product of voltage and current. The voltage across a resistor decreases as current passes through due to the potential drop, calculated by the product of the current and resistance (IR).

The length of the wire close to the charged poles or battery terminals does not affect the voltage supplied by the battery because a battery maintains a specific voltage irrespective of the length of the wire connected to it. Alterations to voltage in a circuit involving a battery, such as a lead-acid battery, are typically due to chemical reactions within the battery that provide energy to the electrons, not the distance the electrons travel through the wire.