[Physics] Why does voltage depend on the conductor resistance in a circuit

electric-circuitselectrical-resistancevoltage

As far as I know electric potential is a characteristic of a point in space and the difference in electric potential (voltage) is the difference between the electric potential of two points.

I was also taught that the electric potential of a point with respect to a charge depends on the charge and the distance from the charge. Also the electric potential of a point due to a system of charges is the sum of the electric potentials caused by every single charge of the system.

Now, in an electric circuit I assume that the Voltage of a battery is caused by a spot where there are more negative charges (negative terminal) and a spot where there are more positive charges (positive terminal). Since the electric potential as discussed above depends just on the system of charges and distances, I expected that the voltage would change just in base of the distance between a terminal, but Ohm's Law states that the voltage changes also because of the characteristic of the conductor (Resistance).

I can think of this drop as the potential energy transformed into heat because of the collisions with the conductor particles, but I find this contrasting with the definition of voltage I was given.

Can anyone help me to solve this doubt?

Best Answer

but Ohm's Law states that the voltage changes also because of the characteristic of the conductor (Resistance).

Actually, Ohm's law does not state that. Ohm's law is just a relationship between - in this case - 3 parameters: Resistance $R$, current $I$ and voltage $V$.

$$V=RI$$

But while it is the relationship between them, it does not state which ones are dependent and will change when another one changes. That depends on the situation.

In the case of a battery connected to a simple circuit, we know that the voltage is constant. Regardless of the resistance in the circuit, the voltage is always, say, 5 V across the two battery terminals. This is true when not connected (open-circuit, effectively infinite resistance), when connected (some specific value of resistance) and when short-circuited (effectively zero resistance).

The voltage is constant and doesn't depend on the resistance that happens to be in the way. So, when looking at Ohm's law, what is then changing, if not $V$? Mathematically, you are right that something else must change when $R$ changes. But it doesn't have to be $V$ - it can also be $I$. And it is.

Think of $V$ as the "pressure" that "pushes" on charges.

  • In the open-circuit case, they are being pushed with 5 V, but they still can't move because there is no conducting path - infinite $R$ but zero $I$. Ohm's law obeyed.
  • In the connected case, they are being pushed still with 5 V, and they flow with whichever current $I$ that fulfills Ohm's law. $R$ limits and alters $I$, not $V$.
  • In the short-circuit case, they are still being pushed with 5 V and this time nothing stops them. They speed up and up and up. At any flow speed (current), the 5 V pushes them faster to gain higher speed, which continues forever (or until the heat generated melts the wire). $R$ is zero and $I$ infinite - Ohm's law obeyed.

In general, be careful when reading a mathematical formula. It only shows a relationship between parameters - it doesn't show which of them that are dependent and which that are fixed. That depends on the particular situation.

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