# Why is the potential difference across a component not constant? [duplicate]

In the diagram above, the resistor has a constant resistance R.

We know that:

$$R=\frac{V}{I}$$ $$V\propto I$$

If the current increases, that means the rate of flow of charge (i.e. the speed at which the charge is flowing) has increased.

However, why should the potential difference across the resistor decrease to maintain the proportionality? The resistance of the resistor hasn't changed, so each coulomb of charge still needs to do the same amount of work on the resistor to flow through it.

In other words, the potential difference across a component is defined as the work each coulomb of charge needs to do on the component to flow through it. In that case, shouldn't the rate of flow of charge and the work done per unit charge be completely independent?

## marked as duplicate by Yashas, honeste_vivere, David Hammen, Jon Custer, Kyle KanosJul 5 '17 at 12:24

• Possible duplicate of The Difference Between voltage and current – QuirkyTurtle98 Jul 4 '17 at 15:40
• I think you are confusing the two expressions for potential and current as being different entities. If you look at the second form and assume a constant resistance, then how can the potential decrease when the current increases? – honeste_vivere Jul 4 '17 at 18:52

Hence, the question is how does the current increase? Answer: Such that $U/I$ is constant.