# Question Video: Recalling How the Current through a Resistor Changes When the Potential Difference across It Increases Science

Complete the following sentence: As the potential difference across a resistor increases, the current through it ＿.

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### Video Transcript

Complete the following sentence. As the potential difference across a resistor increases, the current through it blank.

Here we are asked to complete the sentence by filling in the blank. We have an electric circuit and are told that the potential difference across a resistor with a constant resistance is increasing. And we are trying to figure out what would happen to the current in the resistor. Let’s begin by looking at Ohm’s law, the expression we need to figure out the right answer.

Ohm’s law states for two points in a circuit the potential difference across the points equals the current between the points multiplied by the resistance of the object between the points. Ohm’s law can be written as an equation, where 𝑉 stands for the potential difference across the resistor, 𝐼 stands for the current in the resistor, and 𝑅 stands for the resistance of the resistor. Because we are interested in what would happen to the current, we must make current 𝐼 the subject of the equation.

We can do this by dividing both sides of the equation by the resistance. This gives us the equation current 𝐼 is equal to the potential difference 𝑉 divided by the resistance 𝑅. Now that we have this, we can see how current is affected by a change in potential difference or resistance. As the potential difference increases — notice that potential difference is in the numerator of the expression — the current will increase as well.

Therefore, the correct answer to complete the sentence is “increases.” As the potential difference across a resistor increases, the current through it increases.