### 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.