### Video Transcript

Complete the following
sentence. If the potential difference across
a resistor doubles, the current through it blank.

Here, we’re asked to complete the
sentence by filling in the blank. We’re asked how the current will
change through a resistor with constant resistance if the potential difference
across the resistor doubles.

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.

Since the resistor has a constant
resistance, Ohm’s law is telling us that the potential difference is proportional to
the current. This means that if the potential
difference is doubled to two times 𝑉, then the current must also be doubled to two
times 𝐼. Therefore, the correct answer to
complete this sentence is “doubles.” If the potential difference across
a resistor doubles, the current through it doubles.