Video: Using Ohm’s Law to Find the Current through a Resistor

A 10 Ω resistor in a circuit has a potential difference of 5 V across it. What is the current through the resistor?

01:16

Video Transcript

A 10-ohm resistor in a circuit has a potential difference of five volts across it. What is the current through the resistor?

We see that, in this problem, we want to connect these three things: resistance, potential difference, and current. We can recall a mathematical relationship that does connect all three, called Ohm’s law. This law tells us that if we have a resistor whose value doesn’t change based on how much current is running through it, then if we multiply that resistance by the current running through it, we’ll get the potential difference across it. In this instance, it’s safe to assume that our 10-ohm resistor indeed has a constant resistance value, that 10 ohms won’t depend on the current running through the resistor.

Therefore, we can safely apply this relationship that the potential difference across this particular resistor is equal to the current through it times its resistance. As it’s written, this equation has a solving for potential difference. But of course, we don’t want to solve for potential difference.

We want to solve for current. To do that, we can rearrange this equation so it reads 𝐼 is equal to 𝑉 divided by 𝑅. And from our problem statement, we have values of 𝑉 and 𝑅 that we can substitute in. We’re working with a 10-ohm resistor. And the voltage across it is five volts. And when we calculate this fraction, we find it’s equal to 0.5 amperes. Based on Ohm’s law, that’s the current running through this resistor.

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