WEBVTT
00:00:00.332 --> 00:00:04.952
A 10-ohm resistor in a circuit has a potential difference of five volts across it.
00:00:05.262 --> 00:00:06.932
What is the current through the resistor?
00:00:07.382 --> 00:00:13.042
We see that, in this problem, we want to connect these three things: resistance, potential difference, and current.
00:00:13.512 --> 00:00:17.822
We can recall a mathematical relationship that does connect all three, called Ohm’s law.
00:00:18.192 --> 00:00:28.712
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.
00:00:29.142 --> 00:00:37.582
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.
00:00:37.962 --> 00:00:45.672
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.
00:00:45.942 --> 00:00:48.952
As it’s written, this equation has a solving for potential difference.
00:00:49.122 --> 00:00:51.262
But of course, we don’t want to solve for potential difference.
00:00:51.262 --> 00:00:52.782
We want to solve for current.
00:00:53.202 --> 00:00:58.232
To do that, we can rearrange this equation so it reads 𝐼 is equal to 𝑉 divided by 𝑅.
00:00:58.682 --> 00:01:03.332
And from our problem statement, we have values of 𝑉 and 𝑅 that we can substitute in.
00:01:03.722 --> 00:01:05.572
We’re working with a 10-ohm resistor.
00:01:05.572 --> 00:01:07.562
And the voltage across it is five volts.
00:01:07.892 --> 00:01:11.882
And when we calculate this fraction, we find it’s equal to 0.5 amperes.
00:01:12.252 --> 00:01:15.352
Based on Ohm’s law, that’s the current running through this resistor.