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