A resistor in a circuit has a potential difference of 10 volts across it. The current through the resistor is 10 amps. What is the resistance of the resistor?
Okay, so in this question, we’ve been told that there is a resistor in a circuit and this resistor has a potential difference of 10 volts across it. We also know that the current through the resistor is 10 amps. What we’re asked to do is to find the resistance of the resistor. To do this, we first need to find a relationship between the potential difference across a component in a circuit, the current through that component in a circuit, and the resistance of the component.
The relationship that we’re looking for is known as Ohm’s law. What this tells us is that the potential difference 𝑉 across the component is equal to the current for that component 𝐼 multiplied by the resistance of that component 𝑅. And we can also recall that the standard units of each one of these quantities are the following: the potential difference 𝑉 — otherwise known as the voltage across a component — is measured in volts, the current is measured in amps, and the resistance is measured in ohms.
What this means is that if we’ve been given a voltage or a potential difference in volts and a current in amps, then once we rearrange the equation we’ll find out our resistance in ohms. So let’s start by rearranging the equation. We start with 𝑉 is equal to 𝐼𝑅. And since we’re trying to find out the resistance 𝑅, we want to isolate this on the right-hand side. So what we can do is divide both sides of the equation by the current 𝐼.
This way the current in the numerator and denominator on the right-hand side of the equation cancel out, leaving us with 𝑉 divided by 𝐼 is equal to 𝑅. At this point, all that remains is for us to plug in the values that we’ve been given for 𝑉 and 𝐼 and these values are 𝑉 is equal to 10 volts and 𝐼 is equal to 10 amps. 10 divided by 10 gives us a value of one. And as we mentioned earlier, the unit is going to be ohms. And at this point, we’ve arrived at our final answer: the resistance of the resistor is one ohm.