The current in a circuit varies inversely with the circuit’s resistance, measured in ohms. When the current is 40 amperes, the resistance is 10 ohms. Find the current if the resistance is 12 ohms. Round your answer to two decimal places if necessary.
So the current in a circuit varies inversely with the circuit’s resistance, measured in ohms. Well, first, let’s define a couple of variables. Now, you can choose any letters you like, but I’m gonna let 𝐼 be the current in amperes, and I’m gonna let 𝑅 be the resistance in ohms.
So if the current varies inversely with the resistance, it means that 𝐼 is directly proportional to one over 𝑅 or the current is equal to some constant — let’s call it 𝑘 — times one over 𝑅, which we could just write as 𝑘 over 𝑅. Now, we’re told that when the current is 40 amperes, so when 𝐼 equals 40, then the resistance is 10 ohms. So 𝑅 equals ten.
So let’s use this information to try to work out the value of 𝑘. We just express the relationship between the current and the resistance as 𝐼 is equal to 𝑘 over 𝑅. Now when 𝐼 equals 40, we can replace 𝐼 with 40 in our equation. And when 𝑅 is ten, we can replace 𝑅 with ten in our equation. Now if I multiply both sides by ten, I find out that 400 is equal to 𝑘 or 𝑘 is equal to 400. So I can now plug this back into my original equation and say that 𝐼 is equal to 400 over 𝑅. And I can use that equation to work out the answer to the final bit of the question.
Find the current if the resistance is 12 ohms. That means find the value of 𝐼 when 𝑅 is equal to 12. Well, we said that 𝐼 is equal to 400 over 𝑅. Now we’re saying 𝑅 equals 12; we can replace 𝑅 with 12 in our equation. So this means that 𝐼 is equal to 400 over 12. Well 400 and 12 are both divisible by four. 400 divided by four is 100 and 12 divided by four is three. So this is 100 over three or 33 and a third.
Now, a couple of things that we need to be aware of. The question said round your answer to two decimal places if necessary. So it doesn’t want us to give this exact answer of 33 and a third; it wants us to give our answer in decimal format to two decimal places. We also know that the current is measured in amperes. So the unit is amperes; it’s important to include those in our answer as well.
Well, 33 and a third is 33.3333333 and so on. So if we round that to two decimal places, that’s just going to be 33.33. The next digit is only a three, so that last three won’t round up. So our answer then is 33.33 amperes, correct to two decimal places.