# Video: Pack 3 • Paper 2 • Question 6

Pack 3 • Paper 2 • Question 6

03:47

### Video Transcript

When an electric appliance of resistance 𝑅 ohms is connected to the mains, the current intensity that passes through it is 𝐼 amps. 𝐼 is inversely proportional to 𝑅. 𝐼 is given by 𝐼 equals 230 over 𝑅. Work out the difference in the intensity of the current going through an appliance of resistance 115 ohms and the intensity of the current going through an appliance of resistance 1060 ohms.

When two variables, let’s say 𝑦 and 𝑥, are inversely proportional, we say that 𝑦 is proportional to one over 𝑥. We can write that as an equation by introducing the letter 𝑘, which we call the constant of proportionality. That gives us 𝑦 is equal to 𝑘 over 𝑥.

Often, we’ll be required to calculate the constant of proportionality in these sorts of questions. Here, though, we can see that the intensity and resistance are inversely proportional and the constant of proportionality is 230. We can, therefore, use this equation to help us find the intensity of the current for different resistances.

Let’s start by calculating the intensity when the resistance is 115 ohms. Substituting 𝑅 equals 115 into our formula gives us 𝐼 is equal to 230 divided by 115. 230 divided by 115 is two. So the intensity is two amps. When 𝑅 is 1060 ohms, the formula becomes 𝐼 is equal to 230 divided by 1060. 230 divided by 1060 is 0.2169 amps. Two minus 0.2169 is equal to 1.7831. A suitable level of accuracy for our answer is two or three decimal places. Correct to three decimal places, the answer is 1.783 amps.

Here are six graphs. One of the graphs shows an inversely proportional relationship between 𝐼 and 𝑅. Write down the letter of this graph.

The graph 𝐼 is equal to 230 over 𝑅 is an example of a reciprocal graph. In fact, no matter the value of the constant of proportionality, any two variables that have an inversely proportional relationship will be represented by a reciprocal graph.

We usually see reciprocal graphs in terms of 𝑦 and 𝑥. 𝑦 is equal to one over 𝑥 has this general shape. Notice how the graph never quite reaches the axes. In this case, the 𝑦- and the 𝑥-axes are called asymptotes. The graph of the inversely proportional relationship, therefore, looks very similar. However, since all values for 𝐼 and 𝑅 are positive, we only include the portion of the graph that falls in the first quadrant — that’s E.

In fact, only three of these graphs represent a proportional relationship between 𝐼 and 𝑅. Graph D represents a directly proportional relationship: 𝐼 is proportional to 𝑅. Graph C also represents a directly proportional relationship. In this case though, the shape of the graph suggests that 𝐼 is proportional to 𝑅 squared. And then, of course, there’s graph E, which shows an inversely proportional relationship: 𝐼 is proportional to one over 𝑅.