### Video Transcript

When an electric appliance of
resistance π
ohms is connected to the mains, the current intensity that passes
through it is πΌ amps. πΌ is inversely proportional to
π
. πΌ is given by πΌ equals 230 over
π
. 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, letβs say π¦
and π₯, are inversely proportional, we say that π¦ is proportional to one over
π₯. We can write that as an equation by
introducing the letter π, which we call the constant of proportionality. That gives us π¦ is equal to π
over π₯.

Often, weβll 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.

Letβs start by calculating the
intensity when the resistance is 115 ohms. Substituting π
equals 115 into our
formula gives us πΌ is equal to 230 divided by 115. 230 divided by 115 is two. So the intensity is two amps. When π
is 1060 ohms, the formula
becomes πΌ 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 πΌ and π
. Write down the letter of this
graph.

The graph πΌ is equal to 230 over
π
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 π¦ and π₯. π¦ is equal to one over π₯ has this
general shape. Notice how the graph never quite
reaches the axes. In this case, the π¦- and the
π₯-axes are called asymptotes. The graph of the inversely
proportional relationship, therefore, looks very similar. However, since all values for πΌ
and π
are positive, we only include the portion of the graph that falls in the
first quadrant β thatβs E.

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