When you have obtained your results, the next thing to do is to analyse them. Very often this will be done by plotting a graph.
You may be asked to plot a graph in a particular way, however, the general rule is that the variable you control or alter (the independent variable) is plotted on the x-axis and the variable that changes as a result (the dependent variable) is plotted on the y-axis.
In the example in Table P1.1, the length of the wire would be plotted on the x-axis and the current (or $\frac{1}{{current}}$) would be plotted on the y-axis.
You should label your axes with both the quantities you are using and their units. You should then choose your scales to use as much of the graph paper as possible. However, you also need to keep the scales simple. Never choose scales that are multiples of $3, 7, 11$ or $13$. Try and stick to scales that are simple multiples of $1, 2$ or $5$.
Plot your points carefully using small crosses; dots tend to disappear into the page and larger dots become blobs, the centre of which is difficult to ascertain.
Many, but not all, graphs you meet will be straight lines. The points may not all lie exactly on the straight line and it is your job to choose the best fit line. Choosing this line is a skill that you will develop through the experience of doing practical work.
Generally, there should be equal points either side of the line (but not three on one side at one end and three on the other at the other end). Sometimes, all the points, bar one, lie on the line. The point not on the line is often referred to as an anomalous point, and it should be checked, if possible. If it still appears to be off the line it might be best to ignore it and use the remaining points to give the best line. It is best to mark it clearly as ‘anomalous’.
In Figure P1.11, the line chosen on the first graph is too shallow. By swinging it round so that it is steeper, it goes closer to more points and they are more evenly distributed above and below the line.

Deductions from graphs

There are two major points of information that can be obtained from straight-line graphs: the gradient and the intercept with the y-axis. When measuring the gradient, a triangle should drawn, as in Figure P1.12, using at least half of the line that has been drawn.

$\begin{array}{l}
gradient = \frac{{change\,in\,y}}{{change\,in\,x}}\\
 = \frac{{\Delta y}}{{\Delta x}}
\end{array}$

In the mathematical equation $y = mx + c$, m is equal to the gradient of the graph and c is the intercept with the y-axis. If c is equal to zero, the graph passes through the origin, the equation becomes $y = mx$ and we can say that y is proportional to x.

Curves and tangents

You also need to develop the skill of drawing smooth curves through a set of points, and drawing tangents to those points. When drawing curves, you need to draw a single smooth curve, without any jerks or feathering. As with a straight line, not every point will lie precisely on the curve, and there should be a balance of points on either side.
In the first graph of Figure P1.13, the student has joined each of the points using a series of straight lines.
This should never be done. The second graph is much better, although there is some feathering at the lefthand side, as two lines can be seen. The third graph shows a well-drawn curve.

Figure P1.13: For Question 14.