A graph of voltage V against current I (Fig. 1.7) is a straight line through the origin. It shows that voltage increases at a directly proportional rate to the current.
I (A)
FIG. 1.7 F (Hz)
Inverse proportionality
It is easier to see relationships between variables if the graph plotted is a straight line. For example, Fig. 1.8 shows the results of an experiment testing frequency F against length l. The results for length have been plotted as 1
The graph is a straight line through the origin, showing that F is directly proportional to 1
__ l ; in other words, frequency is inversely proportional to
1 (l in metres) l
FIG. 1.8 F (Hz)
length. This means that as length increases, frequency reduces at a set rate.
Other proportional relationships
Sometimes the relationships between variables are more complex, but the same method works. For example, Fig. 1.9 shows the results of an experiment testing frequency F against tension T. The results for tension have been plotted as √
__ T . The straight–line graph indicates a proportional
relationship between frequency and the square root of tension. T (T in newtons) FIG. 1.9 CHAPTER 1 EXERCISE 1A
1. Express the following in standard SI units: (i) 3 km (ii) 2 mN (iii) 4 GHz (iv) 12 μs
2. Convert the follow quantities to prefi xed units: (i) 300 000 000 m s–1 (ii) 1000 m
(iii)
____________ 1 000 000 s
1 (iv) 2400 N
3. Determine the reading on each of these scales. (i) The micrometer in Fig. 1.10a (in mm):
(ii) The vernier scale in Fig. 1.10b (in degrees):
