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ACTIVITY 1

1. An engineer has completed two tests on two conductors.

The results of the tests are represented by the following expressions:
V = 15R + 5
V = 12R + 8

where V is the voltage and R is the resistance

(a) Plot the results of both tests on the graph paper for values of R between 0 and 4 ohms. Use appropriate scales and axes.

(b) Use the graph to identify when the voltage will be identical for the same
resistance value.

An engineering technician has measured the resistances of 25 resistors.
The values are shown below:
59, 65, 61, 62, 53, 55, 60, 70, 64, 56, 58, 58, 62, 62, 68, 65, 56, 59, 68, 61, 67, 62, 56, 60, 54

(c) Calculate the mean, median and mode values of the resistors.
The technician then groups the data into four ranges:
51–55; 56–60; 61–65; 66–70

(d) Produce a frequency chart for the data and then present the data as a histogram.

2. Use the laws of logarithms and indices to solve the following for the unknown values:

(a) log24 = logz + 2log2
(b) ln(6/x) = 3ln4
(c) logx = log 12 − 2 log 2 + log 3
(d) ln6x+3 = 7.2
(e) ln42x+5= 4.7
(f) The percentage increase of an amplifier is represented by the equation:
PI(%) = (y2 t)2

Solve the equation to find the value of y when the percentage increase is 64% and the value of t = 2.

3. Two AC voltage waveforms are represented by:
V1 = 100sin(100ωt) volts
V2 = 200sin(100ωt − π/6) volts

Draw a phasor diagram to represent the two waveforms and find the resultant value.

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