You work as a Test Engineer for a global manufacturer of electrical and mechanical
components and systems. Your Line Manager is responsible for delegating to you and your
colleagues the testing of theory, principles, and hypotheses from several worldwide
company divisions. She has asked you to undertake a series of such evaluations.

Task 1

Note: You need to have your calculator in radians (RAD) mode for this task (since the angles are
given in radians – i.e., π is featured).

a) A current waveform in a robotic arm may be described by…

is=13cos�2πft−π
4� [𝐴𝐴]

           where frequency, f = 1Hz and t represents time. 

Make time (t) the subject of this formula and hence determine a point in time when the
current waveform has a magnitude of +10A.

b) The instantaneous value of a power signal may be described by;

12∠�3π
8 � [W]

Find the magnitude of the vertical and horizontal components of this signal.
Note that the symbol ∠ indicates ‘angle’.

Task 2

a) A resistor, R, is connected in series with an inductor, L. An a.c. current, 𝑖𝑖, flows through this
RL combination, causing a voltage (𝑉𝑉𝑅𝑅) of 30V to be developed across the resistor, and a
voltage (𝑉𝑉𝐿𝐿) of 40V to be developed across the inductor.

Assuming that 𝑉𝑉𝑅𝑅 is in-phase with 𝑖𝑖, and 𝑉𝑉𝐿𝐿 leads 𝑉𝑉𝑅𝑅 by 90𝑜𝑜, draw a vector diagram for this
arrangement and then calculate the magnitude of the resultant voltage across the whole
RL combination.

b) A current-carrying filament is subjected to a strong magnetic field within an experimental
chamber. It is required to find the force on the filament. The current may be modelled in
three-dimensional space as:

�
�𝐼=2𝑖𝑖+3𝑗𝑗−4𝑘𝑘
and the magnetic field as:
�
�𝐵=3𝑖𝑖−2𝑗𝑗+6𝑘𝑘

Find the Cross Product of these two vectors to ascertain the characteristics of the force on
the filament (i.e., find 𝐼𝐼×𝐵𝐵).

Sketch this Cross Product (or use software to do so).

© 2024 UniCourse Ltd. All Rights Reserved

Page 3 of 4 Issue 1 – 2024/25

Task 3

PART 1
The two signals below are sensed by a signal processor;
�
�𝑣1=40sin(4𝑡𝑡)
�
�𝑣2=𝐴𝐴cos(4𝑡𝑡)
The signal processor adds the signals to form a third signal, which must be described as a distinct
signal in the following form;
�
�𝑣𝑜𝑜=50sin(4𝑡𝑡+𝛼𝛼)
Use a compound angle identity to determine the value of A (the amplitude of 𝑣𝑣2).
Ensure that you have your calculator in Radians (RAD) mode when determining your answer.

PART 2
The third harmonic of a sound wave is given by;
4cos(3𝜃𝜃)−6sin(3𝜃𝜃)
Express this sound wave in the form;
�
�𝑅sin(3𝜃𝜃+𝛽𝛽)