A current waveform in a robotic arm

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)