Task 2:
a) In a circuit under test, a resistor R, is connected in series with an inductor L. An a.c. current ๐๐, flows through this R-L combination, causing a voltage (๐๐๐ ๐ ) of ๏ฟฝ 40 7 ๏ฟฝ ๐๐ to be developed across the resistor, and a voltage (๐๐๐ฟ๐ฟ) of ๏ฟฝ 30 7 ๏ฟฝ ๐๐ to be developed across the inductor.
๐๐๐ ๐ is in-phase with ๐๐, and ๐๐๐ฟ๐ฟ leads ๐๐ by 90๐๐. Draw a vector diagram for this arrangement and calculate the magnitude of the total voltage across the whole R-L combination.
b) You are measuring the force F, acting on an electrical conductor, which is subject to a strong magnetic field. The current may be modelled in three dimensional space as: ๐ผ๐ผ = โ7๐๐ โ 6๐๐ + 9๐๐ and the magnetic field as: ๐ต๐ต = 5๐๐ โ 3๐๐ + 4๐๐ Determine the force F, as the cross product of the current vector and magnetic field vector, (i.e., find ๐ผ๐ผ ร ๐ต๐ต). Using a 3-dimensional Cartesian axis system, draw all three vectors, or use software to do so.
c) Using the dot product, determine the angle between the current vector and the magnetic field vector.
