In a circuit under test, a resistor R, is connected in series with an inductor L. An a.c. current ????????: Engineering Maths Assignment, UK

Task 2:

a) In a circuit under test, a resistor R, is connected in series with an inductor L. An a.c. current ????????, flows through this R-L combination, causing a voltage (????????????????) of � 40 7 � ???????? to be developed across the resistor, and a voltage (????????????????) of � 30 7 � ???????? to be developed across the inductor.

???????????????? is in-phase with ????????, and ???????????????? leads ???????? by 90????????. 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: ???????? = −7???????? − 6???????? + 9???????? and the magnetic field as: ???????? = 5???????? − 3???????? + 4???????? Determine the force F, as the cross product of the current vector and magnetic field vector, (i.e., find ???????? × ????????). 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.

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