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In a circuit under test, a resistor R, is connected in series with an inductor L. An a.c. current ππ: Engineering Maths Assignment, UK
| University | City University of London (CUL) |
| Subject | Engineering Maths Assignment |
Task 2:
a) In a circuit under test, a resistor R, is connected in series with an inductor L. An a.c. current ππ, flows through this R-L combination, causing a voltage (πππ π ) of οΏ½ 40 7 οΏ½ ππ to be developed across the resistor, and a voltage (πππΏπΏ) of οΏ½ 30 7 οΏ½ ππ to be developed across the inductor.
πππ π is in-phase with ππ, and πππΏπΏ leads ππ by 90ππ. 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: πΌπΌ = −7ππ − 6ππ + 9ππ and the magnetic field as: π΅π΅ = 5ππ − 3ππ + 4ππ Determine the force F, as the cross product of the current vector and magnetic field vector, (i.e., find πΌπΌ × π΅π΅). 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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