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

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