Calculate the current flowing in the circuit in polar

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Reference no: EM132785999

Unit 8 Further Engineering Mathematics - BTEC Level 3 National Extended Diploma in Engineering

Purpose of this assignment:

Examine how matrices, determinants and complex numbers can be used to solve engineering problems

Scenario:

You have applied for a work placement at a local company as part of your training as a quality control (QC) and in-service Engineer. The company Training Manager has explained that a number of roles available that involve applying mathematical skills and knowledge.

The Training Manager has said that they would like to see how you approach solving engineering problems before deciding on the most appropriate role for you. This is the second set of problems that they have provided. The problems are based on matrices, determinants and complex numbers.

You have been asked to explore a range of engineering problems that will require you to solve problems involving matrices, determinants and complex numbers.

To do this:
Your tutor will provide you with a set of data for you to use to complete the following activities. You need to:

1 Use your given matrices to solve the problems. Give reasons if the procedure is not possible.

2 Calculate the determinant of each of your given 2x2 and 3x3 matrices

3 Solve your given pair of simultaneous equations (with two variables) using matrix and determinant methods.

Solve for A and F
4 Solve your given set of simultaneous equations (with three variables) using matrix and determinant methods.

Solve for B, C and D

5 Solve your given pair of complex numbers placing them on an Argand diagram.

(a) XA+F
(b) YF-A

6 Convert your pair of complex numbers to polar form

7 Complete multiplication and division of your pair of complex numbers in polar form
(a) X A.F
(b) X A/F

8 Convert the answers to rectangular (Cartesian) form

9 The two complex numbers A and F represent two reactance's connected in series.

Calculate the total reactance by finding their sum.

10 The complex numbers A and F represent two force vectors. Place them on an Argand diagram and calculate the difference between them.

11 Use your given values of A and F to represent the reactances Z1, Z2 (as shown in the circuit diagram).

Calculate the current flowing in the circuit in polar form if the voltage is v = 12∠0° and i = Z_Total.

Reference no: EM132785999

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