Reference no: EM132920775

Unit 52 Further Electrical, Electronic and Digital Principles - Higher National Diploma in ENGINEERING

Assignment - Mathematical techniques and circuit theorems for electrical systems.

Learning Outcome 1: Use appropriate mathematical techniques to solve a range of electrical and electronic problems.

Learning Outcome 2: Apply appropriate circuit theorems to solve problems in electrical networks.

Assignment Brief

SECTION 1 - YOU MUST PRODUCE BASIC SOLUTIONS TO THE FOLLOWING ELECTRICAL AND ELECTRONIC PROBLEMS:
1. (a) The current in an electric circuit is represented by I=7+j3 and the voltage is V=200+j4. Produce the impedance as a complex number.

(b) A circuit draws a current of 15A at a voltage of 220V and its p.f is 0.8 lagging. Produce a solution for the active power and reactive power.

(c) An ac load takes 3kW of power from a 110V supply at 60Hz. The current is 50A. Produce a solution for the power factor and the size of a capacitor required to correct it.

2. Clear logical steps must be shown for the following:
(a) Using the impedance in part 1(a), provide the resistance and reactance for that electric circuit.

(b) Using the active power and reactive power in part 1(b), provide the apparent power for that circuit.

(c) Using nodal analysis in Figure 1, provide the equations to find the voltage at each node of the circuit. Let Node 2 be the reference and thus V2=0.

3. Provide clear justifications and explanation of each step used in each method, by applying an accurate approach to solving:
(a) The voltages in the equations obtained for the nodal analysis in part 2(c).

(b) The current flowing in each branch of the circuit for the mesh analysis in Figure 2.

SECTION 2 - YOU MUST APPLY APPROPRIATE CIRCUIT THEOREMS TO SOLVE THE FOLLOWING PROBLEMS:

4. (a) Provide phasor solutions for the resulting current, I, in a faulted three-phase system, which is the sum of the current in the red phase IR=150sin(ωt), the yellow phase IY=40sin(ωt+90°) and the blue phase IB=90sin(ωt+180°).

(b) Assuming the sources are ideal and using superposition theorem in Figure 3, provide the value of the current in RL due to the DC source.

5. (a) Using the solution in part 4(b) and by providing the value of the current in RL due to the AC source, state the total current in the resistor RL.

(b) Use Thevenin's theorem to find the voltage for the circuit external to RL in Figure 4.

6. Provide clear justifications and explanation of each step used in each method, by applying an accurate approach to:
(a) Evaluate the impedance for the circuit external to RL in Figure 4, using Thevenin's theorem.

(b) Draw the Norton equivalent circuit, if IN=6<0°mA and ZN=200?+j350?.

Attachment:- Further Electrical Electronic and Digital.zip