Assessment Title and Tasks: Phasor Diagram
Learning Outcomes to be assessed:
- To be able to select and apply appropriate analysis methods to DC and AC circuits comprising combinations of RLC, and voltage and current sources
- To be able to derive and discuss transient and steady-state characteristics of fundamental engineering systems containing electro-mechanical devices
Assignment Brief:
You are required to perform an analysis of the A.C. circuits shown in Figure 1 and Figure 2. The analysis is to be performed by Phasor Diagrams.
Submit a report detailing the analysis and subsequent discussion, as define below.
1. A series R/L/C circuit with an alternating current source is shown in Figure 1. The source provides a constant current, IS =2sin(1000t)A.
A. Determine the inductive and capacitive reactances, XL and XC.
B. Draw the phasor diagram and hence determine an expression for the supply voltage, VS, in polar form.
C. Determine an expression the impedance of the series circuit, in polar form.
D. Derive an expression for the voltage gain, VO/VS, in polar form.
E. At what frequency will the circuit present a pure resistance to the source, and what is the relationship between input voltage and output voltage, VS, and VO, at this frequency?
F. Create a computer model of the circuit and verify your theoretical results.
2. A R/L/C circuit with an alternating voltage source is shown in Figure 2. The source provides a constant voltage, VS = 10sin(1000t)V.
A. Draw the phasor diagram and hence determine an expression for the supply current, IS, in polar form.
B. Derive an expression for the output voltage, VO, in polar form.
C. Hence express the gain of the circuit, VO/VS, in polar form.
D. Create a computer model of the circuit, and investigate the frequency response characteristics of the circuit for frequencies in the range: 100 ≤ ω ≤ 10000 rad s-1.
Reporting - A report, comprising the following sections:
1. List of Objectives
2. Experimental Results
3. Analysis and Modelling
4. Evaluation
5. Conclusions
6. References