A series rlc circuit with an alternating current source is

Question

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, I_S =2sin(1000t)A.

A. Determine the inductive and capacitive reactances, X_L and X_C.

B. Draw the phasor diagram and hence determine an expression for the supply voltage, V_S, in polar form.

C. Determine an expression the impedance of the series circuit, in polar form.

D. Derive an expression for the voltage gain, V_O/V_S, 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, V_S, and V_O, 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, V_S = 10sin(1000t)V.

A. Draw the phasor diagram and hence determine an expression for the supply current, I_S, in polar form.

B. Derive an expression for the output voltage, V_O, in polar form.

C. Hence express the gain of the circuit, V_O/V_S, 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