Application of Thevenin and Norton Theorems in AC Circuit Analysis

This assignment explores the application of Thevenin and Norton theorems in AC circuit analysis, specifically for RLC circuits. The solution explains how these theorems are used to simplify complex circuits, focusing on the calculation of equivalent resistance and voltage/current sources. It highlights the similarities and differences between the theorems, emphasizing their interconnectedness and the use of complex numbers in AC circuit calculations. The assignment references online resources to support the analysis and provides a clear understanding of how to apply Thevenin and Norton theorems to solve circuit problems. The solution also discusses the conversion between Thevenin and Norton equivalent circuits and provides relevant formulas.

Assessment

TASK 3
C
In order to solve series and parallel RLC circuits both Norton and Thevenin’s theorem
can be used for reducing a complex circuit into a basic single source with combination of
resistors. Though both of the theorems are utilized for only linear network the type and position
of RLC components make the application of theorem complicated or simpler. Thevenin theorem
uses voltage source with a resistance in series while in case of Nortan theorem a current source is
used with parallel resistor. The equivalent resistance known as Norton resistance or Thevenin
resistance are equivalent in magnitude which indicates that both Norton and Thevenin equivalent
crictuit are interchangeable.
Irrespective of series or parallel positioning of RLC components Thenvenin theorem is
applied to circuits based on battery systems in which multiple energy sources are present. In
Task 1A after removal of load resistance equivalent Thevenin voltage is found by calculating
open circuit voltage across load. On the other hand, in Task 1B when load resistance is short
circuited then conventional circuit analysis is used for finding short circuit current. However, in
both cases equivalent circuit resistance is determined by finding equivalent resistance across
open load.

Figure 1: Thevenin equivalent for ac circuit
(Source: AC Thevenin’s theorem. 2020)

Both the theorems applied in task 1 can be applied in same way in task 3 which consist of
AC- series RLC circuit. However, calculations in task 3 also include manipulation of complex
numbers due to inclusion of impedance Z instead of equivalent resistance. Both Thevenin and
Norton are also interrelated by the following relation:
Vth = IN * Rth
(Also Rth = RN) (vth is Thevenin equivalent voltage; IN is Nortan equivalent current and Rth
or RN is equivalent resistance)
REFERENCES
Online
AC Thevenin’s theorem. 2020. [Online]. Accessed through <http://hyperphysics.phy-
astr.gsu.edu/hbase/electric/acthev.html>
Conversion between Thevenin & Norton equivalent circuit. 2014. [Online]. Accessed through
<https://electronicspani.com/conversion-of-thevenin-norton-equivalent-circuits/>
Thevenin & Norton theorem for AC. 2020. [Online]. Accessed through <
https://electronicspani.com/thevenins-and-nortons-theorem-for-ac/>