Fundamental Theorems used in Electric Circuits (CSCT2102)
Computer Science - COS
Semester: First Semester
Level: 200
Year: 2015
1
EXAM (2014-2015)
Semester 1: CSC112: Electric circuits
Level 100 Duration: 2 hours
Exercise 1: Application of Millman’s theorem (8 marks)
Let us consider the circuit below with
,
,
,
and
.
1) Describe Millman’s theorem
2) By applying Millman’s theorem, give the relation between
and the rest of data.
3) Give the relation between ,
and
and calculate
4) Give the relation between ,
and
and calculate
5) Give the relation between , and
then calculate
6) Give the relation between ,
and
and calculate
7) List at list 4 other theorem applicable to electric circuits
Exercise 3: RLC circuit submitted to direct current using Laplace transformed method (12 marks)
Let us consider the circuit below:
Where R is a resistor, C a capacitor and L an inductance. Let us assume the parameter is defined as :
1) By applying Kirchhoff voltage law, demonstrate that the current i passing in the circuit obeys to the
differential equation :
2) By applying Laplace’s transformed to this differential equation, demonstrate that the complex
current I(s) can be put in the form:
where
is the initial charge of the
capacitor C.
3) If the parameter is positive, give the expression of I(s) and i(t) using parameters
and
and Heasivide’s theorem.
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4) If the parameter is negative, give the expression of I(s) and i(t) using parameters
and
and Heasivide’s theorem.
5) If the parameter is positive, give the expression of I(s) and i(t) using parameters
and
and fractional function decomposition method.
6) If the parameter is negative, give the expression of I(s) and i(t) using parameters
and
and fractional function decomposition method.
7) Compare results given by the two methods
8) If the parameter is positive, draw and describe the curve of i(t).
9) If the parameter is negative, draw and describe the curve of i(t).
10) If you were in secondary school, give the expression of the function i(t).
11) What method did you use in secondary schools for LRC circuits?
12) Do you think that that method is applicable here? Why?
13) Now that you know the reality and what you had in secondary schools, what will you do during
teaching practice to obtain the results given by this circuit with your future students?
14) What condition should verify the voltage E so that this circuit could use Fresnel methodology?
Remarks:
A) Laplace transformed table
s/n Functions Laplace transformed
1
2
3
4
5
6
B) Heasivide’s theorem
C) If
then,
=
Where
are the n roots of the equation Q(s)=0.
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