CIU
EELE202 Circuit Theory I
CMPE222 Fundamentals of Electronics
Chapter I : Introduction
Main source: Electrical Engineering Principles and Applications, 3rd
Edition, by Allan R. Hambley, Pearson Education 2005.
Before we start...
These prefixes provide
convenience in expressing
values of quantities.
Some will also be used
throughout this course.
The SI Prefixes
Electrical systems have two main objectives:
• To gather, store, process, transport, and present information
• To distribute and convert energy between various forms
Electrical circuit:
Electrical Current
Electrical current is the time rate of flow of electrical charge
through a conductor or circuit element. The units are amperes
(A), which are equivalent to coulombs per second (C/s).
dq(t )
i (t ) =
dt
t
q(t ) =  i (t )dt + q(t0 )
t0
Direct Current /Alternating Current
When a current is constant with time, we say that we have
direct current, abbreviated as dc. On the other hand, a
current that varies with time, reversing direction periodically,
is called alternating current, abbreviated as ac.
Electrical Voltage
The voltage associated with a circuit element is the energy
transferred per unit of charge that flows through the element.
The units of voltage are volts (V), which are equivalent to
joules per coulomb (J/C).
A voltage which is constant with time is called dc voltage,
whereas a voltage that varies with time, reversing direction
periodically, is called ac voltage.
examples:
v1(t) = 10V (dc)
v2(t) = 10cos(200πt) V (ac)
Kirchoff’s Current Law (KCL)
A node in an electrical circuit, is a point at which two or
more circuit elements are joined.
Kirchoff’s Current Law states that,
• the sum of the currents entering a node equals the sum
of the currents leaving a node
or alternatively,
• the sum of the currents entering a node is zero.
Series circuits
When elements are connected end to end, we say they are
connected in series.
Example:
KCL at node 1 : ia = ib
KCL at node 2 : ib = ic
➔ ia = ib = ic
All elements in a series circuit
have identical currents.
Kirchoff’s Voltage Law (KVL)
Kirchoff’s Voltage Law states that,
• The algebraic sum of the voltages equals zero for any
closed path (loop) in an electrical circuit.
Parallel circuits
We say that two circuit elements are connected in parallel,
if both ends of an element are connected directly to the
corresponding ends of the other element.
Example:
KVL for loop 1 (along A and B):
-va + vb = 0 → va = vb
KVL for loop 2 (along B and C):
-vb - vc = 0 → vb = -vc
➔ va = vb = -vc
The voltages across parallel
elements are equal in magnitude
and polarity.
Example:
Circuit Elements
Conductors: The lines that connect the elements to each
other.
Independent sources:
Circuit Elements (... cont.)
Dependent (controlled) sources:
Dependent (controlled) voltage sources:
Dependent (controlled) current sources:
Circuit Elements (... cont.)
Resistors: The voltage v across an ideal resistor is
proportional to the current i through the resistor.
Unit of resistance (R) is Ohm (Ω).
Ohm’s Law:
v=iR
Conductance (G) is the inverse (reciprocal) of resistance.
Thus, Ohm’s Law can be rewritten as
i=Gv
Unit of conductance is inverse of Ohm (Ω-1), which is also
called Siemens (S).
Resistance and Resistivity
The resistance of any material with a uniform cross-sectional area A and
length l, depends on A , l and r, where r is the resistivity of the material.
Some Resistor Types
Power
P=vi
= i 2R
= v 2/R
(v=i R)
(i=v/R)
The unit of power is Watt (W).
If P>0 ➔ Energy is being absorbed by the element.
If P<0 ➔ The element is supplying energy to the
other parts of the circuit.
P = v i1
P = -v i2
Conservation of Energy: At a given instant, the sum of the
powers of all elements in a circuit must be zero:
for all elements
Energy calculations
where,
p(t) is power, in Watts (W)
w(t) is energy, in Joules (J)
Note: An extra problem (with solution) will be provided
separately (a more detailed problem, again related with
energy calculation).