CIRCUIT THEORY 1
Rosalie Vertudes, MSEE, REE
CHAPTER 1
BASIC CONCEPTS
ELECTRIC CIRCUIT

An interconnection of electrical elements.
SYSTEMS OF UNITS
CHARGE AND CURRENT

Charge
 most
basic quantity in an electric circuit
 is an electrical property of the atomic particles of
which matter consists, measured in coulombs (C).
 charge
e on an electron is negative and equal in
magnitude to 1.602×10−19 C, while a proton carries a
positive charge of the same magnitude as the electron.
The presence of equal numbers of protons and
electrons leaves an atom neutrally charged.
CHARGE AND CURRENT

Points should be noted about electric charge:
The coulomb is a large unit for charges. In 1 C of charge,
there are 1/(1.602 × 10−19) = 6.24 × 1018 electrons. Thus
realistic or laboratory values of charges are on the order of
pC, nC, or μC.
 According to experimental observations, the only charges
that occur in nature are integral multiples of the electronic
charge e = −1.602 × 10−19 C.
 The law of conservation of charge states that charge can
neither be created nor destroyed, only transferred. Thus the
algebraic sum of the electric charges in a system does not
change.

CHARGE AND CURRENT

Electric charge or electricity is mobile
• Positive charges move in one
direction while negative charges
move in the opposite direction
• Motion of charges creates
electric current
• Conventionally take the
current flow as the movement of
positive charges, that is,
opposite to the flow of negative
charges.
CHARGE AND CURRENT

Electric current is the time rate of change of charge,
measured in amperes (A).
1 ampere = 1 coulomb/second


Direct Current (DC) is a current that remains constant
with time.
Alternating Current (AC) is a current that varies
sinusoidally with time.
CHARGE AND CURRENT (Example)
1. How much charge is represented by 4,600 electrons?
CHARGE AND CURRENT (Example)
2. Calculate the amount of charge represented by 6
million protons.
CHARGE AND CURRENT (Example)
3. The total charge entering a terminal is given by q = 5tsin4πt
mC. Calculate the current at t = 0.5s.
CHARGE AND CURRENT (Example)
4. Determine the total charge entering a terminal between t = 1 s
and t = 2s if the current passing the terminal is i = (3t2 − t) A
VOLTAGE


Voltage (or potential difference) is the energy
required to move a unit charge through an element,
measured in volts (V).
Voltage vab between two points a and b in an electric
circuit is the energy (or work) needed to move a unit
charge from a to b; mathematically,
 where
w is energy in joules (J) and q is charge in
coulombs (C).
 Voltage vab or simply v is measured in volts (V)
1 volt = 1 joule/coulomb = 1 newton meter/coulomb
VOLTAGE

The plus (+) and minus (−) signs are used to define
reference direction or voltage polarity.
(1) point a is at a potential of vab volts higher than point b
(2) the potential at point a with respect to point b is vab
vab = −vba
(a), there is a 9-V voltage drop from a to b or
equivalently a 9-V voltage rise from b to a.
(b), point b is −9 V above point a.
A voltage drop from a to b is equivalent to a
voltage rise from b to a.
constant voltage is called a dc voltage and is represented by V, whereas a
sinusoidally time-varying voltage is called an ac voltage and is represented by v.
POWER AND ENERGY

Power is the time rate of expending or absorbing
energy, measured in watts (W).
where p is power in watts (W), w is energy in joules (J), and t
is time in seconds (s).
 power p is a time-varying quantity and is called the
instantaneous power.


If the power has a “+” sign, power is being delivered
to or absorbed by the element. If, on the other hand, the
power has a “−” sign, power is being supplied by the
element.
POWER AND ENERGY

Passive sign convention is satisfied when the
current enters through the positive terminal of an
element and p = +vi. If the current enters through
the negative terminal, p = −vi.
POWER AND ENERGY

law of conservation of energy must be obeyed:
 algebraic
sum of power in a circuit, at any instant of
time, must be zero.


Energy absorbed or supplied by an element from
time t0 to time t is
Energy is the capacity to do work, measured in
joules ( J).
 electric
power utility companies measure energy in watthours (Wh)
POWER AND ENERGY (Example)
1.
An energy source forces a constant current of 2A for 10s to flow through a
light bulb. If 2.3kJ is given off in the form of light and heat energy,
calculate the voltage drop across the bulb.
POWER AND ENERGY (Example)
2. Find the power delivered to an element at t = 3 ms if the
current entering its positive terminal is i = 5cos60πt A and the
voltage is: (a) v = 3i, (b) v = 3 di/dt .
POWER AND ENERGY (Example)
3. How much energy does a 100-W electric bulb
consume in two hours?
CIRCUIT ELEMENTS

Two types of elements found in electric circuits:
Passive element – not capable of generating energy
(resistors, capacitors, and inductors)
 Active element - capable of generating energy (generators,
batteries, and operational amplifiers)


Two kinds of sources:
Independent Sources - an active element that provides a
specified voltage or current that is completely independent
of other circuit variables
 Dependent Sources - an active element in which the source
quantity is controlled by another voltage or current.
(transistors, operational amplifiers and integrated circuits)

CIRCUIT ELEMENTS

Ideal Independent Voltage Source delivers to the
circuit whatever current is necessary to maintain its
terminal voltage (batteries and generators).
 Symbols
for independent voltage sources: (a) used for
constant or time-varying voltage, (b) used for constant
voltage (dc).
CIRCUIT ELEMENTS

Ideal Independent Current Source is an active
element that provides a specified current
completely independent of the voltage across the
source.
 Symbol
for independent current source
CIRCUIT ELEMENTS

Four possible types of dependent sources:
 Voltage-Controlled
Voltage Source (VCVS).
 Current-Controlled Voltage Source (CCVS).
 Voltage-Controlled Current Source (VCCS).
 Current-Controlled Current Source (CCCS).
 Symbols
for: (a) dependent voltage source, (b) dependent
current source.
CIRCUIT ELEMENTS
1.
Calculate the power supplied or absorbed by
each element
CHAPTER 2
BASIC LAWS
OHM’S LAW


Resistance (R) –of an element denotes its ability to resist
the flow of electric current; it is measured in ohms (Ω).
The resistance of any material with a uniform crosssectional area (A) depends on A and its length (l)


where ρ is known as the resistivity of the material in ohmmeters.
Good conductors, such as copper and aluminum, have
low resistivities, while insulators, such as mica and
paper, have high resistivities.
OHM’S LAW
(a) Resistor, (b) Circuit symbol
for resistance.
OHM’S LAW



Ohm’s law states that the voltage “v” across a
resistor is directly proportional to the current “i”
flowing through the resistor.
Short circuit is a circuit element with resistance
approaching zero.
Open circuit is a circuit element with resistance
approaching infinity.
OHM’S LAW
◼ (a)
Short circuit (R = 0), (b) Open circuit (R =∞).
OHM’S LAW




Conductance is the ability of an element to conduct
electric current; it is measured in mhos ( ) or siemens (S).
Resistance can be expressed in ohms or siemens
The power dissipated by a resistor can be expressed in
terms of R.
The power dissipated by a resistor may also be
expressed in terms of G
OHM’S LAW
1.
An electric iron draws 2 A at 120 V. Find its
resistance.
OHM’S LAW
2. In the circuit shown, calculate the current i, the
conductance G, and the power p.
OHM’S LAW
3. A voltage source of 20 sin πt V is connected across a 5-kΩ
resistor. Find the current through the resistor and the power
dissipated.
OHM’S LAW
4. Determine the resistance of a conductor 0.10 m long with a uniform diameter of 1.0 cm
and having a resistivity which varies as a function of length L measured from one end of
the conductor according to the formula: Resistivity of material = 0.003 + 10^-4 L^2 ohmcm.
EFFECT OF TEMPERATURE IN RESISTANCE
EFFECT OF TEMPERATURE IN RESISTANCE
1. The resistance of a copper wire at 30 degrees Celsius is 50 ohms. If the temperature
coefficient of copper at 0 degrees Celsius is 0.00427, what is the resistance at 100
degrees Celsius?
INSULATION RESISTANCE OF CABLES
INSULATION RESISTANCE OF CABLES
1. A cylindrical rubber insulated cable has a diameter of 0.18 inch and an
insulation thickness of 0.25 inch. If the specific resistance of rubber is 10^14 ohmcm, determine the insulation resistance per 1000-ft length of the cable.
To be continued…………….
