dc circuits: basic...
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EENG223: CIRCUIT THEORY I
DC Circuits:
Basic Concepts Dr. Hasan Demirel
EENG223: CIRCUIT THEORY I
An electric circuit is an interconnection of electrical elements.
A simple electric circuit
Electric circuit of a radio receiver
EENG223: CIRCUIT THEORY I
Six basic SI units and one derived unit relevant to this course.
Quantity Basic Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic Temperature kelvin K
Luminous intensity candela cd
Charge coulomb C
EENG223: CIRCUIT THEORY I
SI Prefixes
micro
pico
Most frequently used
Prefix
EENG223: CIRCUIT THEORY I
Charge and Current • Charge is an electrical property of the atomic particles of
matter, measured in coulombs (C).
1 C of charge requires 6.24 x 1018
electrons. 1 electron charge e = −1.602 x 10
−19 C .
Law of Conservation of Charge: Charge can only be transferred. Cannot be created/destroyed.
Charge Direction
EENG223: CIRCUIT THEORY I
dt
dqi • Current is defined by:
where i = current in amperes (A),
q = charge in coulombs (C),
t = time in seconds (s).
1 A = 1 C/s
• Charge transferred between time t0 and t : t
tdtiQ
0
Charge and Current • Electric current is the time rate of change of charge, in
other words, the flow of charge, measured in amperes (A).
EENG223: CIRCUIT THEORY I
• Alternating Current (ac) is the current that varries sinusoidally with time.
• Conventional current flow: Both methods represents the same current. (a) positive current flow, (b) negative current flow.
• dc current is represented by I and ac current is represented by i.
Charge and Current • Direct Current (dc) is the current that remains constant with time.
EENG223: CIRCUIT THEORY I
Charge and Current : Problems Ex. 1.1:
Ex. 1.2:
EENG223: CIRCUIT THEORY I
Charge and Current : Problems Ex. 1.3:
EENG223: CIRCUIT THEORY I
Voltage • Voltage (potential difference/electromotive force) is the energy
required to move a unit charge through an element, measured in volts (V).
dq
dωυab
• The voltage, between two points a and b:
υ = voltage in volts (V),
ω = energy in joules (J),
q = charge in coulombs (C).
• 1 volt = 1 joule/coulomb
EENG223: CIRCUIT THEORY I
Voltage • Voltage pushes charge in one direction. • We use polarity (+ and −) on batteries to indicate which
direction the charge is being pushed.
Two equivalent representation of the
same voltage: (a) point a is 9 V above point b, (b) point b is −9 V above point a.
• dc voltage is represented by V and ac voltage is represented by υ.
EENG223: CIRCUIT THEORY I
Power and Energy • Power is the rate of expending and absorbing energy,
measured in watts(W).
idt
dωp
p = power in watts (W = J/s),
ω = energy in joules (J),
t = time in seconds (s).
υ = voltage in volts (V).
i = current in amperes (A).
p=±υi
• Circuit elements that absorb power has positive value of p.
• Circuit elements that supply (produce) power has negative value of p.
(a) Absorbing power (b) supplying power.
EENG223: CIRCUIT THEORY I
Power and Energy • Energy is the capacity to do work, measured in joules(J).
t
t
t
tdtidtp
00
p = power in watts (W),
ω = energy in joules (J),
t = time in seconds (s).
υ = voltage in volts (V).
i = current in amperes (A).
• If current and voltage are constant (dc). The power is:
• In adddition to joules, Watt-hour can also be used to measure energy.
1 Wh = 3,600 J
)( 00
ttppdtt
t
• Law of conservation of energy. Total power in a circuit at any instant is must be
zero.
+Power absorbed = −Power supplied
0 p
EENG223: CIRCUIT THEORY I
Power and Energy : Problems Ex. 1.4:
EENG223: CIRCUIT THEORY I
Power and Energy : Problems Ex. 1.5:
EENG223: CIRCUIT THEORY I
Power and Energy : Problems Ex. 1.6:
EENG223: CIRCUIT THEORY I
Passive Sign Convention • Passive sign Convention (PSC) is satisfied when current
enters through the positive terminal of an element.
• Most two terminal circuit elements (i.e batteries, light bulbs, resistors, switches) are characterized by a single single equation that relates voltage to current: υ=±f(i) or i=±g(υ).
• PSC determines the sign relationship
If PSC is satisfied: υ=f(i) or i=g(υ).
If PSC is not satisfied: υ= − f(i) or i=−g(υ).
• This is also true for power
If PSC is satisfied: p= υi
If PSC is not satisfied: p=−υi
EENG223: CIRCUIT THEORY I
Passive Sign Convention Ex. 1.7:
EENG223: CIRCUIT THEORY I
Circuit Elements • Ideal Independent Source: provides a specified voltage or
current that is completely independent of other circuit variables
• Ideal Independent Voltage source: (a) Independent voltage source (constant / time varying)
(b) Independent voltage source (battery).
• Ideal Independent Current source:
EENG223: CIRCUIT THEORY I
Circuit Elements • Ideal dependent sources: controlled by other voltage or current.
(a) dependent voltage source (b) dependent current source