Unit 2. AC SINGLE-PHASE CIRCUITS

300 Pages·2010·8.43 MB·English

ELECTRIC SYSTEMS
Escola d’Enginyeria d’Igualada (UPC)
Author: Dr. Jordi-Roger Riba
Edition: September 2010
11
SISTEMES ELÈCTRICS. SYLLABUS
UNIT 1: Direct Current (DC) Circuits
2 weeks
UNIT 2: Alternating Current (AC) Circuits
2 weeks
UNIT 3: Three-Phase AC Circuits
3 weeks
UNIT 4: Transformers
3 weeks
UNIT 5: Asynchronous AC Machines
3 weeks
UNIT 6: Other Electrical Machines
1 week
UNIT 7: Electrical Installations and Low Voltage Electrical Protections
1 week
22
Unit 1. DC CIRCUITS
ELECTRICAL CURRENT
When a metal wire is connected across the two terminals of a DC voltage source,
the free electrons of the conductor are forced to drift toward the positive terminal.
The free electrons are therefore the current carrier in a typical solid conductor.
I
According to Ampère's law, an electric current
produces a magnetic field.
3
Unit 1. DC CIRCUITS
ELECTRICAL RESISTANCE
Electrical resistance
(cid:131) The electrical resistance of an object is a measure of its opposition to the
passage of a steady electric current.
(cid:131) It was discovered by George Ohm in 1827
(cid:131) The SI unit of electrical resistance is the ohm (Ω).
(cid:131) The resistance R of a conductor of uniform cross section can be computed as:
l
l
R = ρ·
S
S
l is the length of the conductor, measured in meters [m]
S is the cross-sectional area of the current flow, measured in square meters [m²]
ρ (Greek: rho) is the electrical resistivity of the material, measured in ohm-metres
(Ω m). Resistivity is a measure of the material's ability to oppose electric current.
4
Unit 1. DC CIRCUITS
ELECTRICAL RESISTANCE: temperature dependence
Electrical resistance: temperature dependence
(cid:131) The electric resistance of a typical metal increases linearly with rising
temperature as:
R = R ·[1+α·(T −T )]
0 0
Where
(cid:131) T: metal’s temperature
(cid:131) T : reference temperature (usually
0
room temperature)
(cid:131) R : resistance at T
0 0
(cid:131) α: percentage change in resistivity
per unit temperature. It depends
only on the material being
considered
5
Unit 1. DC CIRCUITS
SERIES/PARALLEL CONNECTED LOADS
SERIES PARALLEL
1 n 1
s
n ∑
r =
o ∑
R = R
t R R
s
i equivalent i equivalent i=1 i
s
e i=1 R .R
R 1 2
R //R : Requivalent =
1 2 R + R
1 2
s n 1 n 1
r
o L = ∑ L = ∑
t
c equivalent i
u L L
d i=1 equivalent i=1 i
n
I
s
r 1 n 1
o
n
t = ∑
i
c ∑
C = C
a C C
p equivalent i
equivalent i=1 i
a
C i=1
6
Unit 1. DC CIRCUITS
VOLTAGE AND CURRENT DIVIDERS
The voltage divider
(cid:131) It is a simple linear circuit that produces an output voltage that is a fraction of its
input voltage. I
(cid:131) Voltage is partitioned among the components of the divider.
+
R v R
1 1
General case: V = V· j V + -
-
Rj ∑ R +
v R
i 2 2
-
i R
V = V⋅ 2
In the example shown: R2 R +R
1 2
The current divider
(cid:131) A current divider is a simple linear circuit that produces an output current that is a
fraction of its input current (IT).
I
(cid:131) Current is split between the branches of the divider.
I I
1 2
R ·R ···R ·R ·R
V + R R
General case: I = I⋅ 1 2 i−1 i+1 n - 1 2
i ∑
R
i
i
R
I = I⋅ 2
In the example shown: 1 R +R 7
1 2
Unit 1. DC CIRCUITS
OHM’S LAW
Ohm's law
The current through a conductor between two points is directly proportional to the
potential difference -or voltage across the two points-, and inversely proportional to
the resistance between them.
I = V/R V = I·R
or
(cid:131) The electrical resistance of an object is a measure of its opposition to the
passage of a steady electric current.
(cid:131) The electrical resistance was discovered by George Ohm in 1827
(cid:131) The SI unit of electrical resistance is the ohm (Ω).
The resistance R of a conductor of uniform cross section can be computed as:
8
Unit 1. DC CIRCUITS
KIRCHHOFF’S CIRCUIT LAWS
Kirchhoff's current law (KCL)
At any node (junction) in an electrical circuit, the sum of currents flowing into that
node is equal to the sum of currents flowing out of that node.
∑ ∑
∑ I = 0 I = I
or
input output
i
i
i + i = i + i
The current entering any junction is equal to the current leaving that junction:
1 4 2 3
Kirchhoff's voltage law (KVL)
The directed sum of the electrical potential differences (voltage) around any closed
circuit must be zero.
∑
V = 0
i
i
The sum of all the voltages around the loop is equal to zero: v + v + v + v = 0
1 2 3 4
9
Unit 1. DC CIRCUITS
ELECTRIC POWER
Electric power
(cid:131) Is the rate at which electrical energy is transferred by an electric circuit or
consumed by an electric load.
(cid:131) The SI unit of power is the watt.
(cid:131) The power consumed by a load is considered as positive
(cid:131) The power delivered by a source is considered as negative
V
I
P = + V·I Absorbed power
+ -
V
I
- + P = - V·I Delivered power
I
V V
+ -
P = + V·I Absorbed power
I
V V
+ -
P = - V·I Delivered power 10