Transcript Electrical Engineering 105

Electrical Systems 100
Lecture 1
Dr Kelvin Tan
1
Contents
•
Resistance
• Ohm’s Law
• Series Circuits
• Parallel Circuits
• Voltage Divider Rule
• Current Divider Rule
• Kirchoff’s Voltage Law (KVL)
• Kirchoff’s Current Law
2
Resistance
The flow of charge (q) in a material per unit time is current (i)
I = dq/dt
The resistance of a material is the property to resist the flow of
electrons when an external electric field is applied. The resistance
converts the applied energy into heat much like the mechanical
friction due to colliding electrons and collisions between electrons
and other atoms. The unit of Resistance is known as Ohms ()
3
Resistance
The Resistance of a material depends on its length (l), area (A)
and the resistivity ()
R = l/A ()
Resistivity (ρ) of various materials
Silver
Copper
9.9
10.37
Gold
14.7
Aluminium
17.0
Tungsten
33.0
Nickel
47.0
Iron
74.0
Nichrome
295.0
Chlorite
720.0
Carbon
21,000.0
The Resistivity of some materials at 20 degree
celsius. The unit is CM.  /ft and in SI system is
Ohm-meters
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Resistance
Resistors can be various types:
• Fixed Resistor
•Variable Resistors (Rheostat)
• Varistors
• Thermistors
• Photocells
•Photocells
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Resistance
Fixed and Variable Resistors
The physical size (or shape) of a resistor is no clue to its resistance
value, but can be a rough guide to its power rating.
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Resistance
Variable Resistors (Rheostat) resistance change by turning a knob
Photocells - resistance change in light level
Thermistors - Resistance that
varies rapidly and predictably with
temperature
A Varistor - Voltage Dependent
Resistor or VDR
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Color Coding of
Resistors
Example
Find the resistance of a semiconductor resistance if the bands are:
1st band is Gray, 2nd band is Red, 3rd band is Black, 4th band is
Gold, and fifth band is Brown?
Solution:
82*(10e0) () ± 5% (1% reliability)
77.9  to 86.1  and 1out of every 100 will fail to satisfy
manufacturer’s range after 1000 hr of operation.
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Conductances
Conductances are reciprocal of Resistances
G = 1/R (siemens, S) or Mho
G = A / l (S or Mho)
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A simple resistive circuit
I
Electron flow direction
I
Conventional current direction
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Ohm’s Law
I
+
Ohm’s Law states that
the current through an
electric path is
dependant on the
resistance of the path
and is given by:
V
_
V
I
R
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V-I Characteristic of a Linear Resistor
V
I
R
V  IR
V
R
I
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Electrical Power
Power
P  VI
2
V
PI R
R
2
SI unit is the Watt (I in Amperes, V in Volts
and R in Ohms). 1 Watt is 1 Joules/Sec
1 hp = 746 Watts (the power of an average
dray horse over a full working day)
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Polarity references and the expression for power
• If the power is Negative (P
<0), power supplied by
circuit
+
I
If the power is Positive (P > 0),
power absorbed by the circuit
V
_
Absorb
or supply ?
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Electrical Energy
Energy: Electric Energy is the Electric Power consumed over a
period of time
t
2
2
V
W  P *t  I R *t 
* t   Pdt
R
0
SI unit is the Watt (I in Amperes, V in Volts and R in Ohms).
1 Watt is 1 Joules/Sec
1 hp = 746 Watts (the power of an average dray horse over a full
working day)
How to calculate the
Electric Power consumed in
1 day ?
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Electrical Energy
The unit of Energy is Watt-hours (Wh), kWh, MWh or GWh
Energy (Wh) = Power (W) * Time (h)
1 kWh is 1000 Wh
1 MWh = 1000 kWh
1 GWh = 1000 MWh
We pay for electricity on the basis of kWh consumed in a specified period @
12 cents (approx) per kWh
How many kWh is
this family using ??
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Direct Current Circuits
• Analysis of simple circuits with batteries,
resistors, and capacitors connected in
various combinations (series/parallel).
• Kirchoff’s rules (based on law of
conservation of energy and charge).
• Steady-state (current constant in
magnitude and direction).
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A simple resistive circuit
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Circuit diagram
I
Vr = I × r
VR = I × R
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Battery in Series with a Resistor
Battery
The battery has an internal resistance r and is connected
in series with a resistor R.
V  Vb  Va    Ir
  IR  Ir
E
I
Rr
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Battery in Series with a Resistor
Multiplying by the current yields:
I  I R  I r
2
2
The total power of the battery is converted to
heat in the two resistors.
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Series connection of two resistors
Req = R1 + R2
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Two Resistors in Series
Two or more resistors are in series if connected
together so that they have only one common point
per pair.
V  IR1  IR2  I ( R1  R2 )
The current is the same through each resistor
because any charge flowing through one resistor
must also flow through the other.
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More than Two Resistors in Series
The equivalent resistance of a series
connection of resistors is always greater
than any individual resistance.
Req  R1  R2  R3  ..........
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Parallel connection of two resistors
1
1
1


R eq R 1 R 2
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Two Resistors in Parallel
Two or more resistors are in parallel if there is an
equal potential difference across each resistor.
I  I1  I 2
1
1
1
 
Req R1 R2
The current is not the same through each resistor
because any charge flowing through one resistor
cannot flow through the other. But the Potential
difference (voltage) across each parallel branch is
identical.
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More than Two Resistors in Parallel
The equivalent resistance of a parallel
connection of resistors is always less
than the smallest individual resistance.
1
1
1
1
 
  .......
Req R1 R2 R3
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Kirchoff’s Laws
• The sum of the currents entering any
junction must equal the sum of the
currents leaving that junction. (KCL)
(Conservation of charge)
• The algebraic sum of the changes in
potential across all of the elements around
any closed circuit loop must be zero. (KVL)
(Conservation of energy)
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Kirchoff’s Voltage Law
The algebraic sum of the changes in
potential across all of the elements around
any closed circuit loop must be zero. (KVL)
V

0
 drops or rise
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Kirchoff’s Voltage Law
V1
I
KVL
KVL
V2
 Vdrops or rise  0
E  V1  V2  0
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Kirchoff’s Current Law
Kirchoff’s Current Law states that the amount of
current entering a junction must be equal to the
current leaving that junction.
I
entering
  I leaving
or,
I 0
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Kirchoff’s Current Law
I
I1
entering
  I leaving
or,
I 0
I3
I1  I 2  I 3
I2
Example : I1 = 5A, I2 = 2A and I3 = 7A
Taking current entering the node as reference
I1 +I2 - I3 = 0A
Taking current leaving the node as reference
I3 -I1 -I2 = 0A
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Kirchoff’s Current Law
Example :
I5= 6A
I1=2A
I3=5A
I2=3A
a
b
I4=1A
Node (a) KCL
Node (b) KCL
I1 + I2 + I3 = 0
I3 + I4 + I5 = 0
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Voltage Divider Rule
In a Series Circuit, the Voltage across
resistances divide according to the
magnitude of the resistances
Consider a Series circuit with two elements
R1 and R2 and the total voltage applied
across them is V. Let the current flowing
through each of the two elements (series) be
“I”
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Voltage Divider Rule
E
I
R 1  R2
E
V 1  IR1  V 1 
R1
R 1  R2
+
R1
V1 
E
R 1  R2
V
E
V 2  IR 2  V2 
R2
R 1  R2
R2
V2 
E
R 1  R2
_
V  V1  V2
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Current Divider Rule
The current in parallel circuit elements divide in
ratios according to the inverse of their resistor
values. Consider two parallel elements R1 and
R2 and a total current I, then the current in two
elements are:
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Current Divider Rule
I
R2
I1  I
R1  R2
R1
I2  I
R 1  R2
I  I1  I 2
I1
I2
I1
I2
I
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Single Subscript Voltage Notation
Va means that the voltage of point “a” is Va
with respect to the ground.
Va
Vb
38
Double Subscript Voltage Notation
Vab means that the voltage of point
“a” with respect to point “b” is Vab
Vab = Va – Vb
Vba = Vb – Va = -Vab
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If point “b” is at ground potential
then Vab is simply Va
Vab = Va – 0 = Va
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What is Vab?
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Measurement of Voltage
Voltages are measured by an instrument called
Voltmeter. They can be either analog (AVO) or digital
(DMM).
Voltmeters are always connected in parallel with circuit
where the voltage is to be measured. Voltmeters should
have very high resistance, so that they do not allow
current flowing through the circuit to enter in them due
to their insertion.
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Measurement of Voltage
I
+
VR
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Measurement of Current
Currents are measured by an instrument called Ammeter.
An Ammeter can be analog or digital. An Ammeter is
always connected in series with the circuit where current
need to be measured.
An Ammeter should have almost zero resistance, so that
they do not alter the magnitude the of the current due to
their insertion.
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Measurement of Current
I
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An Open Circuit
An Open circuit is one which have voltage across
it but current through it is zero. An open circuit is
represented by infinite resistance.
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A Short Circuit
A short circuit is one which allow current through
it but voltage across it is zero. A short circuit is
represented by zero resistance.
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