l02 kvs circuit fundamentals full
DESCRIPTION
Introduction to electronics IIT KanpurLecturesTRANSCRIPT
ESc201: Introduction to ElectronicsESc201: Introduction to Electronics
Circuit Fundamentalsquick
A RA RecapDr. K. V. SrivastavaDr. K. V. Srivastava
Dept. of Electrical Engineering
IIT KIIT Kanpur1
ConceptsConcepts
• Charge Current Voltage Power and EnergyCharge, Current, Voltage, Power, and Energy
• Ohm’s Law
C• KCL
• KVL
2
Electrical Current
Th ti t f fl f l t i l hThe time rate of flow of electrical charge
– The units are amperes (A), which are equivalent to p ( ) qcoulombs per second (C/s)
André-Marie Ampère1775-1836
3
Flow of electrons through a wire or other electrical conductor i i t tgives rise to current
• Electrons are negatively charged particles
The charge per electron is -1.602×10-19 C
g y g
I
1016 electrons flow per secondp
How much current flows?
19 1631.6 10 10 1.6 10
1QI At
−−− × ×
= = =− ×4
I
Current has a magnitude and a direction
I
1016 electrons flow per second
Direction of current flow is opposite to direction of electron flow
Large number of electrons have to flow for appreciable current
Exercise 1: For q(t) = 2 - 2e-100t, t > 0 and q(t) = 0 for t < 0, fi d i(t)find i(t)
5
Direct Current (DC) & Alternating Current (AC)
When current is constant with time we say that we haveWhen current is constant with time, we say that we have direct current, abbreviated as DC.
~
O th th h d t th t i ith ti i di tiOn the other hand, a current that varies with time, reversing direction periodically, is called alternating current, abbreviated as AC
6
VoltageVoltage difference is a Source of current flow
Units of Voltage: Volts (V)
Alessandro Giuseppe Antonio Anastasio Volta 1745-1827
12V 12V
0V0V12V
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Voltage Sources
8
DC and AC voltages
12V V V+ −− =
9
Electrical Systems are made of Voltage sources, wires and avariety of electrical elements
Resistor Capacitor Inductor
Diode
TransformerTransistor
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Current flows in a loop
El t i l t ll d l t i l i itElectrical systems are called electrical circuits
11
Connection of several circuit elements in closed paths by
Electrical Circuit
Connection of several circuit elements in closed paths by conductors
Before we learn how to analyze and design circuits, we mustBefore we learn how to analyze and design circuits, we must become familiar with some basic circuit elements.
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Resistance
( ) ( )v t R i t= ×( ) ( )v t R i t= ×
Ohm’s law
The constant R is called the resistance of the component and
Ohm s law
The constant, R, is called the resistance of the component and is measured in units of Ohm (Ω)
RResistor Symbol:
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Conductance
( ) ( )v t R i t= ×( ) ( )v t R i t×
( )t( )( ) ( )v ti t G v tR
= = ×
G = 1/R is called conductance and its unit Ernst Werner von Siemens
1816-1892is Siemens (S)
1816 1892
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vR =iiiGv
=
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Resistance Related to Physical Parameters
LRA
ρ= ×
Resistance is affected by the dimensions and geometry ofResistance is affected by the dimensions and geometry of the resistor as well as the particular material used
ρ is the resistivity of the material in ohm meters [Ω-m]ρ is the resistivity of the material in ohm meters [Ω m]– Conductors (Aluminum, Carbon, Copper, Gold)– Insulators (Glass, Teflon)
Semiconductors (Silicon)– Semiconductors (Silicon)
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Any electrical element which obeys ohms law can be modeled as a resistor
Can we model an electric bulb as a resistor?17
Electrical Bulb
Even though characteristics are non-linear, over a certain grange, the bulb can be thought of as a resistor
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Power and Energy
12VQ
X
0VThe charge loses energy = Q x 12 Joules
0V
This energy is taken from the voltage source and delivered t th i it l tto the circuit element
19
12VI Q Q I t×
X
I QIt
= Q I t= ×
X
In 1 second charge equal to Q = I flows0V
In 1 second, charge equal to Q = I flows through the element X
Every time a charge q goes from 12V to 0V it transfers energy qx12 J to the element X
Total Energy transferred in 1 second = I x 12 J
Power = Energy/time P = I x 12 Watts
Joules/second = watts20
P = I x V
A charge of 1 coulomb receives or delivers an energy of 1 joule in moving through a voltage of 1 volt.
dwv =d
j g g g
dqdtdqi =
(( )) ( )dw dw dqP td d d
v t i t= = =dt
2td
(( )) ( )dt dq dt
2
1
( ) ( )t
t
d wP t w p t d td t
= ⇒ = ∫1t
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V1
Power
I1 2( )P V V I= − ×
X
V2
If V1 > V2 then P is positive and it means that power is being delivered to the electrical element X
If V1 < V2 then P is negative and it means that power is being extracted from the electrical element X. X is a source of power !X is a source of power !
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Note on direction of current
X2A -2AX
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12V
Examples
X
1A P = ?
X1 2( )
(12 6 ) 1 6P V V I
W= − ×= − × =
6V( )
12V1A
P = ?
1 2( )P V V I= − ×X
1 2( )(12 6 ) 1 6W= − × − = −
6V24
Power is supplied by element X instead of dissipation
6V P = ?
X
6V1A
1 2( )P V V I= − ×X 1 2( )(6 12 ) 1 6V V
W= − × − =12V
power is being delivered to the electrical element Xelectrical element X
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There is only one battery in the circuit. Can you find which element is a battery?y
A battery is a source of power, so Power dissipated is negativeA battery is a source of power, so Power dissipated is negative
Answer is C
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Power dissipated in a Resistor
+ i v i R= × viR
=R
-
v
P i
R- P v i= ×
22vPR
=2P i R= ×
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Circuit Analysis
R3R1
R2
R3
R4VS
R1
IX
What is current in R2 ?Procedure:
Use Kirchhoff's voltage law (KVL) and Kirchhoff's Current law(KCL) to transform the circuit into a set of equations whose( ) qsolution gives the required voltage or current value
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Engineering Analysis
Real-life SystemReal life System
Abstract Model
Mathematicalproblem
2 2v v
1 2
v vPR R
= +29
Nodes and loops
Node: A point where 2 or more circuit elements are connected.
R2
R3
R4VS
R1
IX
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A loop is formed by tracing a closed path through circuitelements without passing through any intermediate node morep g g ythan once
R2
R3
R4VS
R1
IX2 R4VS IX
This is not a valid loop !
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Kirchhoff's Current Law (KCL)
Sum of currents entering a node is equal to sum of currents leaving a node
1 2 3i i i+ =
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Kirchhoff's Current Law (KCL)N
Net current entering a node is zero1
0ji =∑
Current entering a node is considered positive and current leaving a node is considered as negative
0i i i+1 2 3 0i i i+ − =
33
3 4i i=3 4
1 3 0ai+ − = 1 3 2 0bi+ + − =
4ai A= 2bi A= − 34
1 3 4 0i
8i A
1 3 4 0ci+ + + =
8ci A= −35
Example
36
The sum of currents entering/leaving a closed surface is zero
KCL: More general formulation
The sum of currents entering/leaving a closed surface is zero.
i i2i1
R2
R3
R4VS
R1
IX
i3 i4
1 2 3 4 0i i i i+ + − =37
Series Circuit
Two elements are connected in series if there is no otherTwo elements are connected in series if there is no otherelement connected to the node joining them
A, B and C are in series
The elements have the same current going through them
a b ci i i= =38
A and B are in series E, F and G are in series
39
Th l b i f th lt l f
Kirchhoff's Voltage Law (KVL)
The algebraic sum of the voltages equals zero for any closed path (loop) in an electrical circuit
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Example
41
L oop3 : 0e d b av v v v− + − + =
KVL and Conservation of Energy
V Th h l Q (V V ) J lV1
Q
The charge loses energy = Q x (V1-V2) Joules
X
V22
Energy gained Energy lost
KVL: law of conservation of Energy 42
Parallel CircuitsTwo elements are connected in parallel if both ends of one pelement are connected directly to corresponding ends of the other
A and B are connected in parallel
D E and F are connected in parallelD, E and F are connected in parallel
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The voltage across parallel elements are equal (both g p q (magnitude and polarity)
a b cv v v= = −
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Example
3 5 0 8c cv v V− − + = ⇒ =
( 10 ) 0 2c e ev v v V− − − + = ⇒ = −( )c e e
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Use KVL , KCL and Ohm’s law to solve the given problem
+ v1 -
+
V
i1
V2
-
i2
1 2 1 20x xv v v v v v− + + = ⇒ = +
1 1 5v i= × 2 2 1 0v i= ×1 1 5v i × 2 2 1 0v i ×46
Next Problem: Find currents i1 and i2
i11 2xv v v= +
i
1 1 5v i= ×
i22 2 10v i= ×
( 2 ) 5v i i= + ×1 2( 2 ) 5xv i i= + ×
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Use ohm’s law : v = I x R
I1 = ?
+
5V
+
5V1A
+
5V0.5A
5V
-
5V
-
5V
-
Apply KCL at the indicated node
1 10 .5 1 1 0 2 .5i i A− − − = ⇒ = 1 1 5 12 .5v i V= × =
1 2 12 .5 5 17 .5xv v v V= + = + =48
Independent Sources
12V12V
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Dependent (Controlled) Voltage Sources
+
-Vx2Vx
+- Ix
3Ix+-
Current-controlledVoltage-controlledVoltage source
Very useful in constructing circuit models for real-world devices such as transistors and amplifiers
Voltage sourceVoltage source
devices such as transistors and amplifiers
For a voltage controlled source: V = K1Vx , K i i t ith itK1 is a gain parameter with no units
For a current controlled source: V = K2Ix, 2 xK2 is a gain parameter with units [V/A]
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Dependent (Controlled ) Current Sources
+Vx2Vx Ix
3Ix-
Current-controlledVoltage-controlled
Very useful in constructing circuit models for real-world f
Current-controlledcurrent sourcecurrent source
devices such as transistors and amplifiers
For a voltage controlled source: I = K3Vx,g 3 x,K3 is a gain parameter with units [A/V]
For a current controlled source: I = K IFor a current controlled source: I = K4Ix, K4 is a gain parameter with no units
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SummaryCurrent: The time rate of flow of electrical charge
Voltage difference is the Source of current flow
Units of Voltage: Volts (V)g
– The units are amperes (A), which are equivalent to coulombs per second (C/s)
Units of Voltage: Volts (V)
V1 IPower( )Direction of current flow is opposite to direction of electron flow
X
V2
I1 2( )P V V I= − ×
2
1
( ) ( )t
t
d wP t w p t d td t
= ⇒ = ∫Ohm’s law V2
( ) ( )v t R i t= ×
( )( ) ( )v ti t G v tR
= = ×
Kirchhoff's Current Law (KCL)Sum of currents entering a node is equal to sum of currents leaving a node
R+
-v
i 2vPR
=
2P i R= ×currents leaving a node
1 2 3i i i+ =
Kirchhoff's Voltage Law (KVL)Two elements are connected in series ifthere is no other element connected tothe node joining them. Same currentflows The algebraic sum of the voltages
equals zero for any closed path (loop) in an electrical circuit
Two elements are connected in parallel if both ends of one element are connected directly to corresponding ends of the other. Same voltage
flows
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