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EngineeringBasic Electrical and Electronics
Engineering
EE 104
L-T-P (2-1-0)
Lecture #1 (20110105)
Course Instructors
• Dr. Vipul Singh
• Dr. Abhinav Kranti
• Analog
• Digital
Circuit
Def: A circuit is an arrangement of electric or electronic components that perform a useful operation/function.
Some of the common circuit components are the following:-• Voltage/Current Sources.• Resistors.• Inductors.• Capacitors.• Operational Amplifiers.• Transistors etc.
Circuit Classification
Closed Circuit:Path is complete and therefore current flows.
Open Circuit:Path is incomplete, thus no current flows.
Switch symbols
More than often the flow of current in a circuit is controlled by using a switch. Some of the common types of Switches used in circuits are shown below:-
Knife or gate switch
Push-button switch
(Push to ON)
Push-button switch
(Push to OFF)
Current flow convention
e
e
e
e
e
e
I
By Convention the direction of flow of current is opposite to the direction of flow of electrons.
Ideal circuit element
i
+ -vCircuit element
A circuit element is ideal if its voltage and current are related by constant of proportionality a differential or integral representation
An ideal circuit element has linear behavior.
Ohm’s Law
Ohm’s law states that the current flowing through a resistor is directly proportional to the voltage applied across its terminals.
i
+ -v
R
A resistance conducts current from one node to the other and in the process, voltage drop occurs across the element in the direction of the current flow.
V = iR
v
i
Circuit terminologies
• A branch represents a single element viz. a voltage source or a resistor.• A node is a point of connection between two or more branches.• A loop is any closed path in a circuit.
For example in the circuit shown adjacently the total number of branches is 4, number of nodes is 3 and the number of loops is 3.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s voltage law (KVL) states that around any loop within a circuit the algebraic sum of voltages across various elements is zero.
10 V+ -V1
2 KΩ
3 KΩ
V2
+
-
iApplying KVL we have:
mA2i03000i-2000i10
0VV-10 21
Kirchhoff’s Current Law (KCL)
Kirchhoff’s current law (KCL) states that around any node of a circuit the algebraic sum of all the currents is zero.
10 V+
-V1
2 KΩ
5 KΩV2
+
-
i
i1 i2
Applying KCL @ node 1 we have:
21
21
iii0)-i()(-ii
Applying KVL in loop 1 & 2 we have:
mA2imA;5i 21
Series Circuit
Resistances are said to be connected in series if there is only one path for the current to get from one point to another through these resistances.→ Resistances connected in series have same current flowing through them.
R3
R1 R2
V
i 321eff
321
RRRRiV
0iR-iR-iR-V
Voltage drop across R1is given by
1321
R11R1 RRRR
VViRV
Voltage divider rule
R3
R1 R2
V
i
1
Starting from node 1 and traversing the loop in a clockwise direction, plot potential as a function of distance.
VR1
VR2
VR3
V
position
R3 has the highest value amongst these resistances
Parallel Circuit
R1 R2V
ii1 i2
Resistances are said to be connected in parallel when the voltage across each of them is the same.
21 ii i
1111 R
ViRi V 2
222 RViRi V similarly
21eff21 R1
R1
R1
Vi
RV
RVi
iRRRi
iRR
Ri
21
12
21
21
Current divider rule
Example
R2 R3V0
i1i2 i3R1
Problem: Determine the current in the resistor R3, in the circuit shown below
32
321
01
RRRRR
Vi
Since R2 and R3 are in parallel by current divider rule we have
32
321
0
32
231
32
23
RRRRR
VRR
RiiRR
Ri
Voltage and Current Sources
V volts +-V voltsΞ I Amperes
Ideal voltage source Ideal current source
An ideal voltage source is a device that produces a fixed potential difference across its terminals regardless of what is connected to it.
An ideal current source is a device that moves a fixed amount of current in the direction indicated by the arrow regardless of what is connected to it.
These are all Independent current/voltage sources
Dependent Sources
Def: An ideal dependent current or voltage source is a source whose value depends upon some variable (usually a voltage or current) in the circuit to which the source belongs. Dependent sources are also called controlled sources.
+-
+-2v1 3i1 4i1 5v1
Voltage dependentVoltage source
Current dependentVoltage source
Current dependentCurrent source
Voltage dependentCurrent source
Example
+-
+-2 Ω
3.5 Ω
i0.5i
2 V
Problem: The circuit shown below contains a current dependent voltage source. Determine the current i in the circuit, also find the voltage drop across 3.5 Ω resistor.
Applying KVL we have
03.5i-0.5i2i-2
A 0.4i
Let voltage drop across 3.5 Ω resistor be v2
V4.15.34.0v2
Combining Sources
+-
+-
a
b
v1
v2
+-v1+v2
a
b
Voltage sources in series add up
a
b
i1 i2 i1+i2
a
b
Current sources add up in parallel
Wheatstone Bridge
i1i2
R1
VS
R3
R4
i3
(i1-i3) R0
(i1-i3+i2)R2
)(0RiRiV 3311s i
)(0)Rii-i(RiV 423122s ii
)(0Ri)Ri-i(Ri 2203111 iii
)(0)Ri-i()Rii-i(Ri 031423133 iv
Applying KVL in loop 1 & 2 we get
Under balanced condition (i1-i3) is zero, thus substituting the same in eqn 3 & 4 we get
4
3
2
1
RR
RR
Power Dissipated by a Resistor
Rti E 2
Energy dissipated by a resistance in time t is given by
The rate at which energy is converted or supplied is defined as power,
RitE P 2
Thus for an ideal resistor, Power is given by
RV ViRi P
22