ESC201: INTRODUCTION TO ELECTRONICS

MODULE 1: CIRCUIT ANALYSIS

Dr. Shubham Sahay,
Assistant Professor,
Department of Electrical Engineering,
IIT Kanpur
Re-cap
• Why electronics?

• Easily available electrical energy can be controlled precisely with electronics.

• ‘Imagination’ is the limit!

• Can solve problems in other domains: make them smart!!.

Dr. Shubham Sahay ESC201 2

Why ESC201?

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Charge
Unit of electric charge: Coulomb
Charles-Augustin de Coulomb
1C=1Ax1s (14 June 1736 – 23 August 1806)

Common symbols: q or Q
An electronic charge: - 1.6 x 10-19 C

Electron carries negative charge

Proton carries positive charge

Negative charge carriers:

• electrons, negative ions, …

Positive charge carriers: Wikipedia

• positive ions, holes (absence of electrons), …

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Current
• The time rate of flow of electrical charge
• Unit: ampere (A) → which is coulomb per second (C/s)
• Ampere is one of the seven basic SI units
• Popular symbol is i or I André-Marie Ampère
1775-1836

commons.wikimedia.org

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Electrical Current
Flow of electrons through a wire or other electrical conductor gives rise to current

• Electrons are negatively charged particles

The charge per electron is -1.602×10-19 C

I

1016 electrons flow per second

How much current flows?

Q −1.6  10 −19  1016

Dr. Shubham Sahay ESC201
I= = = − 1.6  10 −3 A 6
t 1
Electrical Current
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 has to flow for appreciable current.

Exercise 1: For 𝑞 𝑡 = 2 − 2𝑒 −100𝑡 , for 𝑡 > 0 and 𝑞(𝑡) = 0 for 𝑡 < 0,

find 𝑖(𝑡).
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Sign of current

2A -2A
X X

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Direct Current (DC) & Alternating Current (AC)
When current is constant with time, we say that we have direct current,
abbreviated as DC.

On the other hand, a current that varies with time, reversing direction periodically, is
called alternating current, abbreviated as AC
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Voltage
• Voltage difference causes current to flow

• Potential difference for a unit positive charge between two points

• Work done to move unit positive charge between two points

• Units of Voltage: volt (V)

• Popular symbol: v or V

12V 12V
Alessandro Giuseppe Antonio
12V Anastasio Volta 1745-1827
0V
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Light comes on Light does not come on 10
Voltage Is Relative

• In practice, it is V that matters +

x V

-
• In a circuit (system), we choose a reference
• Reference is called “ground”
• Rest of the voltages in the circuit are w.r.t. ground
V3

V2 V1

Dr. Shubham Sahay ESC201

Reference 11
V= 0
Water Analogy
• Current flow from
high voltage to low
High
voltage potential

• (Potential) energy is Flow

direction
consumed in the path

• Higher resistance: Low

potential
smaller flow

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Voltage Sign

Terminal B is 5 V higher Terminal A is 5 V higher

than terminal A than terminal B

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DC and AC voltages

V+ − V− = 12V

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Electrical elements
Electrical Systems are made of Voltage sources, wires and a variety of electrical
elements

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A Circuit
A path for current to flow

https://www.britannica.com/technology/electric-circuit

Electrical systems with closed current paths are often called electrical circuits

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Electric Shocks
Small currents (70–700 mA) can trigger fibrillation in the heart.
Larger currents will permanently damage the heart

220 V in India

Page 54 Hayt, Kemmerly, Durbin 17

Electrical Circuit
Analyze circuit

Questions
Compute current given voltage
Compute light intensity generated from bulb
How to solve these questions?
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Back to Maxwell’s Equations

• Should we write Maxwell’s equations

everytime

• Gainful employment of Maxwell’s

equations to build interesting
systems

• Create an abstraction layer

• Avoid dealing with Maxwell’s eq

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Abstraction
• Example: point mass abstraction

• What is the acceleration? 𝑎 = 𝐹/𝑚

• Ignoring the object’s shape, rigidity, temperature

• Point-mass discretization or lumping

• Useful at all levels

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Lumped Circuit Abstraction
V I
3 1
6 2
9 3
12 4

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Bulb’s behavior
Any electrical element which obeys ohms law can be modeled as a resistor

Can we model an electric bulb as a resistor?

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Bulb’s behavior

Even though characteristics are non-linear, over a certain range, the bulb
can be thought of as a resistor

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Resistor

v (t ) = R  i (t )
Ohm’s law
The constant, R, is called the resistance of the component and is measured in units
of Ohm (Ω)

R
Resistor Symbol:
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Conductance

http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Ernst_Werner_von_Siemens.jpg/225px-Ernst_Werner_von_Siemens.jpg

v (t ) = R  i (t )
v(t )
i (t ) = = G  v(t )
R
Ernst Werner von Siemens
G = 1/R is called conductance and its unit is Siemens (S) 1816-1892

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Resistance Related to Physical Parameters

L
R=
A

Resistance 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]

– Conductors (Aluminum, Carbon, Copper, Gold)
– Insulators (Glass, Teflon)
– Semiconductors (Silicon)
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Short vs Open Circuit

v
R=
i
i
G=
v

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Short & open circuit

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Voltage Source

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Current Source

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Power
• A battery stores energy (measured in Joules)

• Power delivered by the battery = V x I

• Power delivered by battery when current flows out of the positive terminal
(discharging)

• Otherwise, battery consumes energy (charging)

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Variable Convention
V1
I
P = (V1 − V2 )  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 !
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Associated variables convention
12V
P= ? P = (V1 − V2 )  I
1A
X = (12 − 6)  1 = 6W
Power is being delivered to
the electrical element X
6V
P = (V1 − V2 )  I
12V P= ?
= (12 − 6)  −1 = − 6W
1A
Power is supplied by element x
X
instead of dissipation

6V

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Spot the battery!
• Given that there is only one battery, which one is it?

A battery is a source of power, so power dissipated is negative

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Power dissipated in a resistor

i v
+ v =i R i=
v R R
- P =vi
2
v
P =i  R
2 P=
R

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Nodes
Node: A point where 2 or more circuit elements are connected.

R1 R3
VS R2 R4 IX

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What is a Loop?
A loop is formed by tracing a closed path through circuit elements without passing
through any intermediate node more than once

R1 R3
VS R2 R4 IX

This is not a valid loop !

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Circuit Analysis
• Kirchhoff’s Laws

• KCL and KVL

• Conservation of Charge and Energy

Gustav Kirchhoff

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Kirchoff’s Current Law (KCL)
Sum of currents entering a node is equal to sum of currents leaving a node

i1 + i2 = i3

A direct result of conservation of charge

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Kirchhoff’s Current Law (KCL)

At any node in a circuit, the sum of all current arriving is 0

N

i
1
j =0

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KCL: examples

i3 = i4

1 + 3 − ia = 0

ia = 4 A
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KCL: examples

𝑖1 𝑖𝑏 − 2 + 𝑖1 = 0
1 + 3 − 𝑖1 = 0

1 + 3 + ib − 2 = 0

ib = − 2 A
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KCL: combining nodes

1 + 3 + ic + 4 = 0

ic = − 8 A
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KCL: generalization

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KCL: general form

i1
i2

R1 R3
VS R2 R4 IX

i3 i4

i1 + i2 + i3 − i4 = 0

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Series Circuit
Two elements are connected in series if there is no other element connected to
the node joining them

A, B and C are in series

The elements have the same current going through them

Dr. Shubham Sahay ESC201

ia = ib = ic 46
A and B are in series E, F and G are in series

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Kirchhoff's Voltage Law (KVL)
The algebraic sum of the voltages equals zero for any closed
path (loop) in an electrical circuit.
In applying KVL to a Loop

voltages are added (or subtracted)

depending on their polarities relative

to the direction of travel around the
loop

Conservation of energy!
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KVL: example

Loop3: - ve + vd - vb + va = 0

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Parallel Circuits
Two elements are connected in parallel if both ends of one element are
connected directly to corresponding ends of the other

A and B are connected in parallel

D, E and F are connected in parallel

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The voltage across parallel elements are equal (both magnitude and polarity)

va = vb = − vc
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Example

−3 − 5 + vc = 0  vc = 8V
−vc − ( −10) + ve = 0  ve = − 2V
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Ready to use KCL-KVL?

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Tidy circuits are easier to understand

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