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