l6 cap induc circuits

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ESc102: Introduction to Electronics

Basic Circuit Analysis

A R Harish

Dept. of Electrical Engineering

IIT Kanpur

Aug 2, 2010



Linearity and Superposition

2

IRV

kV kIR Increasing the current by a constant k

R I V 11

Response to two excitations:

R I V 22

212121 V V R I R I R I I V



Superposition Principle

The superposition principle states that the total responseis the sum of the responses to each of the independentsources acting individually.

3



0 V

0 A

4L5_basic_circuit_analysis



Example

15 V

2 A I T

V T

V V

V

V V

T

T

T T

335

23

2103

02510

15



Example

Circuit with only voltage source active. Current source isopen circuited.

V s=15 V

I 1

V 1

V V 5155

151



Example

Circuit with only current source active. Voltage source is

short circuited.

I s=2 A I 2

V 2

21

21

I I I

V V V

T

T

V V 3

201510252

V V V V T 335

320

521



Example


20 V 10 V



Example


I 1V 1



Example

11

10 V

21

21

I I I

V V V

T

T

I 2V 2



Example


V x

0.1V x




V1=2.5 V

V1

0.1V 1




V2=10 V

V2

0.1V 2



L5_basic_circuit_analysis 15

4 A 1

3+

V 1-

2

I 10.5V 1

3I 1

5

R +

V 0

-

12

Determine the resistance R in the following circuit, if V 0=10 V.



16

4 A 1

3+

V 1

-

2

I 10.5V 1

3I 1

5

R

+

V 0-

12

Rt

V t Thevenin Equivalent



We can apply Thevenin equivalent to any part of the circuit

Vt1

R t1

Vt2

R t2




Thévenin Equivalent Circuit What is V t ?

+

V oc

-


Rt

V t

+

V oc

-

oct V V



Examples

21

sc I

33.3315.0

5

15.0100

15

sc

t t

sc

I

V R

A I

100



Finding the Thévenin Resistance Directly

Suppose we make all independent sources zero in the circuit

Circuit with noIndependent

sourcest R



1.Turn off independent sources in the original network:

-A voltage source becomes a short circuit

-A current source becomes an open circuit

2. Compute the resistance between the terminals

Finding the Thévenin Resistance Directly

Circuit with noIndependent sources

t R

24



5 2 045 2 0eq R



Find Thevenin resistance for each of the circuits shown below

26



Circuit with dependent Sources

?t R

28



V Z

IZCircuit with dependent Sources

Z

t Z

V R I

29



Norton’s equivalent

Anycircuit

Any circuit

30



Norton’s equivalent How do we find I N ?


sc I

sc I

scn I I



Norton’s equivalent

+

Voc

-

+Voc

-

How do we find R N ?


sc

oct

I

V R

t noc R I V



34



E l



Examples

36

+-

Using Thevenin’s theorem find the equivalent circuit to the left of the terminals



Using Thevenin s theorem, find the equivalent circuit to the left of the terminalsin the circuit shown below. Hence find i.

6o cv V 3t R

1 .5i A37L5_basic_circuit_analysis

Source Transformation



Source Transformation

t n

t

V I

R

t n t V I R


Example



Example

39

Example



Example

40

Maximum Power Transfer for dc circuits



R L

R

V S

What value of R L will give rise to maximum load power ?

S

L

V I

R R2 2

2( ) L

L L S L

RP I R V

R R

0 L

LP

R

L R R2

m ax 4S

L L

V P

R

I




R L5V

1K

1 6 .2 5 L L R K P m W

1 0 2 L L R K P m W

0 .2 3 .4 7 L L R K P m W

Maximum power is delivered to the load when RL = R


General Case



R L

Resistors and

Sources R LV t

R t

Maximum power is delivered to the load when RL = R t


l6 cap induc circuits

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