7/26/2019 Theorems Linearity and Overlay Inf Final

http://slidepdf.com/reader/full/theorems-linearity-and-overlay-inf-final 1/4

THEOREMS LINEARITY AND OVERLAY 

 Nejith K.Cifuentes 45151015, Marco Castellanos45151000,CristianH.Cristancho, 45151043

Abstract —  In this lab they were experimentally verified

the theorems of linearity and superposition , to this werecarried out a series of assemblies whose elements were

linear as dependent and independent voltage and current

and resistance sources , fed a DC and AC signal ,

likewise making the respective analysis for each

assembly 

I. 

INTRODUCTION

Circuit analysis is fundamental to the preparation of

a related thereto career, for these are different ways

to analyze linear circuits, step the property of the

element that describes a linear relationship between

its input and output , one of the is the superposition

 principle which states that the tension between the

ends of an element of a linear circuit is the algebraic

sum of the voltages or currents through it , as each

independent source acting alone . To better

understand how they work experimentally linear

circuits and the superposition principle was given

answers to the following questions:

1.  Is it possible to alter the linearity of a

circuit, without changing any of its

components?

It is not possible because the linearity of a circuit depends

on whether your output is linearly related to its input , iemust satisfy both the properties of homogeneity as

aditivita . A circuit is linear if the equations relating itsvoltage and current are linear , and vice versa , or in the

case of linear circuits is always possible to express oneof these quantities as a linear function of the other . 

Figure 1 Linearity of a circuit

2. 

If the power is not linear , it is possible to

calculate the power using the

superposition theorem ?

If possible since the superposition theorem helps

analyze a linear circuit with more than one independent

source, by calculating the contribution of each

independent source separately , allowing us to calculate

the current and voltage in each of the sources to analyze

the power at the circuit. To calculate the power circuit

must calculate the total current and then proceed to the

calculation of the power knowing that the relationship

 between the power is not linear but quadratic.

3. 

If a linear circuit is not supplied with

DC signal , but a signal whose

magnitude varies in time , the circuit

remains linear?

 No remains linear as the signal varies over time so theway in which components act changes, becomes anonlinear circuit where the relationship between voltageand current .

The main feature of an alternating current is that for a

moment of time a pole is negative and the other positive,

while in the next instant the polarities are reversed many

times as cycles per second or Hertz possesses that power

. However, although a constant change of polarity occurs

, the current will always flow from negative to positive.

Figure 2 Alternating current circuit  

II.  GUIDELINES FOR MANUSCRIPT

PREPARATION.

To start the laboratory was considered the proper

use of the gown, laboratory items such as the current

source, DMM, oscilloscope and others

subsequently mounting a linear circuit was

 performed by analyzing the current, voltage, power

It is circulating the same, just as varying the

temperature of the resistors (Graph 1).

Assembly to verify the superposition principle

consisting of two sources of voltage 8V to 5 v,

an independent source of current of 0.11 A and

resistors connected in series and in parallel

(Graph 2) was performed, then he proceeded to

7/26/2019 Theorems Linearity and Overlay Inf Final

http://slidepdf.com/reader/full/theorems-linearity-and-overlay-inf-final 2/4

make a short circuit on the source of 24 V, on

the open circuit current source for the current

flowing through the circuit obtained (Graph 3)

.In the same way a short circuit was the source

of 12 V and left open in the current source to

find the current flowing through the mesh 2

(Graph 4) circuit finally short-circuit was made

in the two voltage sources to find the currentthrough the mesh 3 (Graph 5) ; thus finding the

absorbed power and supplied by each of the

elements.

III. 

ANALYSIS OF RESULTS. 

 

ASSEMBLY 1

Graph 1 Linear Mounted

To verify circuit linearity different values of voltage

and current, varying the temperature at 82 Ω resistor

1 W.

RESISTANCE 1W

V(v) I(A) P(w) R(Ω) T(°C )

0 0 0 100 26,2

5 0,06 0,3 83,3333333 26,1

10 0,11 1,1 90,9090909 39,2

15 0,15 2,25 100 65,8

20 0,2 4 100 117,4

25 0,24 6 104,166667 150

The relationship was plotted of : voltage and current ;

 power and current, resistance and temperature.

Figure 1 Curve P-I

Figure 5 Curve V-I

Figure 6 Curve v-I

Figure 5 Curve R-I

7/26/2019 Theorems Linearity and Overlay Inf Final

http://slidepdf.com/reader/full/theorems-linearity-and-overlay-inf-final 3/4

 

Mounting 2

Where I=0,08 A

Graph2

Mounting linear superposition

Superposition principle analysis

 

Mesh 1

ℎ 3, ∶   0,02 

 

Mesh 2

ℎ 4, ∶   0,07 

 

Mesh 3

ℎ 5, ∶   0,03 

Where  +  +  -0,02+0,07+0,03=0,08

In the lab the following results were obtained: I=0,082

  =−. 

  =. 

  =. 

Where  +  +   

-0,023+0,076+0,022=0,0816 A

 .8−.8

.8*100=2%

  Calculation of theoretical power : Where

i=0.08 A, V=1.79V,it must :

  P=I*V= (0.08*1.79) =0.1432w

    0.02 ∗ 1.02 0.0204 

    0.07 ∗3.67=0.2569 w

    0.03 ∗ 1.53=0.0459 w

 

P= + + 0.3232 w

  Calculation of experimental power :

Were i=0.082 A, V=1.70V, it must P=I*V= (0.08*1.79)

=0.1394w

 .−.9

.*100=2.5%

    0.0204 ∗ 1.06 0.0254 

    0.076 ∗3.28=0.2493 w

    0.026 ∗ 1.68=0.0469 w

  P= + + 0,3216w

IV. 

DISCUSSION OF RESULTS 

 

For assembly 1 shows that there is alinear relationship between voltageand current as shown in Figure 3 , as

to the obtained power it is that this isa function of the current squared(Figure 4) and varying thetemperature of the resistance

obtained it is seen that this decreases because the material propertiesallow this.

  As to mount overlay analysis it

shows that one can’t calculate the

 power using the superposition

 principle as to calculate the currentsof each of the meshes and then the

 powers are affected as add or rise to

the same square so it does not

identify which power is absorbed or

supplied  

7/26/2019 Theorems Linearity and Overlay Inf Final

http://slidepdf.com/reader/full/theorems-linearity-and-overlay-inf-final 4/4

V. 

CONCLUSIONS

  Theorems of linearity and superposition were

experimentally verified, recognizing the

different factors that affect it.

  The superposition principle is an effective

method of analysis of circuits per 1 May this

requires work and to be analyzed each

independent source of voltage and current.

  The power circuit can’t be calculated by

means of the superposition principle as this is

not linear so they affected their proportions so

it does not identify which is absorbed or

supplied.