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Instituto Politécnico Nacional Escuela Superior de Computo

Practice N. 3: “Kirchhoff’s Laws"

Members: -López Salazar Victor Manuel - Hernández Rivera Ángel Edmundo

Group: 1CV7 Team: 11 Fundamental Circuit Analysis Raúl Santillán Luna Date: 20/03/18

Index

1. Index…………………………………………………………………………………...2 2. Introduction……………………………………………………………………………2 3. Development: measurements, calculated and simulated………………………3-12 4. Questionaire………………………………………………………………………..13 5. Conclusions………………………………………………………………………....13

Introduction To the analysis of circuits it has Ohm's law, but not enough to understand their behavior, so the German Gustav Kirchhoff postulate two laws for circuit analysis, calls, Kirchhoff's current law that says "the algebraic sum of the currents affecting a node is zero" and Kirchhoff's voltage law which says that "the algebraic sum of the voltages around any closed path in a circuit is zero at all times". Kirchhoff's laws are two equations that are based on energy conservation and load on electrical circuits. They were first described in 1845 by Gustav Kirchhoff They are widely used in electrical engineering. Both laws circuit can be derived directly from Maxwell's equations, but Kirchhoff preceded Maxwell and thanks to their work Georg Ohm was widespread. These laws are widely used in electrical engineering and electronic engineering to find currents and voltages at any point in an electrical circuit.

Development Calculations for the practice Circuit 1: V1= 9V

V2=5V

R1=470Ω

R2=330Ω

-V1-V2+R1+R2+R3=0 -9V- 5V+IT(R1+R2+R3) =0 (1360Ω)IT=14V IT=14/1360 IT= 0.01029 mA

R3=560Ω IT(470Ω+330Ω+560Ω)=14V

VAB = (470Ω) (0.01029 mA) = 4.83 V VCD = (330Ω) (0.01029 mA) = 3.39 V VD0 = (560Ω) (0.01029 mA) = 5.76 V

V0A = 9V VBC = 5V

P0A = (9V) (0.01029mA) = -92.61 mW PBC = (5V) (0.01029mA) = -51.45 mW PD0 = (5.76 V)^2 / (560Ω) = 59.24 mW

PAB = (4.83 V)^2 / (470Ω) = 49.63 mW PCD = (3.39 V)^2 / (330Ω) = 34.82 mW

Circuit 2: V1= 9V

V2=5V

R1=470Ω

-V1+VR1+VR2=0 -V1+I1R1+ (I1-I2)R2=0 -9V+I1(470Ω)+(I1-I2)330Ω=0 880ΩI1-330ΩI2=9V

R2=330Ω

R3=560Ω

VR3+VR2+V2=0 I2R3+(I2-I1)R2+V2=0 I2(560Ω)+(I2-I1)330Ω+5V=0 890ΩI2-330ΩI1=-5V

(880*890)-(-330*-330)= 783200-108900= 674300=6.743x105 = ∆ (9*890)-(-5*-330)= 8010-1650=6360 I1=6360/6.743x105 =10.5 mA (-5*890)-(-330*9)= -4450+2970=-1470 I2=-1470/6.743x105 = 12.3 mA I1=I2+I3

I3=I1-I2

I3=10.5mA-12.3mA= -1.71mA

VOA = −9V VAB = (470Ω)(10.5 mA) = 4.93V VBC = (560Ω)(−1.71mA) = .957 V VC0 = −5V P0A = (−9V)(10.25 mA) = −94.77mW PB0 = (4.05 v)2 /(330Ω) = 50.57mW PB0 = (5V)(−1.71 mA) = −8.55mW

VB0 = (330Ω)(12.3mA) = 4.05V

PAB = (4.93V)2 /(470Ω) = 52.11mW PBC = (.957V)2 /(560Ω) = 1.63mW

DEVELOPMENT OF PRACTICE II. 1. - Verification of the Kirchhoff Law for voltage To start the practice, we build the circuit shown in figure 1. Subsequently we proceeded to turn on the voltage sources and set them to their required value ELEMENT VS1 VS2 R1 R2 R3

VALUE 9V 5V 470 Ω 330 Ω 560 Ω

POWER

1/2 watt 1/2 watt 1/2 watt

A) Applying Kirchhoff's voltage law to this circuit, find in a theoretical way (algebraic analysis), and the corresponding voltage valuesat the marked points. I=V/R

I = 14/1360 = 0.01029 mA -9 + VR1 + VR2 + VR3 - 5V = 0 VR1 + VR2 + VR3 = 14V IR1+ IR2 +IR3 = 14V I (R1+R2+R3) = 14V SUST. 0.01029 mA (470Ω + 330Ω + 560Ω) = 14V 4.8363 + 3.3957 + 5.7624 = 14V 14 = 14 14 – 14 = 0 0 = 0. VR1 = 4.8363 V VR2 = 3.3957 V VR3 = 5.7624 V

B) Find the resulting current and describe it graphically with its reference address on the circuit diagram.

Rt = R1 + R2 + R3

Vt = V1 + V2

Rt = 470Ω + 330Ω + 560Ω

Vt = 9V + 5 V

Rt = 1360 Ω

Vt =14V

I = 14V/1360Ω I = 0.01029 mA

C) Check the validity of these calculations by means of the measurements with the voltmeter and report their theoretical, experimental and practical values in table 1.

D) Check the validity of these calculations by means of the measurements with the voltmeter and report their theoretical and experimental values in table 1. E) Apply the statement of the voltage law on the results to your measurements by performing the algebraic sum of the voltages. Record your results in the table. F) Obtain the power in each element of the circuit. G) Determine the sign of the voltages and powers according to the passive convention of signs, and through this convention determine which elements provide power and which absorb.

Measure V0A VAB VBC VCD VD0

Theoretical Measured value value (Volts) (volts) -9 V 4.83 V -5 V 3.39 V 5.76 V ∑v = 0V

Simulated value (volts)

Theoretical power (miliwatt)

Measured power (miliwatt)

Simulated power (miliwatt)

-8.97 V 4.8 V -5.01 V 3.41 V 5.77

-9 V 4.84 V -5 V 3.4 V 5.76 V

-92.61 mW 49.76 mW -51.45 mW 34.94 mW 59.29 mW

-92.61 mW 49.76 mW -51.45 mW 34.94 mW 59.29 mW

-92.61 mW 49.81 mW -51.45 mW 34.97 mW 59.34 mW

∑v = 0V

∑v = 0V

∑p = 0W

∑p = 0W

∑p = 0W

Table 1. Theoretical, experimental and simulated voltage values

Absorb (A) Supplies (S) S A S A A

SIMULATED CIRCUITS TABLE 1.

II. 2. - Checking the current Kirchhoff Law. After finishing filling the first table with the results obtained, we continued with the next part of the practice, it was about building another circuit, but this was in parallel form, we configured the voltage sources and we started the measurements. ELEMENT VS1 VS2 R1 R2 R3

VALUE 9V 5V 470 Ω 330 Ω 560 Ω

POWER

1/2 watt 1/2 watt 1/2 watt

II.2.1. - In the circuit of figure 2 A) Assign direction of arbitrary regency of currents in each branch of the circuit.

B) Apply the equation of voltages in both meshes and the equation of currents in node B. C) Simulate the circuit with the help of a software tool and allow it to do so and determine the correct direction in each of the currents and each of the voltages in the resistors with the proper polarity.

II.2.2. A) With the ammeter, make the measurements of the three branch and inset currents in table 2. Theoric Measurements value (mA) Current I1 (Branch on the left) Current I2 (Branch of the center) Current I3 (Branch on the right)

Measured Simulated value value (mA) (mA)

10.53 mA

10.893

10.5 mA

12.38 mA

12.423

12.3 mA

-1.69 mA

-1.536 mA

-1.71 mA

Table 2. Theoretical, measured and simulated current values.

SIMULATED CIRCUITS TABLE 2.

B) With the voltmeter, make the measurements of the voltages in the resistances and write down in table 3. C) Apply the law of currents, on the currents measured in node "B" and write down your result in table 2.

D) Obtain the theoretical, measured and calculated powers and write them down in table 3.

Measure V0A VAB VB0 VBC VC0

Theoretical Measured value value (Volts) (volts) 9V 4.94 V 4.08 V 0.949 V 5V

8.97 V 4.94 V 4.03 V 0.978 V 5.01 V

Simulated Theoretical Measured value power power (volts) (miliwatt) (miliwatt) 9V 4.96 V 4.04 V 0.956 V 5V

-94.77 mW 52.11 mW 50.57 mW 1.63 mW -8.55 mW ∑P=0

-94.77 mW 52.10 mW 50.55 mW 1.60 mW -8.55 mW ∑P=0

SIMULATED CIRCUITS TABLE 3.

Absorb (A) Supplies (S) -94.71 mW S 52.27 mW A 49.55 mW A 1.63mW A -8.55 mW S ∑P=0 Simulated power (miliwatt)

QUESTIONARY 1. Defined to be a node in an electrical circuit. Is a point of interconnection between two or more branches 2. Define which is an electrical circuit. Is a set of interconnected elements that allows the flow of electric current 3. Expressed as mathematical Kirchhoff's law for current. I1 + I2 + I3 = I4 + I5 4. Define a closed path in an electrical circuit. Is any path taken by the current in an electrical circuit 5. Define a voltage output. Voltage drop of a conductor to the potential difference between the ends there of.

Conclusions Hernández Rivera Ángel Edmundo: In this practice we reinforce the knowledge about Ohm's Law and Kirchhoff's laws with classroom learning and practice, we can say that are 2 Kirchhoff's laws; Kirchhoff's Tension Law and the Kirchhoff Current Law; being the algebraic sum of the all voltages is equal to 0 and that the amount of intensity that enters through a node, is the same amount that leaves by the same node, without losing or gaining intensity of current. In practice it was developing both these two laws as Ohms Law is the best known circuits in the area for easy handling. López Salazar Victor Manuel: This practice cost me a lot of work to understand, since you had to use the knowledge of Kirchhoff's laws, but what really hindered me was the algebraic sum part, it did not give me an idea how to manipulate the voltages of my elements In order to obtain the desired results in practice, review the notes given by the teacher in order to understand a bit, at the end of accounts I obtained the desired results. This type of practice helps me a lot, helps me to reinforce my knowledge and to demand of myself, provokes that need to know more and consequently I obtain new knowledge.