Kirchhoff’s Circuit Laws Lab Report PDF

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Kirchhoff’s Circuit Laws Experiment PHYS 1420 – 501 April 6, 2020 Denise Harris McMurrian

Abstract The purpose of this experiment was to verify Kirchhoff’s Laws. By building our own circuits we were able to test whether the current flowing through a junction point is 0 at all times and if the sum of the voltage drop when it travels around any closed loop is equal to 0. Using Kirchhoff’s laws, the relationship between current (I) and voltage (V) was established using the equations ∑i I i =0 and ∑i V i

= 0; these equations aided our understanding of the difference between

Kirchhoff’s junction and loop laws which is important in understanding the transfer of energy through electrical circuits. Percent error yielded an average of 40%, meaning that we did encounter significant error when calculating our current values (I1, I2, and I3); this is important because it does not accurately or precisely give us a real life demonstration of the current flow which hinders our ability to fully understand the relationship between Kirchhoff’s laws or the effect of patterns on current flow. This high percent error could be due to factors that weren’t considered when making calculations, such as the internal resistance of the wires used to build the circuit, faulty machinery, or incorrect setup of the circuit; all of these errors could have caused much higher current values and aided in our percentage. Introduction Kirchhoff’s laws are important in describing the transfer of energy through electrical circuits; they give us a better understanding of the connections in the circuit, they quantify current flows, and they explain how voltage varies around a loop. The Junction Law states that when traveling a parallel path, the total current entering a circuit’s junction is equal to the total current leaving the junction; this is due to the fact that current is the rate of the flow of charge and charge is always conserved so, the current flowing in must equal the current flowing out: 

Equation 1 Junction Law: ∑i I i =0 o ∑= sum of currents o I = Current

The Loop Law states that the sum of all of the voltages around a closed loop must equal 0. As stated earlier, as a current passes through a junction point the sum of the current entering must be equal to the sum of the current exiting the point; this still kind of reigns true for closed circuits,

except this law focuses on the work done by electric forces on a unit of charge which is called voltage and the voltage doesn’t exit the point, instead, the sum of the potential differences across the loop must equal 0: 

Equation 2 Loop Law: ∑i V i

=0

o V = voltage To have a complete understanding of Kirchhoff’s Laws the following equations were used: 

Equation 6 Current 1: I 1 =

V F −V B R1

o Was used to calculate the experimental value of Current 1 o R = resistor 

Equation 7 Current 2: : I 2 =

V O −V B R2

o Was used to calculate the experimental value of Current 2 Apparatus 

1 AC/DC Electronics Laboratory



DC Regulated Power Supply



Digital Multimeter



Short Patch Cords



2 100  resistors (brown-black-violet-gold)(red-black-violet-gold)



2 330  resistors (orange-orange-violet-gold)



1 100  resistors (red-black-violet-gold)



1 1000  resistors (violet-black-red-gold)

Procedure Setup To begin this experiment, first obtain the resistors, test their resistance, and record those values into Table 1. Next, construct the circuit board to reflect the one below:

Finally, connect the board together using the connection wires and the alligator clips to connect to the power supply:

Procedure A To begin this portion of the experiment, first, set up the digital multimeter to measure voltage. Next setup the power supply to 15 volts and 0.060 A. Then, touch the black lead to any ground point on the board, and record this for value V0. Repeat this step two more times, touching the red lead to Point F, this is point VF, then to a point between point A and B, this is point VB. To test I3, remove the wire between Point D and G and replace it with your leads, that’s value I3. Using Ohm’s law, calculate the theoretical values of I1 and I2. To test the experimental values of I1 and I2, replace the wire between D and G, and remove the wire between C and E. Touch your leads to point C and E, this is your I2 value. To measure I1, replace the wire to C and E and remove the wire from A to F, replace with your leads and record these values into Table 2.

Data Table 1: Measured Resistance Values R1: 100  99.3 Brown-black-

R2: 330  327.3 Orange-orange-

R3: 100  98.3 Red-black-

R4: 330  326.3 Orange-orange-

R5: 1000  1000 Violet-black-

violet-gold

violet-gold

violet-gold

violet-gold

red-gold

Table 2: Experimental DC Circuit Voltages and Currents V0

VB

VF

I1

I2

I3

(V)

(V)

(V)

(mA)

(mA)

(mA)

14.9

4.85

6.71

5.45

30.3

25.1

Calculations Theoretical Current Values (mA) I1 :

6.71 −4.85 =18.73 99.3

I2 :

14.98 −4.85 =30.95 327.3

Theoretical DC Circuit Currents (mA) – matrix used I 1 : ¿ 18.5 I 2 : ¿ 30.4

I 3 : ¿ 48.9 Percent Difference (%) I1 :

5.45 −18.5 =70.5 18.5

I2 :

30.3 −30.4 =18.7 30.4

I 3 : 25.1 −48.9 =48.6 48.9

Discussion of Results and Error Analysis Overall, the percent differences between the theoretical and measured current values varied: I1

yielded 70.5%, I 2

yielded 0.13%, and

I 3 yielded 48.6%. Any error that did occur

could have resulted from faulty machinery, unaccounted for variables such as internal resistance of short patch connection wires, and incorrect setup of circuits and calculations. We expected for all of our experimental values to be precise and accurate with our theoretical values to verify the patterns of voltage and current in open parallel and closed loop circles. As states before, these large error differences could have occurred for multiple reasons. But, the downfall for this error is not allowing us to see an accurate representation of these current values, their sum, and how it aligns with Kirchhoff’s laws. This experiment could benefit from upgraded machinery; old and faulty machines cause for accidents and inaccurate readings. This experiment could also benefit from an in-class demonstration of the set up of the circuit board, resistors, and wires and how to preform the calculations, these could help prevent human error. Lastly, this experiment could benefit from unaccounted for variable like the internal resistance of the small patch connection wires. Conclusion The purpose of this experiment was to verify Kirchhoff’s junction and loop laws by exploring the paths and patterns currents and voltage. Through the completion of this experiment, we are now able to define and differentiate between Kirchhoff’s junction and loop law, continue to verify Ohm’s law, and continue to gain further understanding about electrical systems. Although our percent difference values were high, we were still able to gain an understanding of the experiment. We believe our high values were due to factors that weren’t considered when making calculations, such as the internal resistance of the wires used to build the circuit, faulty machinery, or incorrect setup of the circuit. Better machinery or a demonstration to students prior to the experiment could help reduce preventable errors. This method of experimentation did appear to work accurately for our Current 2 values, but neither accurately or precisely for our

Current 1 and 3 values. Our current 2 value verified that sum of the current going into the junction point is the same as the sum exiting the point....