Download Lab #3 Report: KVL and KCL Adam Stokes Partner: Davis Roberts 9

Lab #3 Report: KVL and KCL
Adam Stokes
Partner: Davis Roberts
9/28/2015
I. Introduction
In this lab we used the voltage meter and ammeter to measure the voltage and
current at certain parts of a circuit. We also practiced building simple two-loop
circuits using resistors, a voltage source and a breadboard.
The main objective of this lab was to demonstrate Kirchoff’s Current and Voltage
Laws in the real world. Also, this lab was meant to allow the students to become
more comfortable with the use of the ammeter and voltmeter.
II. Data and Analysis
The voltage and current in a circuit can be calculated by writing out a system of KVL
and KCL equations and then solving for the missing variables. The values can also be
found by using an ammeter and voltmeter and measuring in parallel (for voltage)
and series (for current). For circuit 3, multisim was used to construct the circuit and
measure the theoretical currents and voltages.
KVL: The sum of all of the voltages in a loop equals zero.
KCL: The sum of currents entering a node equals the sum of the currents leaving a
node.
Circuit 1:
I1
I2
I3
V1
V2
V3
V4
V5
V6
Table 1: Circuit 1 Values
Calculation
-3.75 mA
1.5 mA
2.25 mA
3.75 V
1.5 V
4.5 V
1.5 V
1.5 V
3.75 V
Measurement
-3.774 mA
1.511 mA
2.264 mA
3.723 V
1.4927 V
4.492 V
1.4986 V
1.5008 V
3.778 V
The current at each node can be represented by the KCL equation below:
I1+ I2 + I3 = 0
For nodes b and e, using calculated values:
(-3.75 mA) + (1.5 mA) + (2.25 mA) = 0 mA
For the three loops in the circuit:
Loop 1 (left): (12 V) + (-3.75 V) + (-4.5 V) + (-3.75 V) = 0 V
Loop 2 (right): (1.5 V) + (1.5 V) + (1.5 V) + (-4.5 V) = 0 V
Loop 3 (outside): (12 V) + (-3.75 V) + (-1.5 V) + (-1.5 V) + (-1.5 V) + (-3.75 V) = 0 V
Circuit 2:
I1
I2
I3
V1
V2
V3
V4
V5
V6
Table 2: Circuit 2 Values
Calculation
3.5 mA
1 mA
-2.5 mA
3.5 V
1V
5V
1V
1V
3.5 V
Measurement
3.519 mA
1.004 mA
-2.516 mA
3.571 V
0.9886 V
4.991 V
0.9949 V
0.9964 V
3.523 V
The current at each node can be shown by the following equation:
Iin = Iout
For node b:
(1 mA) = (3.5 mA) + (-2.5 mA)
For node e:
(3.5 mA) + (-2.5 mA) = (1 mA)
For the loops in the circuit:
Loop 1 (left): (12 V) + (-3.5 V) + (-5 V) + (-3.5 V) = 0 V
Loop 2 (right): (1 V) + (1 V) + (2 V) + (1 V) + (-5 V) = 0 V
Loop 3 (outside): (12 V) + (-3.5 V) + (-1 V) + (-1 V) + (-1 V) + (-35 V) + (-2 V) = 0 V
Circuit 3:
Table 3: Circuit 3 Values
Calculation
-5.691 mA
3.041 mA
2.65 mA
4.667 V
1.034 V
6.081 V
1.802 V
1.246 V
1.252 V
I1
I2
I3
V1
V2
V3
V4
V5
V6
Measurement
-5.692 mA
3.058 mA
2.641 mA
4.659 V
1.0346 V
6.070 V
1.7925 V
1.2338 V
1.2542 V
The current at the nodes can be found by the following equation:
I1 + I2 + I3 = 0
For nodes b and e:
(-5.691 mA) + (3.041 mA) + (2.65 mA) = 0 mA
For the loops in the circuit:
Loop 1 (left): (12 V) + (-4.667 V) + (-6.081 V) + (-1.252 V) = 0 V
Loop 2 (right): (1.034 V) + (1.802 V) + (1.246 V) + (2 V) + (-6.081 V) = 0 V
Loop 3 (outside): (12 V) + (-4.667 V) + (-1.034 V) + (-1.802 V) + (-2 V) + (-1.246 V) +
(-1.252 V) = 0 V
By looking at all of the data collected and calculated, we can see that
Kirchoff’s laws work for a theoretical circuit. Also, we can see that when the circuits
are made in the real world, the KCL and KVL laws still apply.
III. Conclusion
Lab three focused on Kirchoff’s Current Law and Kirchoff’s Voltage Law. By building
circuits and measuring them with an ammeter/voltmeter we were able to replicate
with reasonable accuracy the values that were shown in the schematics. We then
applied KVL and KCL to these real world circuits and the laws held true.