Kirchhoff’s Voltage and Current Law Laboratory - #1 report Kehali B. Haileselassie & Faisal Abdulrazaq alsaa

1. Kirchhoff’s Voltage and Current Law
Laboratory - #1
Kehali B. Haileselassie& Faisal Abdulrazaqalsaa
07/16/2013
ELC ENG 305 – Circuit Analysis II
Instructor - EbrahimForati

2. Introduction
The purpose of this report is to verify Kirchhoff’s Current Law and Kirchhoff’s Voltage Law by
constructing a simple three loop circuit that containing six resistors. The purpose of the report
also includes measuring the current through each resistors and the voltage at each nodes in the
circuit. The circuit was built using a given Elenco DC power supply (Model XP-770), digital
multi-meter, breadboard, electrical wires and six random resistors.
Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) is very important to
analysis a linear circuit. It is mainly deals to relate voltage to current and resistance. Kirchhoff’s
Voltage Law (KVL) states that the algebraic sum of all voltages in a closed loop must be equal to
zero. A closed loop is a path in a circuit that does give a return path for a current. Kirchhoff’s
Current Law (KCL) deals with the current flowing into and out of a single node. It states that the
sum of the current flowing into the node and the current flowing out from the node must equal to
zero.

3. Procedure
The six resistors were chosen randomly from the kit. Their resistance nominal and measured
Values of each resistor are shown in the table below.
Item Reference Nominal Value (kῼ) Measured Value(kῼ)
1 R1 1 0.98
2 R2 2 1.96
3 R3 2 1.96
4 R4 1 0.98
5 R5 2 1.96
6 R6 1 0.98
Table_1
Data and Analysis
We used loop analysis to figure out the voltage of each nodes and the current that flow through
each resistors. In addition to Kirchhoff’s law, We applied the ohm’s law ( V = IR ) and mesh’s
law to solve the current that passes through each resistors. We measured the voltage across each
resistor and the power supply by connecting a voltmeter in parallel with the resistors and the
power supply.
The simple resistive circuit that we designed to verify KVL and KCL with three loops and
tworesistor per loop; three nodes with three branches in this laboratory is shown below in
figure 1.

4. Figure:1
KVL was applied to the three closed loops of the circuit using the symbolic label stated as in figure 2.
The equation is shown below.
V4 + V1 - Vs = 0 → -10 + 1KI1 + 1K ( I1 – I2 ) = 0
V5 + V2 – V1 = 0 → 1K ( I2 – I1 ) + 2KI2 + 2K ( I2 – I3 ) = 0
V6 + V3 – V2 = 0 → 2K ( I3 – I2 ) + 1KI3 + 2 I3 = 0
Each node also generates KCL equation. The equation is stated as bellow.
((N2 – N1) 1k)) + ( N2 1k ) + ((N2 – N3 ) 2k) = 0
((N3– N2) 1k)) + ( N3 2k ) + ((N3 – N4 ) 1k) = 0
((N4– N3) 1k)) + ( N4 2k ) = 0

5. The experimental and analytical measured values of the current and voltage are specified in
detail in table 2 and 3.
Current Lable Experimental Current (mA) Analytical Current (mA)
IS 5.65 5.67568
IR_1 4.23 4.32433
IR_2 0.80 0.810809
IR_3 0.53 0.540541
IR_4 5.65 5.67568
IR_5 1.3 1.35135
IR_6 0.53 0.540541
Table_2
Voltage Label Experimental Voltage ( Volt ) Analytical Voltage ( Volt )
Vs 10.01 10.0
Node Voltage_1 (N1) 10.01 10.0
Node Voltage_2 (N2) 4.402 4.32432
Node Voltage_3 (N3) 1.6504 1.62162
Node Voltage_4 (N4) 1.098 1.08108
VR_1 4.402 4.32432
VR_2 1.6504 1.62162
VR_3 1.098 1.08108
VR_4 5.6521 5.67568
VR_5 2.7516 2.7027
VR_6 0.5524 0.54054
Table_3

6. In order to verify the Kirchhoff’s Voltage Law and Kirchhoff’s Current Law, let’s see the
algebraic sum of the voltages in each loop and the algebraic sum of the current that flowing into and
out of each nodes.
Substituted in experimental Voltage:
∑Vloop_1 = V4 + V1 - Vs↔ 5.6521 + 4.402 – 10.01 = 0.0441
∑Vloop_2 = V5 + V2 – V1↔ 2.7516 + 1.6504 – 4.402 = 0
∑Vloop_3 = V6 + V3 – V2 ↔ 0.5524 + 1.098 – 1.6504 = 0
∑ IN_2= IR_4 - IR_1 – IR_5 ↔ 5.65 – 4.3 – 1.3 = 0.05
∑ IN_3 = IR_5 - IR_2 – IR_6 ↔ 1.3 – 0.80 – 0.53 = -0.03
Substituted in Analytical Voltage and Current:
∑Vloop_1 = V4 + V1 - Vs ↔ 5.67568 + 4.32432 – 10 = 0
∑Vloop_2 = V5 + V2 – V1 ↔ 2.7027 + 1.62162 – 4.32432 = 0
∑Vloop_3 = V6 + V3 – V2 ↔ 0.54054 + 1.08108 – 1.62162 = 0
∑ IN_2= IR_4 - IR_1 – IR_5 ↔ 5.67568 – 4.32433 – 1.35135 = 0
∑ IN_3 = IR_5 - IR_2 – IR_6 ↔ 1.35135 – 0.810809 – 0.540541 = 0
There was no any error in our calculation because the expected value was zero. But there was still
some error between the measured (experimental) values and the calculated (analytical) values.
%error = |((measured – calculated) measured)| * 100%
To verify the ohm’s law, let’s see a sample calculation below:
%error = |((measured – calculated) measured)| * 100% = |((10.01 – 10 ) 10.01)| * 100% = 0.099%
%error = |((measured – calculated) measured)| * 100% = |((4.402 – 4.32432)/4.402)| * 100% = 1.764%

7. Conclussion
Ohm’s law and Kirchhoff’s law are the most basic techniques to analysis linear circuits. The
main purpose of this lab was to verify these two laws. There were six unknown current and
voltage in the circuit. We did build the circuit in breadboard. In order to verify the accuracy of
the values we measured experimentally, we simulated the circuit through using LTspice. We did
also calculated analytically by using Kirchhoff’s law and Ohm’s law to predict our calculated
value and the experimental values are the same. In addition to that, we applied the percent error
analysis as well. The percent error between the experimental values and calculated values are
less than three percent. The calculated values, the experimental values and the simulated values
from the LTspice are almost the same. As a result, we concluded that the Kirchhoff’s Law (KVL
& KCL) and the Ohm’s Law are valid.