1) The document describes an experiment to verify Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) using a circuit containing resistors, capacitors, and an inductor. 2) Mesh analysis and Kirchhoff's laws were used to analyze the circuit and calculate current and voltage values. 3) The calculated, experimental, and simulated values matched, validating that KCL, KVL, and Ohm's law accurately describe the circuit.

1. Kirchhoff’sVoltage&and&Current&Laws&for&Circuits&with
andReactive&Components
Laboratory - #2
Kehali B. Haileselassie& Faisal Abdulrazaqalsaa
07/21/2013
ELC ENG 305 – Circuit Analysis II
Instructor - EbrahimForati

2. Introduction
The purpose of this report is to verify Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current
Law (KCL) using a circuit containing both resistive and reactive components in it. The purpose
of the report also includesinvestigating the amplitude and phasing angle in RLC circuits using
the properties of capacitors and inductors. The circuit was built using the given Elenco DC
power supply (Model XP-770), Agilent Signal Generator (Agilent 33220A) digital multi-meter,
breadboard, electrical wires and three 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
We designed a simple circuit with resistive and reactive element that was available in our kit in
order to verify the KVL and KCL.
The three resistors, the resistive and reactive component were chosen randomly from the kit.
Theirnominal and measured values of each components and resistors are shown in the table
below for further elastration.
Item Reference Nominal Value (kῼ) Measured Value(kῼ)
1 R1 1kῼ 1kῼ
2 R2 2kῼ 2kῼ
3 R3 1kῼ 1kῼ
4 C1 0.01 0.01
5 C2 0.01 0.01
6 L1 200mH 200mH
Table_1
The measured values of the amplitude and the phase angle of each element is shown in table 2
bellow for further elastration.
Item Reference Amplitude Angle Phi
1 R1 5.375
2 R2 4.00
3 R3 2.12
4 C1 3.175
5 C2 1.40
6 L1 2.25
Table_2

4. The simple resistive circuit that we designed to verify KVL and KCL with three loops; one
resistor and one reactive element per loop in this laboratory is shown below in figure_1.
Figure_1
Data and Analysis and Culculation
We used mesh analysis to figure out the voltage and the current of each elemens. In
addition to Kirchhoff’s law, We applied the ohm’s law ( V = IR ). 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 impedance Z across the capacitors and inductor are specified as bellow.
Zc_1 = 1/ (jwc-1) = 1/( j*1000*0.01*0.000001) = -100000j
Zc_2 = 1/(jwc-2) = 1/(j*1000*0.01*0.000001) = -100000j
ZL_1 = jwL = J*1000*200*0.001 = 200j

5. KVL was applied to the three closed loops of the circuit using the symbolic label stated in
figure_1. The equation is shown below.
Vc_1 + V1 - Vs = 0→ R_1I1 + Zc_1(I1_I2) – VS = 1000*I1 -100000j(I1 _I2) – 10 = 0
Vc_1 + V2 + VL_1 = 0→R_2I2 + Zc_1(I2 – I1) – VSL = 2000*I2-100000j(I2 – I1) +200j(I2 – I3) = 0
V3 + Vc_2– VL_1 = 0→ R_3I3 + Zc_2I1 – VL = 1000I3-100000Ji3 +200j(I3 – I2) = 0
Solutions
I1 =

6. 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 and investigating the amplitude and phasing angle in RLC
circuits using the properties of capacitors and inductors. There were five 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. The calculated values, the experimental values
and the simulated values from the LTspice are almost the same. In addition, we did figure out
that the voltage across the inductor lead the current through the resistors and capacitors. At a
high frequencies, the impedance of the inductor will be much larger than the capacitors and the
impedance of the resistors. The current will be small. In contradict, at low frequencies, The
impedance of the capacitors will be much larger than the impedance of inductor and the
impedance of the resistors. The current still remain small.The As a result, we concluded that the
Kirchhoff’s Law (KVL & KCL) and the Ohm’s Law are valid.