PHYSICS 2240
Date: 9/27/2013
Experiment: 4
Kirchhoff’s Circuit Laws
Shabuktagin Photon Khan
Introduction
The objective of the experiment is to verify the laws for a resistive circuit using a DC input and
for a time varying RC circuit. Kirchhoff’s current law and Kirchhoff’s voltage law are verified
through “Y” circuit and RC circuit. The DC portion and the RC portion of the lab are each standalone labs.
Theory
Kirchhoff’s Rules (sometimes called laws) state
1) Junction Rule: the total current flowing into any point is zero at all times where we use
the convention that current into a point is positive and current out of the point is negative.
This rule is also known as Kirchhoff’s current law. In other words, the algebraic sum of
all the currents at any node is zero.
(summation of current) ∑ I = 0
Equation: 1
2) Loop Rule: the sum of the voltage drops around any closed loop must equal zero where
the drop is negative if the voltage decreases and positive if the voltage increases in the
direction that one goes around the loop. This rule is also known Kirchhoff’s voltage law.
In other words, Kirchhoff’s voltage law states that the algebraic sum of all the voltages
around any closed path is zero.
(summation of voltage) ∑ V = 0
Equation: 2
Kirchhoff’s rule is applied to the “Y” circuit shown in Figure 1. Vo supplies voltage to
output 1 of the 850 Universal Interface. Vc is produced by the voltage divider shown in
Figure 2. Vc is measured directly instead of calculating it. Three equations are needed to
solve for three unknown currents. Applying equation 1 at point A in the circuit,
equation 3 is derived.
I
1
+I 2 +I3 =0
Equation 3
Here current in is taken as positive and current out as negative. Applying Equation 2
Around 1 and 2 yields:
R1I1 + R3I3 – Vc = 0
Equation 4
-R2I2 – R3I3 + Vo = 0
Equation 5
From Ohm’s law we know V = IR (voltage = current * resistance); A = Ammeter
The voltage is negative as we go from high voltage to low voltage (with the same
current arrow across a resistor).
Figure 1
Figure 2
B
Vo
I2
I1
R4 = 330Ω
R1= 100Ω
R2= 330Ω
Vo
Vc
Vc
A
I3
R3= 100Ω
R5=1000Ω
Experimental Procedure
FOR DC SETUP: The circuit was constructed like Figure 1. The voltmeter and the ammeter
was setup in the experiment. The resistor’s value was determined by color coding method. R1
and R2 resistors were attached from top to bottom like the Figure 3. R3 resistor was attached at
the top center. At point B in the circuit, Vc supplied voltage at point B on the left end of R1 by
voltage divider Figure 2. Right end of R2 was connected to ground by jumper wire. Another
jumper wire was connected from the lower left spring to the left end of the 1000ohms resistor.
Three more jumper wires had one end attached to springs as shown in Figure 3. Jumper wires
were not connected to springs with alligator clips because it is easy to pull the springs loose from
the circuit board.
Figure 1
Figure 2
B
Vo
I2
I1
R1= 100Ω
R4 = 330Ω
R2= 330Ω
Vo
Vc
Vc
A
I3
R3= 100Ω
R5=1000Ω
Figure 3: Showing the connections of the jumping wires using red line. The blue box represents
the springs.
DC Circuits: The ammeter was attached by clipping the red end of the ammeter to the
connecting wire attached to the bottom of 100 ohm resistor (R3). The black side of the ammeter
was attached wire coming from the lower left spring. The black wire from Output 1 on the 850
was attached to the ground. Voltage probes were attached to analog inputs B and c on the 850.
The black leads from both were attached to the black side of the circuit. The red lead from
analog input C was attached to the lower banana input (Vc) on the circuit board. The red lead
from Analog input B was to connecting wire coming from the junction point A between the three
resistors. That gave Va.
The resistors that were used in the experiment were one R1 = 100 ohm, two R2 =R4= 330
ohms, one R3 = 100ohm and one R5=1000ohm. Several connecting wires were used.
Dc current procedure: Dc waveform was set at 850 for Output 1. Dc voltage of 15V was set up.
Then record button was pressed and waited for few seconds. Afterwards the value of voltage and
current was recorded.
RC setup: The circuit was set as shown in the Figure 4. 3600pF capacitor and the 47kohms
resistor was set up in series. The red lead from the 850 Output1 was attached to the right side of
the capacitor and the left side of the capacitor and the left side of the capacitor attached to the
right side of the resistor. Voltage sensors were attached with right polarities. The voltage sensor
across the resistor was attached to Analog input C and the Voltage Sensor across the Capacitor
was attached to Analog input D.
Figure 4
3900uF
+
V
+
V
47k ohm
_
V
output 1
+
_
Rc Procedure: Signal generator was set at 1000Hz and 10V for square wave generator. Monitor
was click at lower left of the computer screen. Oscilloscope recorded one cycle and stopped. The
pattern of the oscilloscope gave the input voltage, the voltage across the resistor and the voltage
across the capacitor. Then the wanted value was found out using the co-ordinate tool on the
graph toolbar.
Drawing of the Apparatus:
List of Apparatus:
1
1
3
2
1
1
1
Resistive/Capacitive/inductive network
AC/DC Electronics Laboratory
Voltage Sensors
Current Probe
Short Patch Cords
Not included but required
850 Universal Interface
PASCO Capstone
UI-5210
EM-8656
UI-5100
PS-2184
SE-7123
UI-5000
UI-5400
Data
Analysis
Table: DC Current Procedure
Vo (V)
14.97
Vc (V)
6.71
Va (V)
4.88
I3 (mA)
49.5
I2 (mA)
30.5
I1 (mA)
18.3
From the experiment, Vo, Vc, Va and I3 average was found out.
Using the equation I2 = (Vo – Va) / R2
= (14.97 – 4.88) V / 330 ohm = 30.5 mA
Using the equation I1= (Vc – Va) / R1
= (6.77 – 4.88) V / 100 ohm = 18.3 mA
Table: DC Analysis
R1(ohm) R2(ohm) R3(ohm) Vo(V)
100
330
100
14.97
Va(V)
4.88
I3th(mA) I2th(mA) I1th(mA) %diff i3
48
29
19
3.03 %
I3(mA)
49.5
%diff i2
4.91 %
I2(mA)
30.5
%diff i1
3.68 %
*th = theory
Using the equations,
I1 + I2 + I3 = 0
I2 = I3 – I1 ……..equation 1
R1I1 + R3I3 – Vc = 0…..equation 2
-R2I2 – R3I3 + Vo = 0….equation 3
Substituting the value of I2 from eq: 1 to eq: 3
-R2( I3 – I1) - R3I3 + Vo = 0
I1(mA)
18.3
Calculation:
100I1 + 100I3 = 6.71……..eqn 2 ….multiply with 3
300I1 – 430I3 = -14.97….eqn 3
Using the elimination method,
300I1 + 300I3 = 20.13
(subtracting) 300I1 – 430I3 = -14.97
I3 = 48mA
Plugging the value of I3 in in eq 2
I1 = 19.0mA
Pluggin the value of I1 and I3 in equation 1
I2 = 29mA
Table: RC analysis
Time (ms)
0.2
0.4
0.4
0.8
1.0
Vo (V)
-9.960
-9.967
-9.969
9.984
9.984
Graph: RC analysis
VR (V)
13.944
4.076
1.306
-7.580
-2.248
VC (V)`
-4.143
5.836
8.677
-2.398
-7.646
V loop (V)
-0.159
-0.53
0.14
0.006
0.09
Discussion of Results
For Dc analysis,
Percentage of error for i3 is = [(49.5 – 48) / 49.5] * 100 = 3.03%
Percentage of error for i2 = [(30.5 – 29) / 30.5] * 100 = 4.91%
Percentage of error for i1 = = [(19 – 18.3) / 19] * 100 = 3.68%
This percentage error is due to some heat energy dissipation to the surroundings. The error
probably could be due accumulation in the calculations. Slight errors like rounding in
intermediate calculation step might also happen. The last possible error was in the values of the
resistors chosen. The resistors might not be the exact value like the color code.
Conclusions
The purpose of this lab was to prove the Kirchhoff’s law. Ohm’s law, KVL and KCL are three of
the most basic techniques for the analysis of linear circuits. A circuit was given with unknown
voltages and unknown currents. The voltage and current values were measured and placed into
KVL and KCL equations to determine whether it follows the Kirchhoff’s law or not. The
calculated and measured values of current were compared with theoretical value. The percentage
error was small. Hence the test was considered valid. The errors could be eliminated using
shorter connecting wires. Error could be reduced using by not rounding up the voltage or current
values. The method could be better if we used breadboard to build the circuit. Therefore, the
method we used was precise and accurate.