INC 253 Digital and electronics laboratory I
Laboratory 2
Kirchhoff’s Law
Author:
…………………………… ID …………………
Co-Authors:
1. …………………………… ID …………………
2. …………………………… ID …………………
3. …………………………… ID …………………
Experiment Date: ………………… Report received Date: …………………
Pre lab
Full
10
Results
15
……………………………………
Discussion
25
……………………………………
Questions
Conclusion
10
5
Total
65
Comments
……………………………………
……………………………………
……………………………………
Marks
……………………………………
……………………………………
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For Instructor
Department of Control System and Instrumentation Engineering
Faculty of Engineering
King Mongkut’s University of Technology Thonburi
Objectives
1. To measure resistance, voltage and current.
2. To verify, experimentally, the relationship between the sum of the voltage drops across
series-connected resistors, and the applied voltage.
3. To verify, experimentally, the relationship between the sum of the current entering any
junction of an electric circuit and the current leaving that junction.
4. To introduce the concept of maximum power transfer.
Equipments Required
1. DC power supply
2. VOM
3. Circuit construction breadboard
4. Digital multimeter
Devices Required
1. Resistors; each for 270 Ω, 360 , 470 , 560 ,1 kΩ, 2.2 kΩ. All are  5 % tolerance.
Basic Information
1. Kirchhoff’s Voltage Law
Kirchhoff‟s voltage law is used to solve complex electric circuits. The law, named for Gustav
Robert Kirchhoff (1824-1887), the physicist who formulated it, is the basis for modern circuit
analysis.
VOLTMETER
+
V2
V1
A
- COM
C
B
+
R1
-
+
R2
IT
+
E
R3
V3
DC
D
Figure 1 voltage across resistors in a series circuit.
In the circuit of Figure 1 , the series resistors R1, R2 and R3 can be replaced by their total or
equivalent resistance RT, where
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Lab. 2: Kirchhoff‟s Law
RT = R1 + R2 + R3
(1)
Use of RT will not affect the total current IT. The relationship between
source E is given by Ohm‟s law,
,
and the voltage
(2)
Substitute equation (1) in (2) gives
E = IT (R1 + R2 + R3 )
= IT R1 + IT R2 + IT R3
(3)
Where
IT R1 = the voltage drop across R1 =
IT R2 = the voltage drop across R2 =
IT R3 = the voltage drop across R3 =
Equation (3) can now be rewritten as
V1
V2
V3
E = VAB + VBC + VCD
(4)
Equation (4) is the mathematical expression of Kirchhoff‟s voltage law and states that
“In a closed circuit or loop the applied voltage equals the sum of the voltage drops in the
circuit.”
Or can be generalized as follows.
“The algebraic sum of the voltages in a closed circuit equals zero.”
Applying the convention on sign and Kirchhoff‟s law to closed circuit in Figure 1, we may
write the following:
- V1 - V2 - V3 + E = 0
(5)
2. Kirchhoff’s Current Law
The total current I in a circuit containing resistors connected in parallel is equal to the sum of
the currents in each of the parallel branch. This was one demonstration of Kirchhoff‟s current
law. However the law is general and applies to any circuit.
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Lab. 2: Kirchhoff‟s Law
A
IT
I1
R1
E
I2
R2
B
Figure 2 Current through resistors in a parallel circuit.
From Figure 2 voltage across the parallel circuit can be found using Ohm‟s law
(6)
Where
is an equivalent resistance of the parallel circuit,
From equation (6)
is the current passing through
.
(7)
By adding branch current gives
(8)
Since
(9)
Therefore
(10)
Kirchhoff‟s Current Law states that
“The
current entering any junction of an electric circuit is equal to the current leaving
that junction.”
States in another way:
“The algebraic sum of the currents entering and leaving a junction is zero.”
I4
A
=
5
1
=
A
I2
3A
I 1=
I3
I5 = ?
=
2
A
Figure 3 Current entering and leaving a junction
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Lab. 2: Kirchhoff‟s Law
From Figure 3
Procedure
Sections marked * are pre-lab preparation and must be completed BEFORE coming to
the lab.
1. Part A. Resistance in a series circuit.
1.1. From the circuit in Figure 4, with E = 12 V, R1 = 470(1 ± 5 %) , R2 = 1(1 ± 5 %)
k, compute equivalent resistance between points A and C. Calculate the uncertainty
(Maximum permissible error) in the equivalent resistor due to the uncertainty of a
given resistors. Enter the calculated value below.
* Requivalent = (Rcalculated ± uncertainty) 
= …………………………
1.2. Calculate current passing through points A, B and C including voltage drop VR1 and
VR2. Record the calculated data in Table 1.
A
470
R1
E = 12 V
B
R2
1k
C
Figure 4Experimental circuit of part A.
* Table 1.
IA (mA)
IB (mA)
IC (mA)
VR1 (V)
VR2 (V)
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Lab. 2: Kirchhoff‟s Law
1.3. Connect the circuit as Figure 4 using the breadboard. Using your VOM measures
equivalent resistance between points A and C (disconnect power supply) record the
result at “Requivalent (ohmmeter)” below.
Requivalent (ohmmeter) = ( Rmeasured ± uncertainty) 
= ………………………………
Set dc voltage E = 12.0 V using the digital multimeter. Then apply voltage E between points
A and C, measure current using your ammeter and voltage using your voltmeter at specified
points and record the data obtained in Table 2.
Table 2.
Meter range
IA (mA)
IB (mA)
IC (mA)
VR1 (V)
VR2 (V)
1.4. Find “Requivalent(meas)” calculate using data from Table 2
and record as follow.
Requivalent (meas) = ( Rmeas ± uncertainty) 
= …………………………
Question for part A
Explain, if any, the difference of results between computation in step 2 and measurement in
step 3.
2. Part B. Resistance in a parallel circuit.
2.1. Compute equivalent resistance between point ‟a„ and ‟d„ of the circuit in Figure 5,
with E = 9 V, R1 = 470 (1 ± 5 %) , R2 = 2.2 (1 ± 5 %) k, Calculate the uncertainty
(Maximum permissible error) in the equivalent resistor due to the uncertainty of a
given resistors. Enter the calculated value below.
* Requivalent = (Rcalculated ± uncertainty) 
= …………………………
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Lab. 2: Kirchhoff‟s Law
a
c
b
Ia
E=9V
R1
470
Ib
R2
2.2 k
Ic
Id
d
Figure 5. Current and voltage in parallel circuit
Then compute the current passing through points‟ a‟ and „d‟, passing through resistors R1 and
R2, Ib and Ic respectively, including computation of voltage drop VR1 and VR2 .Record the
calculated data in Table 3.
* Table 3.
Ia (mA)
Ib (mA)
Ic (mA)
Id (mA)
VR1 (V)
VR2 (V)
2.2. Connect the circuit as in Figure 5, using your VOM measures equivalent resistance
between point „a‟ and „d‟ (disconnect power supply) record the result at “Requivalent
(using ohmmeter)”.
Requivalent (using ohmmeter) = ( Rmeasured ± uncertainty) 
= …………………………
2.3. Set dc voltage supply E = 9 V using the digital multimeter. Then apply the voltage E
between points a and d, measure current using your ammeter (open circuit and
connect the ammeter) and voltage using your voltmeter at specified points and record
the data obtained with meter range in Table 4.
Table 4.
Meter
range
Measured
Ia (mA)
Ib (mA)
Ic (mA)
Id (mA)
VR1 (V)
VR2 (V)
2.4. Find “Requivalent(meas)” calculate using data from Table 4 from the relation
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Lab. 2: Kirchhoff‟s Law
and record as follow.
Requivalent (meas) = ( Rmeas ± uncertainty) 
= …………………………
3. Part C. Series – parallel circuit and Kirchhoff’s Law.
3.1. Instead of using direct method of current measurement using ammeter, the current
passing through a resistor can be obtained indirectly using voltmeter and Ohm‟s law.
From Figure 6, E = 15.0 V, R0 = 560(1 ± 5 %) , R1 = 1 (1 ± 5 %) k and R2 =
470(1 ± 5 %) . Calculate voltage across R0, R1 and R2, that is VR0, VR1, VR2
respectively, as the expected reading of an ideal voltmeter and record them in Table 5.
Calculate the corresponding current passing through each resistor, IR0, IR1 and IR2 and
record them in Table 5. Calculate the uncertainty in current due to the uncertainty of
the given resistors. Show all of your calculations on a separate sheet of paper.
a
R0
b
560
1k
E = 15 V
R1
R2
470
c
Figure 6. Series- parallel circuit
* Table 5
VR0 (V)
R0 ()
VR1 (V)
560
IR0 (mA)
R1 ()
VR2 (V)
1k
IR1 (mA)
R2 ()
470
IR2 (mA)
3.2. Connect the circuit as shown in Figure 6 using the breadboard. Set dc voltage E =
15.0 V using the digital multimeter. Measure voltage drop across each resistor using
your voltmeter set to the appropriate range. Record the readings with the selected
range in Table 6. Find the corresponding current through each resistor from its
voltage drop and record the data in Table 6.
* Table 6
Meter range
Meter range
Meter range
VR0 (V)
VR1 (V)
VR2 (V)
R0 ()
IR0 (mA)
560
R1 ()
IR1 (mA)
1k
R2 ()
470
IR2 (mA)
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Lab. 2: Kirchhoff‟s Law
Questions for part C
1. State in your own words, the relationship between the voltage drop across resistors and
the voltage applied to the entire circuit, and then express your answer as a mathematical
formula.
2. State in your own words, the relationship between the currents entering and leaving at
junction point “a”, and then express your answer as a mathematical formula.
3. Do your experimental data support your answer in 1 and 2? If not, explain the discrepancy.
4. Part D. Voltage Divider.
4.1. Connect the circuit as shown in Figure 7 using the breadboard. Set dc voltage E =
15.0 V using the digital multimeter. Given R1 = 560 (1 ± 5 %) , R2 = 1(1 ± 5 % )
k .
4.2. Before connecting
, estimate the suitable range of voltage before measurement.
Ideal voltage drop at point B with respect to point C can be calculated from
A
R1
E = 15 V
560
B
R2
1k
RL
C
Figure 7. Voltage divider circuits.
 R2 
 E
VBC  
R

R
2 
 1
Record the result as VBC (calculated).
* VBC (calculated) = __________
V
Measure the voltage drop across R2 using your VOM as a voltmeter. Select the voltage range
that is the most appropriate. Record the data with range as VBC (measured) below.
Meter range = _______________V
VBC (measured) = ___________
V
4.3. Connect RL = 270(1±5%) Ω as a load parallel to R2 (across point B and point C) of
the divider circuit, calculate the voltage drop across RL and its power dissipation.
Record the result in Table 7 as “Calculated voltage” and “Calculated
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Lab. 2: Kirchhoff‟s Law
power“ respectively. Calculate the uncertainty in power due to the uncertainty of the
given resistors. Show all of your calculations on a separate sheet of paper.
4.4. Measure the voltage across the load RL using your voltmeter and record the result as
“Measured voltage”. Find power dissipation from P = V2/R and record in Table 7 as
“Measured power”.
4.5. Repeat step 3 and 4 with RL = 360  and 470 Ω ( All are ± 5 % tolerance).
Table 7
* Calculated
voltage (V)
RL ()
* Calculated
power (mW)
Measured
voltage (V)
Measured
power (mW)
270
360
470
Questions for part D
1. To use voltage divider circuit as in Figure 7 it is desired to have voltage output VBC
across R2 when at maximum loaded differs from when at no-load not more than 10 %.
How can you give the limit on resistance value or criteria for load selection?
2. Explain the concept of maximum power transfer from source to load using the circuit and
data from part D.
3. From circuit of Figure 8.
a) Find the current through each resistor.
b) Determine the voltages and their proper polarities for each resistor
R1
R3
470
820
R2
E1
560
E2
2V
E3
4V
6V
Figure 8.
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Lab. 2: Kirchhoff‟s Law