ENGI 241 LABORATORY EXERCISE 2
KIRCHHOFF'S LAWS
PURPOSE
The purpose of this experiment is to verify Kirchhoff's Voltage Law and Kirchhoff's Current Law for
the dc circuit by experimental methods. The power dissipated in the circuit will also be determined.
EQUIPMENT AND PARTS REQUIRED
1
Powered Protoboard
2
Simpson 260 VOM
2
Fluke Model 37 DVM
1
each Resistor 1/4 W, 5%, 5600Ω, 4700Ω, 3000Ω, 1500Ω, 470Ω
INTRODUCTION
KIRCHHOFF'S VOLTAGE LAW AND THE SERIES CIRCUIT
There are three fundamental laws of electricity upon which we may analyze the behavior of a circuit.
These laws are Ohm's Law, Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL).
Ohm's Law is used in any circuit that we wish and is commonly expressed:
V = IR
<2−1>
KVL is used in the analysis of series circuits. A series circuit is shown
in Figure 2−1. KVL states the sum of all voltages around a closed loop
is zero or ΣV = 0.
If we define the source voltage as VAD, KVL allows us to represent
this as the sum of the individual voltage drops in the circuit.
VAD = VAB + VBC + VCD
<2−2>
Since VAB, VBC, and VCD are Ohm's Law voltage drops, equation 2−2
FIGURE 2−1
may be written as:
VAD = IR1 + IR2 + IR3
<2−3>
Recall that the total resistance of the series circuit is the sum of the individual resistances. If we solve
equation 2.3 for the total resistance, we obtain:
VAD
= RT = R1 + R2 + R3
<2−4>
I
On the basis of the analysis of Figure 2−1, we can state the five characteristics of the series circuit:
1.
Each component has an individual Ohm's Law voltage drop.
2.
The current is the same everywhere in the circuit.
3.
KVL applies or ΣV = 0.
4.
The total resistance is the sum of all the resistors.
5.
The total power delivered by the source is equal to the sum of the powers dissipated by each
component.
KIRCHHOFF'S CURRENT LAW AND THE PARALLEL CIRCUIT
KCL is used in the analysis of the parallel circuit similar to the circuit of Figure 2−2. KCL states that Σ
I = 0 or:
<2−5>
IT = I1 + I2
Page 1
ENGI 241 LABORATORY EXERCISE 2
KIRCHHOFF'S LAWS
Equation 2−5 indicates each component has an individual current and that the sum of all the branch
current is equal to the current drawn from the source. Looking at the circuit we observe that the
voltage drop across R1 and R2 are equal to the source voltage. By applying Ohm's Law to equation 2−5
we obtain:
VAB
VAB
VAB
=
+
<2−6A>
RT
R1
R2
1
1
1
=
+
<2−6B>
RT
R1
R2
The five characteristics of the parallel circuit:
1.
Each branch has an individual current.
2.
The voltage across each branch is the same.
3.
KCL applies or ΣI = 0.
4.
The inverse of the total resistance is the sum of the inverse of
each resistor.
5.
The total power delivered by the source is equal to the sum of
the powers dissipated by each component.
FIGURE 2−2
SERIES−PARALLEL CONFIGURATION
Figure 2−3 is a series−parallel circuit configuration. We can
see that R2 and R3 are in parallel, and that combination is in
series with R1. To analyze the series−parallel circuit, we
apply the laws of the series circuit to series connected
components, and the laws of the parallel circuit to the
parallel connected components. For this circuit, we would
calculate RBC as a single resistor whose value is equal to:
FIGURE 2−3
R 2 R3
RBC =
R2 + R 3
We now have a series circuit consisting of R1 and RBC. We could apply the voltage divider theorem to
obtain VBC:
RBC
VBC = VAC (
)
R1 + RBC
Now that we know VBC, we can use Ohm's Law to solve for each branch current. We may have
proceeded another way. Since we can solve for IT using Ohm's Law and the total resistance, we could
have solved for the branch current I2 using the current divider equation. Note that:
VBC = IT RBC
The current divider equation is based on the parallel section of the circuit.
R 2 R3
)
VBC = I2 R2 = IT (
R 2 + R3
Solving for the unknown current, we obtain:
IT
R2 R3
R3
I2 =
(
)
= IT (
)
R2 R2 + R3
R2 + R3
Page 2
ENGI 241 LABORATORY EXERCISE 2
KIRCHHOFF'S LAWS
PROCEDURE
COMPONENT USAGE
1.
2.
3.
4.
5.
6.
Circuit Configuration
R1
R2
R3
Series
3000Ω
1500Ω
470Ω
Series−Parallel
1500Ω
5600Ω
4700Ω
Record the BCC ID numbers for the equipment used. Use VOM 1 and DVM 1 to measure
current and VOM 2 and DVM 2 to measure voltage.
Use DVM 1 to measure each resistor and record its value in Table 2 − 1.
Build the circuit of Figure 2−1 using VOM's. The values for the resistors are shown in the
Component Usage Table. Determine the polarity of all meters and note the polarity on your
schematic. Set the meters to the proper range and function before connecting the meter. Connect
the voltmeter across the power supply terminals. Set the two VOM's to the proper function and
range. Apply power and adjust for a supply voltage of +15V.
Measure VAB, VAC, VAD, VBC, VBD, VCD, and I, and record these Data values in Table 2−2. Also
record the range selected on the meter and the scale used to make the reading. Use the
appropriate range to make the most accurate reading possible.
Repeat step 3 using the two DVM's. Make sure the meters are selected to operate in their
autoranging mode.
Build the circuit of Figure 2−3 using VOM's for the ammeter and voltmeter. The values for the
resistors are shown in the Component Usage Table. As you proceed, estimate the optimum
position for the range switch to make the voltage and current readings before connecting the
meter. Connect the voltmeter across the power supply terminals. Set the two VOM's to the
proper function and range. Apply power and adjust for a supply voltage of +15V.
Measure VAB, VBC, and VAC, IT, I1, and I2, and record these Data values in Table 2−2. Also
record the range selected on the meter and the scale used to make the reading. Use the
appropriate range to make the most accurate reading possible.
Repeat this step using two DVM's.
Perform a PSpice Bias Point analysis for the two circuits using measured values for the
components. After running the simulation, display the voltages abd current on the schematic.
Print each circuit. Perform KVL and KCL calculations as appropriate. In your discussion,
compare the measured values, the simulation values, and the calculated values using measured
resistace and power supply values.
Page 3
ENGI 241 LABORATORY EXERCISE 2
Device
Power Supply
KIRCHHOFF'S LAWS
VOM 1
VOM 2
DVM 1
DVM 2
BCC ID #
EQUIPMENT LIST
470Ω
Rated Value
1500Ω
3000Ω
4700Ω
5600Ω
Measured Value
TABLE 2 - 1
Measured
VOM
Calculated
I
VAB
VAC
VAD
VBC
VBD
VCD
PAB
PBC
PCD
I
VAB
VAC
VAD
VBC
VBD
VCD
PAB
PBC
PCD
Range
Scale
Data
Error
Abs
%
DVM
Data
Error
Abs
%
TABLE 2 - 2
Measured
VOM
Calculated
IT
I1
I2
VAB
VBC
VAC
PT
PR1
PR2
PR3
IT
I1
I2
VAB
VBC
VAC
PT
PR1
PR2
PR3
Range
Scale
Data
Error
Abs
%
DVM
Data
Error
Abs
%
TABLE 2 – 3
Page 4
ENGI 241 LABORATORY EXERCISE 2
7.
KIRCHHOFF'S LAWS
Using the voltage and current data in Table 2−2 and Table 2-3, Calculate the power dissipated in
R1, R2, R3. Make a Data Table in your report similar to the one below to record your calculation.
Discuss the results. Error is the error expressed as a numeric value.
Power
Error (±)
R1
R2
R3
Page 5
% Error