Lab 3 v6- Series-Parallel Circuits and Kirchhoff Laws
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Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
EECE 2317-A
Electrical & Electronic Systems
Laboratory
LAB 3: Series-Parallel Circuits and
Kirchhoff Laws
Student Name:
Cessar Lechuga
Gerardo Gamez
1
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
LAB 3: Series-Parallel Circuits and Kirchhoff Laws
A. OBJECTIVES
Test the theoretical analysis of series-parallel networks through direct measurements
Improve skills of identifying series or parallel elements
Measure properly the voltages and currents of a series-parallel network
Practice applying Kirchhoff’s Voltage and Current Laws, the current divider rule, and the
voltage divider rule
B. EQUIPMENT
HP-3631A DC Power Supply
Digital Multimeter (DMM)
Prototype Board
Device Test Leads and Cables
C. PARTS
1/2 Watt Resistors: 1 kΩ, 2.2 kΩ, 3.3 kΩ
Hook-up Wires (#20 or #22 gauge solid conductor)
D. BEFORE THE LAB
1) Series and Parallel Resistor Circuits
The analysis of series-parallel DC networks requires a firm understanding of the basics of both series and parallel networks. In the series-parallel configuration, you will have to isolate series and parallel configurations and make the necessary combinations for reduction as you work toward the desired unknown quantity.
A series circuit is a circuit in which resistors are arranged in a chain, so that the current has only one path to take. This way, the current value is the same through each resistor in series
.
A parallel circuit is a circuit in which the resistors are arranged with one of their terminals connected together, and the remaining terminal connected together. In this case, the current breaks up, with some flowing along each parallel branch and recombining when the branches meet again. The voltage across each resistor in parallel is the same value
.
Electric circuits tend to have many combinations of series and parallel resistors. The total resistance in such circuits is found by reducing the different combinations on a step-by-step 2
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
procedure until ending up with a single equivalent resistance R
eq
for the circuit. This allows the power supply current I
S
to be determined easily using Ohm’s Law
.
I
S
=
V
S
R
eq
Note that V
S
is the voltage value of the power supply. The current flowing through individual resistors can then be found by undoing the reduction process and using the now known supply current.
2) Resistor Combinations
There are two general rules for simplifying (reducing) a resistive circuit:
1.
Series Combination:
Two resistors R
1
and R
2
connected together so that one terminal of one of the resistors is connected to one terminal of the other resistor, forming a node. This node should not connect to any other path for the current to flow (Figure 1). This setup can be reduced to a single resistor R
eq
by using the series resistance equation:
R
eq
=
R
1
+
R
2
For N resistors placed in series, then:
R
eq
=
R
1
+
R
2
+
⋯
+
R
N
Figure 1: Series Combination
Figure 2 shows an example circuit with two resistors in series. To determine the voltage across each resistor in this circuit, we utilize the voltage division equation:
v
1
=
R
1
R
1
+
R
2
v
, v
2
=
R
2
R
1
+
R
2
v
3
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Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
Notice that the source voltage v
is divided among the resistors in direct proportion to their
resistances; the larger the resistance, the larger the voltage drop. This is called the principle of voltage division
, and the circuit in Figure 2 is called a voltage divider
.
In general, if a voltage divider has N
resistors (R
1
, R
2
, …, R
N
) in series with the source voltage v
, the nth resistor (R
n
) will have a voltage drop of:
v
n
=
R
n
R
1
+
R
2
+
…
+
R
N
v
Figure 2: A single-loop circuit with two resistors in series
2.
Parallel Combinations:
Two resistors R
1
and R
2
connected together using both of their terminals, forming two nodes. These nodes could have other connections/paths, and the resistors would still be in parallel with each other (Figure 3). This setup can be reduced to
a single resistor R
eq
by using the parallel resistance equation:
R
eq
=
(
1
R
1
+
1
R
2
)
−
1
For N resistors placed in parallel, then:
R
eq
=
(
1
R
1
+
1
R
2
+
⋯
+
1
R
N
)
−
1
4
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
Figure 3: Parallel Combination
Figure 4 shows an example circuit with two resistors in parallel. To determine the current through each resistor in this circuit, we utilize the current division equation:
i
1
=
R
2
R
1
+
R
2
i
, i
2
=
R
1
R
1
+
R
2
i
Notice that the total current i
is shared by the resistors in inverse proportion to their resistances; the larger the resistance, the smaller the current it draws. This is called the principle of current division
, and the circuit in Figure 4 is called a current divider
.
Knowing that conductance G
=
1
/
R
, in general, if a current divider has N
conductors (G
1
, G
2
, …, G
N
) in parallel with the source current i
, the nth conductor (G
n
) will have a current of:
i
n
=
G
n
G
1
+
G
2
+
…
+
G
N
i
5
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
Figure 4: A two-loop circuit with two resistors in parallel
E. IN THE LAB
1) Series-Parallel Network I
(a)
In your breadboard, build the series-parallel network of Figure 5.
Figure 5: Series-Parallel Circuit I
(b) Measure each one of the resistors’ resistances used in the circuit. Remember: isolate the resistor from the rest of the circuit before attempting to measure its resistance.
R
1
= 2.17 kOhms
Color Code: Red Red Red Gold
R
2
= 0.98 kohms
Color Code Brown Black Red Gold
R
3
= 3.25kohms Color Code: Orange Orange Red Gold
6
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Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
(c) Next, calculate
the total resistance R
T
(using measured values from step (b)) by combining resistors. In order to do this, you need to identify resistors placed in series and in parallel, then combining accordingly.
R
T
(calculated) = 2.97 kohms
(d) Now measure
the total resistance R
T
of the circuit built in the breadboard. To achieve this, connect the test probes across the open terminals on the left of the diagram.
R
T
(measured) = 2.92kohms
(e)
Determine the magnitude of the percent difference between the calculated and measured values of steps (c) and (d) using the equation:
%
Error
=
|
Calculated Value
−
Measured Value
Calculated Value
|
×
100%
%Difference = 1.6%
Note
:
Use the above equation for all percent difference calculations in this and the following laboratories. Use the following score to check the quality of your work
Error magnitude
Quality Comment
Action
Less than 1 %
Very good
Continue
1 % < error < 5 %
Good
Continue
5 % < error < 10 %
Bad
Review
Greater than 10 %
Very Bad
Review
(f)
If 18 V were to be applied to the circuit, as shown in Figure 6, calculate the labeled currents using the measured
resistor values. Use pSpice to calculate the voltages and currents of the resistors R1, R2 and R3.
Figure 6: Series-Parallel Circuit I Connected To DC Supply
Pspice SIMULATION:
7
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
I
S
= 6.06 mA I
1
=6.066 mA I
2
=4.655 mA I
3
= 1.411mA
(g) Apply 18 V to your circuit and measure the currents I
1
, I
2
, and I
3
using the multimeter (
use the milliAmmeter terminal
). Remember: be sure the meter is in series with the resistor through which the current is to be measured (open/break the circuit to achieve this).
MEASUREMENTS:
I
1
= 6.16mA I
2
=4.74mA I
3
= 1.426mA
(h) Calculate the percent difference between the calculated and the measured values of current.
I
1
%Difference = -1.65%
I
2
%Difference = -1.8%
I
3
%Difference = -1.06%
(i)
Using the calculated
current values from step (f) and the measured
resistor values from (b), calculate the voltages V
1
, V
2
, and V
3
.
Pspice SIMULATION:
V
1
= 13.3V V
2
=4.74V V
3
= 4.65V
(j)
Next, measure the voltages V
1
, V
2
, and V
3
. Remember that voltmeters are connected in parallel to the component to be measured.
MEASUREMENTS:
V
1
= 13.353 V
2
=4.64 V
3
= 4.64
(k) Calculate the percent difference between the calculated and the measured values of voltage.
V
1
%Difference = -0.3%
V
2
%Difference = 2%
V
3
%Difference = 0.2%
(l)
Question: How are the voltages V
2
and V
3
related? Why? They are the same because the resistors are in parallel.
8
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
Answer: (m)Referring to Figure 6, does E = V
1
+ V
2
, as required by Kirchhoff’s Voltage Law (KVL)? Use the measured values of step (j) to check this equality.
Answer: 13.353 V + 4.64V does equal the source’s voltage so KVL holds true.
2) Parallel-Series Network II
(a)
In your breadboard, build the series-parallel network of Figure 7.
Figure 7: Series-Parallel Circuit II
(b) Measure each one of the resistors’ resistances used in the circuit.
R
1
= 2.17kohms R
2
= 3.257kohms
R
3
= 0.979 kohms
(c) Next, calculate
the total resistance R
T
(using measured values from step (b)) by combining resistors.
R
T
(calculated) = 1.466Kohms
(d) Now measure
the total resistance R
T
of the circuit built in the breadboard.
R
T
(measured) = 1.43kohms
(e)
Determine the magnitude of the percent difference between the calculated and measured values of steps (c) and (d).
%Difference = 2.45%
9
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Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
(f)
If 12 V were to be applied to the circuit, as shown in Figure 8, calculate the labeled currents using the measured
resistor values. Show your calculations below
. Hint: Same procedure as in part 1, step (f) of this section; Voltage Division then Ohm’s Law can also help.
Figure 8: Series-Parallel Circuit II Connected To DC Supply
CALCULATIONS (pSpice)
I
S
=8.245mA I
1
=5.455mA I
2
= 2.791mA I
3
= 2.791mA
(g) Apply 12 V to your circuit and measure the currents I
1
, I
2
, and I
3
using the multimeter (use the milliAmmeter terminal).
MEASUREMENTS:
I
1
=5.53mA I
2
=2.833mA I
3
= 2.834mA
(h) Calculate the percent difference between the calculated and the measured values of current.
I
1
%Difference = -1.37%
I
2
%Difference = -1.50%
I
3
%Difference = -1.50%
(i)
Question: How are the currents I
2
and I
3
related? Why?
Answer: The currents are the same because the resistors are in series and there is no current division.
10
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
(j)
Referring to Figure 8, does I
S
= I
1
+ I
2
, as required by Kirchhoff’s Current Law (KCL)? Use the measured values of step (g) to check this equality. 5.53mA + 2.833mA does add up to 8.245mA so KCL holds true.
Answer: (k) Using the calculated
current values from step (f) and the measured
resistor values from (b), calculate the voltages V
1
, V
2
, and V
3
.
CALCULATIONS (pSpice):
V
1
= 12V V
2
=9.2V V
3
= 2.791V
(l)
Next, measure the voltages V
1
, V
2
, and V
3
.
MEASUREMENTS:
V
1
= 11.998 V V
2
= 9.222V V
3
= 2.774V
(m)Calculate the percent difference between the calculated and the measured values of voltage.
V
1
%Difference = 0.01%
V
2
%Difference =0
V
3
%Difference = 0.61%
(n) Question: How are the voltages E, V
1
, and the sum of V
2
and V
3
related? Use the measured values of step (l) to find this relationship. Answer: The sum of V2 & V3 is equal to 12v, and because R2 & R3 are in parallel with R1, the voltage will be the same. ** Show your results to your instructor to obtain a signature.
Instructor’s Signature: Jaime Ramos **When done with the laboratory, please return every component to its respective storage. Thank you!
F. AFTER THE LAB
11
Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
The After the Lab section is to be completed either at the laboratory or at home, after the main lab work has been finished. Data and results from both In the Lab and After the Lab sections are to be included in the laboratory report.
1)
For the series-parallel network in Figure 9, determine V
1
, R
1
, and R
2
using the information provided. SHOW ALL YOUR WORK BELOW! Assume that internal resistance R
internal
of the current meters is equal to zero ohms.
Figure 9: Series-Parallel Network Exercise 1
V
1
= 8V R
1
= 8kΩ R
2
= 4kΩ
(v-14/2)+1+2=0
V=8V
V1=8V
IR1=V/R1
1=8/R1
R1=8kΩ
IR2=V/R2
2=8/R2
R1=4kΩ
Hints- One: R2 has the same voltage as R1. Find an equation relating R1 and R2, using the currents I1 and I2.
Two: You can find the current thru R3, hence its voltage v3. Apply KVL and find v1
2) For the series-parallel network in Figure 10, determine V
1
, R
2
, and R
3
using the information provided. SHOW ALL YOUR WORK BELOW! Assume that internal resistance
R
internal
of the current meters is equal to zero ohms.
12
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Lab 3:
Series-Parallel Circuits and Kirchhoff Laws
Electric Systems Lab
Figure 10: Series-Parallel Network Exercise
34-(4x10^3)*(4x10^-3)=V1
V1=18V
34-4x10^3*4x10^-3-V2-6=0
V2=12V
I1*R2=V2
R2=12/3x10^-3
R2= 4kΩ
1x10^-3*R3=12
R3=12kΩ
V
1
= 18 R
2
=4kΩ R
3
= 12kΩ
Hints: First find the current thru R2, hence find an equation relating R3 and R2. Next find the
voltage on R4. Apply KVL and find the voltage on R3. Now, use Ohm’s law two times to find R2 and R3
13
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