Lab 3 Parallel Series Capacitor Experiment
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Electrical Engineering
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Dec 6, 2023
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ELECTRICAL ELECTRONIC PRINCIPLES: LAB EXPERIMENT # 3 SERIES-PARALLEL CAPACITOR NETWORKS
GROUP PROFESSOR: J5
LAB #3
APR
20
TH
,22
Objective: This experiment aims to measure the effects of voltage across capacitance versus the time of several capacitors building a charge connected in a series and parallel circuit. This will be accomplished in two ways. First, by direct measurement using a DMM. Second, by using the definition
τ
=
R
∗
C
∧
Vc
=
E
(
1
−
e
−
t
τ
)
.
Equipment used:
Resistors and Capacitors
No. #
Resistors
Resistor Color Code
1
2.2 M Ω
Red, Red, Green, gold.
1
10 M Ω
DMM
Gray, Black, Green, gold.
2
2µF
1
0.56µF
(2) 4
1
2
Digital multimeters (ammeter, ohmmeter and voltmeter)
Model: Bk Precision 2831E
Breadboard and Variable DC power supply {0 – 10 volts}. Model: Global Specialties PB-505 Deluxe Analog and Digital Design Workstation
Jumper Wires Solid Core
Alligator Clip Wires
Multisim Live Online Circuit Simulator (https://www.multisim.com/create)
20M Ω rated Ohm meter Page | 1
Circuit Operation: Figure 1
1.
Set the DC power supply for 10 volts on the Model: Global Specialties PB-505. Use alligator clips to connect the DC supply to the circuit above with solid core jumper wires and resistors. 2.
Measure the voltage across the source and capacitors with Model: Bk Precision 2831E
and set the DMM function to read DC volts.
3.
With a smart phone set to record video, measure the total time in seconds the circuit of capacitors will become fully charged with another Model: Bk Precision 2831E and set the
DMM function to read DC Voltage
.
The Voltmeter connection should be in parallel with the capacitors, not series. 4.
Once the capacitors equal the same value as the source voltage (E), at that very second you have Steady State
the maximum amount of voltage a capacitor can store.
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Calculations:
Capacitors in Parallel
Equation – Parallel Total Capacitance
C
T
=
C
1
+
C
2
+
⋯
+
C
n
[farads, F Ω]
Capacitors in Series
Equation – Parallel Total Capacitance
C
T
=
1
1
C
1
+
1
C
2
+
⋯
+
1
C
n
[farads, F Ω]
Time Constant Is the rate at which a capacitor charges depending on its Resistance and Capacitance.
Procedure:
Page | 3
1.
Check the color codes of the resistors to ensure that you select the proper ones. Measure the individual resistances—record data.
2.
Find the Mathematic Expression for V
C , I
C and it’s time constant for the network to calculate values in Table 1
; begin with calculating the nominal values of total resistance and total capacitance. Use Figure 1 for schematic.
3.
Calculate the voltage across the total Capacitance when t=1,2,3,4,5
τ
. Record data in Table 1. 4.
Assemble the circuit in figure 1 *
without connecting to a DC power source*
with a Model: Global Specialties PB-505 breadboard. Use the appropriate resistors, capacitors and solid core jumper cables to create the circuit. Use the ohmmeter set to ohms with a model: Bk Precision 2831E
first to measure the 2.2M ohm resistance before wiring the 10-volt DC power supply to the circuit. Also make sure capacitors used are fully discharged before proceeding.
5.
Build the circuit in the schematic. Place a Voltmeter across the capacitor network and the Power Source. 6.
Use the Voltmeter from the DMM to measure the voltage across the capacitor network when t=1,2,3,4,
5
τ
.
7.
Using a Stopwatch on Camera, record the increasing voltage at the proper times in Table 1. (If using a Camera make sure the Voltmeter is in Frame and that a timestamp is used with the recording.)
8.
Turn of Power.
9.
Calculate the steady-state voltages (
t
>
5
τ
¿
across each capacitor in the network using the capacitor divider rule and place data in Table 2.
10. Make sure all the capacitors are fully charges, then measure across each capacitor the voltage at steady-state by placing a Voltmeter in Min/Max mode Schematic:
Page | 4
Data: Page | 5
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Observations:
Page | 6
As a group, we discovered that the Capacitor was not charging its whole source voltage of 10 volts. After investigating this phenomenon, we found that a voltage divider between two resistors was taking place. The 1st resistor is 2.2M, and the second comes from the DMM connected in parallel, giving a resistance of around 9.73M. It prevented the total capacitance of 1.34 microfarads from achieving a maximum charge of 10 volts instead of 8.155 volts. We also found out that due to limited resources effective component substation was needed to achieve the goals
of this experiment.Also, a Voltmeter with a large resistance will continually discharge the total capacitance
Conclusion
In this experiment, charging and discharging of the capacitors with different
resistors were observed. The main goal was to charge up the capacitor. For this, the circuit that we used included the resistor and the capacitors with the power supply. To extend the charging process, the resistors were used. In result, we saw that as capacitors was being charged, we saw an increase in the voltage. Thus, the increasing phase represents charging of the capacitor and decay represents the discharging. Time constant was also taken in account to represent the relation between the time constant, the resistance, and the capacitor. The time constant shows how long it takes to charge up the capacitor. As time constant increase, the voltage reaches the maximum voltage of the capacitor achieving steady state. It is also important to mention that calculating the mathematical formulas for charging
capacitors to steady state and finding the voltages along its transient route was important to prove how capacitor in series and parallel work together to achieve charge.
The purpose of this experiment was achieved because the charging and discharging was observed with the expected results. The charging showed the exponential increase and the discharging showed the decay. Thus, it shows that the charging and discharging is an exponential phenomenon.
Page | 7
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