Electrical Principles: Chapter 3: Capacitors
Publish Date: Mar 27, 2013
Overview
The Electrical Principles/Fundamentals series present the basic theories and concepts taught at entry level electronics courses
both 2 year and 4 year institutions. This series of content provides examples to professors to enable them to easily teach conce
to students, who can develop a solid underlying knowledge of electronics using the NI solution. This series focuses on some of
basic theory as well as providing the NI Multisim circuits to enable practical implementation end experimentation as homework
students.
Table of Contents
1.
2.
3.
4.
5.
6.
7.
In this Chapter
Example Courses
Capacitors in Series
Capacitors in Parallel
Example Problem
Suggested NI Solution
References
1. In this Chapter
We begin this chapter by exploring of a circuit’s basic components: the capacitor. We will learn how to simplify a series, paralle
and a series and parallel combination circuits to measure the equivalent capacitance, voltage drop, and the charge of each dev
If you do not have NI Multisim installed on your computer, you can download a free 30 day evaluation at
http://www.ni.com/multisim/try/ (http://www.ni.com/multisim/try/)
2. Example Courses
Listed below are example courses that teach this concept at their schools.
Course Name
School
Learn More
Electrical
Principles
Conestoga College
http://www.conestogac.on.ca/fulltime/0071.jsp
Electronic
Technology 1
Macomb
Community College
http://www.macomb.edu/noncms/Search/Courses/coursekey.asp?coursekey=ELEC-11
3. Capacitors in Series
For a combination of capacitors in series, note that it is not just simply adding the values of the capacitances but it is adding the
reciprocal values of each individual capacitance (same as resistors in parallel).
1/Ceq = 1/C1 + 1/C2 + ... + 1/Cn (where n is the number of capacitors in series) [1]
4. Capacitors in Parallel
As for a combination of capacitors connected in parallel, it is important to note that the potential difference is the same however
the charge Q differs and is added together. Therefore the equivalent charge Qeq = Q1 + Q2
Therefore adding capacitors in parallel is simply adding the values of the capacitances:
Ceq = C1 + C2 + ... + Cn (where n is the number of capacitances in parallel) [2]
Note that this means if we added more capacitors in parallel this will increase the equivalent capacitance (unlike what we saw
earlier for capacitors in series).
5. Example Problem
Let us now examine the following capacitor circuit and calculate the equivalent capacitance.
STEP 1: Open circuit file “capacitor_circuit.ms12” using NI Multisim. You will notice the following circuit [3].
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Circuit 1
Answer Sub-Step 1: Calculate the individual values of the charge Q for each capacitor.
We begin by simplifying the circuit until we get to a simple circuit with one battery and one equivalent capacitor and then star
solving for the equivalent charge Qeq. After which we can reconstruct our circuit and determine the individual values of Q for
each capacitors.
We start with the switch open (meaning no current is flowing through the capacitors). Once we close the switch, current will f
into the circuit and is faced with the first capacitor C1. Since the current is not able to flow through C1 it will start to charge an
1 is formed across C1 and the charges are labelled as below:
Circuit 2
Note that the current flows until the capacitors are full and cannot store any more charge and no more current can be forced
them and this is what is called the steady state [3].
Answer Sub-Step 2: Calculate the equivalent capacitance Ceq
We have a combination of series and parallel capacitors. Break the combinations down and solve one combination at a time.
Answer Sub-Step 3: Calculate the equivalent capacitance Cseries for C3 and C4:
1/Cseries = 1/C3 + 1/C4 = ¼ + ¼ therefore Cseries = 2F
Now, the equivalent circuit looks like this:
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Circuit 3
Answer Sub-Step 4: Calculate the equivalent capacitance Cparallel for C2 and Cseries:
Cparallel = C2 + Cseries therefore Cparallel = 10 F
Thus, the equivalent circuit will look like this:
Circuit 4
Answer Sub-Step 5: Calculate the equivalent capacitance Ceq for C1 and Cparallel:
1/Ceq = 1/Cparallel + 1/C1 = 1/10 + 1/15 therefore Ceq = 6F
And the final representation of our circuit becomes (open circuit file “capacitor_eq_circuit.ms12”):
Circuit 5
Answer Sub-Step 6: Calculate the equivalent charge Qeq
Since ΔV = Q/C then Q = ΔV x C [3]
Ceq = 6F
Therefore Q
= 10 x 6 = 60 Coulombs
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Therefore Qeq = 10 x 6 = 60 Coulombs
Now we can reconstruct our circuit by finding the individual charge values of each capacitor using the equivalent circuits that we
created for each step:
Using circuit 4: since the capacitors are connected in series : Q1 = Qparallel = 60 Coulumbs
Since ΔV = Q/C
Therefore : VC1 = 60/15 = 4 V
VCparalel = 60/10 therefore VCparallel = 6 V (this can also be calculated by using KVL: since the battery is supplying 10 V and
has 4V then the remaining 6 V have to be across Cparallel).
Using circuit 3:
For C2 and Cseries connected in parallel, then VC2 = VCseries = 6 V
And therefore:
Q2 = 8 x 6 = 48 Coulombs
and
Qseries = 2 x 6 = 12 Coulombs
Using circuit 2 :
For C3 and C4 connected in series:
Q3 = Q4 = 12 Coulombs
And finally the potential differences can be calculated as follows:
VC3 = 12/4 = 3 V
and
VC4 = 12/4 = 3 V
Notes:
In series, the equivalent capacitance has a smaller value than any of the original capacitors. Another important characteristic
about capacitors in series is that the smallest capacitor will always store the most energy and that is because the charge is the
same and since energy is defined as Q2/2C so when the capacitor value is smaller the energy is greater [3].
As for capacitors in parallel, the equivalent capacitance has a larger value than any of the original capacitors. Another importan
characteristic about capacitors in parallel is that the largest capacitor will always store the most energy and that is because for
parallel combinations the potential difference ΔV is the same and since energy E = ½ x C x ΔV2 and since ΔV is constant then
the bigger the value of C the larger the amount of energy E [3].
6. Suggested NI Solution
National Instruments offers a number of products that combine to provide a scalable and powerful teaching platform for educato
The solution includes:
NI Multisim circuit teaching environment: Combining an intuitive circuit definition environment, with powerful SPICE simulation
technology, educators can use NI Multisim to easily teach the ins-and-outs of circuits in a safe environment.
NI ELVIS teaching and measurement platform allows educators to provide students with a compact, all-in-one unit for their
measurement and analysis needs. Combining an oscilloscope, function generator, DMM, bode analyzer and 8 other instrument
into a small platform; it simplifies the laboratory experience for students and lab instructors.
7. References
[1] Hoppe, Patrick, Wisconsin Technical College System. “Capacitance”. Series Capacitance.
[http://www.wisc-online.com/objects/ViewObject.aspx?ID=DCE2602]. (17/01/2013)
[2] Hoppe, Patrick, Wisconsin Technical College System. “Capacitance”. Parallel Capacitance.
[http://www.wisc-online.com/objects/ViewObject.aspx?ID=DCE2902]. (17/01/2013)
[3] Brightstorm. “Capacitor Circuits”. Capacitor Circuits.
[http://www.brightstorm.com/science/physics/electricity/capacitor-circuits/]. (18/01/2013)
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