In this lesson Reading task
activity can be organized differently. For example, one group can use printed
text and do the reading task. The second group can investigate and find
information by themselves by using the internet resources. However, is there is
no access to the internet, teacher might spread out applications from the
article and students working in small groups read only one application and
present it. During the poster presentation teacher add some more applications
from the slides or use Attachment 1.
During watching a video clip
teacher might stop at any time and make sure that students are getting well
with it. There is also option during this activity. Each group can look for
answer of only one question. More able student will be given an extended
question about energy stored in series of capacitors. If class English level is
not enough to understand the topic, teacher can give them model answer (Attachment
2) and ask them explain what they have understood.
can replace homework problems so students solve them in a class and the
problems from the slide 12 solve at home.
Theoretical material: Energy stored in a charged capacitor
Most of us have seen dramatizations in which medical
personnel use a defibrillator to pass an electric current
through a patient’s heart to get it to beat normally. Often realistic in
detail, the person applying the shock directs another person to “make it 400
joules this time.” The energy delivered by the defibrillator is stored in a capacitor
and can be adjusted to fit the situation. SI units of joules are often
employed. Less dramatic is the use of capacitors in microelectronics, such as
certain handheld calculators, to supply energy when batteries are
charged.Capacitors are also used to supply energy for flash lamps on cameras.
Energy stored in a capacitor is electrical potential energy, and
it is thus related to the charge and voltage on the capacitor. We must be careful when applying the equation
for electrical potential energy to a
capacitor. Remember that is the potential energy of a charge going through a voltage . But the capacitor starts
with zero voltage and gradually comes up to its full voltage as it is charged.
The first charge placed on a capacitor experiences a change in voltage , since the capacitor has
zero voltage when uncharged. The final charge placed on a capacitor experiences
, since the capacitor now has its full voltage on it. The average voltage
on the capacitor during the charging process is , and so the average voltage
experienced by the full charge is . Thus the energy stored in a capacitor, , is
where is the charge on a capacitor
with a voltage applied. (Note that the
energy is not , but .) Charge and voltage are
related to the capacitance of a capacitor by , and so the expression for can be algebraically manipulated into three equivalent
where is the charge and the voltage on a capacitor . The energy is in joules
for a charge in coulombs, voltage in volts, and capacitance in farads.
In a defibrillator, the
delivery of a large charge in a short burst to a set of paddles across a
person’s chest can be a lifesaver. The person’s heart attack might have arisen
from the onset of fast, irregular beating of the heart—cardiac or ventricular
fibrillation. The application of a large shock of electrical energy can
terminate the arrhythmia and allow the body’s pacemaker to resume normal
patterns. Today it is common for ambulances to carry a defibrillator, which
also uses an electrocardiogram to analyze the patient’s heartbeat pattern.
Automated external defibrillators (AED) are found in many public places (Figure 2). These are designed to be
used by lay persons. The device automatically diagnoses the patient’s heart
condition and then applies the shock with appropriate energy and waveform. CPR
is recommended in many cases before use of an AED.
the light bulb lights up when it connected with a capacitor?
capacitor is stores energy. When a charged capacitor connected to a light bulb,
energy turns into light and heat energy.
kind of energy stored in a capacitor?
stores electric potential energy
do we calculate the energy stored in a capacitor?
is the significance of the coefficient ½ in a capacitor energy equation?
During discharging not all of the charges
drop through the total initial voltage V. In fact only the first charge that
gets transferred is going to drop through total initial voltage V. All of the
charges that get transferred after are going to drop through less and less
voltage. The reason for this is that each time charges get transferred it
decreases the total amount stored on the capacitor. As charges on the capacitor
keeps decreasing, the voltage of the capacitor keeps decreasing as well. As
more and more charge gets transferred, there will be a point where a charge
only drops through ¾ of the initial voltage. Wait longer and when a
charge gets transferred through only a half of the initial voltage V, than
¼ of the initial voltage V and so on. And last charge to get transferred
drops through almost no voltage at all, because there is basically no charge
left that’s stored in a capacitor. If we add up all of these drops in
electrical potential energy, you would find that the total drop in energy of
the capacitor E=Q V/2
So, on average the charges dropped
through only a half the initial voltage.
are the alternative equations for the capacitor energy?
part: (from 5.45min)
do we calculate the energy stored in a capacitor for a multiple capacitors
connected in a circuit?
order to find the energy of the single capacitor, we have to use the voltage
across that particular capacitor (and not the battery)
problems with solutions: Low level
What is the energy stored in the capacitor of a heart defibrillator charged to ? (b) Find the amount of stored charge.
open heart surgery, a much smaller amount of energy will defibrillate the
heart. (a) What voltage is applied to the capacitor of a heart defibrillator that stores 40.0 J of
energy? (b) Find the amount of stored charge.
3: A capacitor is used in conjunction with a motor.
How much energy is stored in it when 119 V is applied?
Suppose you have a 9.00 V battery, a capacitor, and a capacitor. (a) Find the charge and energy stored if the
capacitors are connected to the battery in series. (b) Do the same for a
nervous physicist worries that the two metal shelves of his wood frame bookcase
might obtain a high voltage if charged by static electricity, perhaps produced
by friction. (a) What is the capacitance of the empty shelves if they have area
and are 0.200 m apart? (b) What is the voltage between them
if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that
this voltage poses a small hazard, calculate the energy stored.
Show that for a given dielectric material the maximum energy a parallel plate
capacitor can store is directly proportional to the volume of dielectric (). Note that the applied voltage is limited by the
problems with solutions: High level
7: Construct Your Own Problem
a heart defibrillator similar to that discussed in Example 1. Construct a problem in which you examine the charge
stored in the capacitor of a defibrillator as a function of stored energy.
Among the things to be considered are the applied voltage and whether it should
vary with energy to be delivered, the range of energies involved, and the
capacitance of the defibrillator. You may also wish to consider the much
smaller energy needed for defibrillation during open-heart surgery as a
variation on this problem.
8: Unreasonable Results
On a particular day, it takes of electric energy to start a truck’s engine. Calculate the
capacitance of a capacitor that could store that amount of energy at 12.0 V.
(b) What is unreasonable about this result? (c) Which assumptions are
9. A heart defibrillator delivers of
energy by discharging a capacitor initially at .
What is its capacitance?
1: (a) 405 J
2: (a) 3.16 kV
4: (a) ,
5: (a) (b) 452 V
8: (a) 133 F
(b) Such a
capacitor would be too large to carry with a truck. The size of the capacitor
would be enormous.
(c) It is
unreasonable to assume that a capacitor can store the amount of energy needed.
are given E and V, and we are asked to find the capacitance . Of the three expressions in the equation
for E, the most convenient relationship is E=CV2/2
this expression for C and entering the given values yields
is a fairly large, but manageable, capacitance at .
Additional multiple choice questions:
Capacitors in Series and Parallel (Average level)
72. Which one of the following statements is true
concerning capacitors of unequal capacitance connected in series?
(a) Each capacitor holds a different amount of
(b) The equivalent capacitance of the circuit is
the sum of the individual capacitances.
(c) The total voltage supplied by
the battery is the sum of the voltages across each capacitor.
(d) The total positive charge in the circuit is
the sum of the positive charges on each capacitor.
(e) The total voltage supplied by
the battery is equal to the average voltage across all the capacitors.
73. Three parallel plate capacitors, each having a
capacitance of 1.0 µF are connected in parallel.
The potential difference across the combination
is 100 V. What is the equivalent capacitance of this combination?
(a) 0.3 mF (c) 3 mF (e) 30
(b) 1 mF
(d) 6 mF
74. Three parallel plate capacitors, each having a
capacitance of 1.0 µF are connected in parallel.
The potential difference across the combination
is 100 V. What is the charge on any one of the capacitors?
(a) 30 mC (c) 300 mC (e) 3000 mC
(b) 100 mC (d) 1000 mC
75. A 3.0-µF capacitor is connected in series with a
4.0-µF capacitor and a 48-V battery. What quantity of charge is supplied by
the battery to charge the capacitors?
(a) 3.4 ´ 10–4 C (c) 3.0
´ 10–5 C (e) 1.8
´ 10–6 C
(b) 7.3 ´ 10–4 C (d) 8.2 ´ 10–5 C
76. What is the equivalent capacitance of
the combination of capacitors shown in the circuit?
(a) 0.37 µF (d) 0.67 µF
(b) 3.3 µF (e) 2.1
(c) 4.6 µF
77. How much energy is stored in the combination of
(a) 0.01 J (d) 0.04
(b) 0.02 J (e) 0.05
(c) 0.03 J
78. A battery supplies a total charge of 5.0 mC to a circuit that consists of a series
combination of two identical capacitors, each with capacitance C.
Determine the charge on either capacitor.
(a) 5.0 mC (c) 1.5 mC (e) 0.50
(b) 2.5 mC (d) 1.0 mC
79. When two capacitors are connected in
series, the equivalent capacitance of the combination is 100 µF. When the two
are connected in parallel, however, the equivalent capacitance is 450 µF.
What are the capacitances of the individual capacitors?
(a) 200 µF and 250 µF (d) 150 µF and 300 µF
(b) 125 µF and 325 µF (e) 80
µF and 370 µF
(c) 175 µF and 275 µF
Additional multiple choice questions: Capacitors in
Series and Parallel (Average level)
Questions 80 through 82 pertain to the situation
A 10.0-µF capacitor is charged so that the potential
difference between its plates is 10.0 V.
A 5.0-µF capacitor is similarly charged so
that the potential difference between its plates is 5.0 V.
The two charged capacitors are then connected to each
other in parallel with positive plate connected to positive plate and negative
plate connected to negative plate.
80. How much charge flows from one capacitor to the
other when the capacitors are connected?
(a) 17 mC (c) 67 mC (e) zero
(b) 33 mC (d) 83
81. What is the final potential difference across the
plates of the capacitors when they are connected in parallel?
(a) 5.0 V (c) 7.5
V (e) 10 V
(b) 6.7 V (d) 8.3 V
82. How much energy is dissipated when the two
capacitors are connected together?