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Capacitance
Battery
A capacitor is a device that stores electrical energy and releases this energy is short bursts. A Parallel-Plate Capacitor
has equal and opposite charges stored on two identical flat conducting parallel plates (as shown to the left) separated
by a non-conducting material (air, paper, rubber).
Capacitors are typically charged by connecting it to a battery which essentially removes electrons from one of the
plates and places them on the other plate. This electron flow will continue until the battery and capacitor are at the
same potential (typically you can assume this to be the voltage of the battery).
Capacitor
Q.1. Using the diagram above, which plate lost the electrons? Gained them? What is the total charge on the capacitor?
The amount of charge the capacitor can hold is defined as its capacitance and is measured in the units of farads (F).
https://phet.colorado.edu/en/simulation/legacy/capacitor-lab
Factors that determine capacitance:
Factors:
Relation:
Units:
Vector/Scalar:
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Formula:
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Q.2. A parallel plate capacitor is made up of square plates whose sides are 27 cm long and 3.5 mm apart.
What is the capacitance of this capacitor if the area between the plates is filled with air? Filled with water?
Q.3. If the plates were doubled in length on all sides, what would happen to the capacitance?
Q.4. If the separation of the plates were doubled, what would happen to the capacitance?
Q.5. Using the chart above, what material would be the best dielectric constant if you wanted to maximize the
amount of capacitance?
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Charging up a Capacitor
The amount of charge a capacitor can hold is determined by…
C=
This capacitator is then connected to a battery. The total charged stored on the
capacitor will be dependent on…
Q=
Items that use capacitors:
1.
2.
3.
Q.1. Determine the amount of charge stored on a capacitor of 4.0µF when connected to a 12.0 Volt battery.
Q.2. Calculate the voltage of a battery connected to a parallel plate capacitor with a plate area of 2.0 m 2 and a plate separation of 2 mm if the
charge stored on the plate is 4.0 pC.
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Q.3. The electric field between two parallel plates is given as 𝐸
=
𝑉
𝑑
however on the AP 2 References Table it is given as 𝐸
=
𝑄
𝜀0 𝐴
.
Derive this second equation.
Q.4. The charge on a parallel plate capacitor is 4.0 µC. If the distance between the plates is 2 mm and the capacitance is 1 µF, what is the
strength of the electric field?
Q.5. The plates of a parallel-plate capacitor are separated by a distance of 2 mm. The capacitance is 1 µF. How much charge needs to be
transferred from one plate to the other in order to create a uniform electric field whose strength is 10 kV/m?
Conclusions:
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Energy Stored in a Capacitor
Since the capacitor stores charge it can do work and therefore has potential energy, will call it Uc. Remember that work is the change in energy.
What is the relationship between work, voltage and charge?
𝑊 = 𝑈𝑐 = 𝑞∆𝑉𝑎𝑣𝑔
Where ∆Vavg is the average potential difference as the capacitor is charging (which becomes ∆V/2 due to the zero-initial potential and the ∆V
final potential). This leads to the following three formulas:
1
1
𝑞2
2
𝑈𝑐 = 𝑞∆𝑉 = 𝐶∆𝑉 =
2
2
2𝐶
Derive the second and third formulas:
Another way to think of energy is by using the graph to the right that shows potential differences
versus charge . What does the area under the graph represent?
Q.1. How much energy and charge is stored in a 5.0 μF capacitor when it is connected to a 120 V power source?
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Q.2. A fully charged defibrillator contains 1.2 kJ of energy stored in a 110 μF capacitor. In a discharge through a patient, 600 J of electrical
energy are delivered in 25 ms. How much voltage is needed to store the fully charge defibrillator? How much power is delivered to the patient?
Conclusions:
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