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## MCAT

### Kurs: MCAT>Jednostka 8

Lekcja 15: Kondensatory

# Kondensatory

## Czym są kondensatory?

Cartoon showing the difference between the area of a large and small plate.
Q = CU
Stałą C nazywamy pojemnością. Pojemność określa, jak dużo ładunku gromadzą okładki kondensatora w zależności od przyłożonego napięcia. Jeżeli kondensator ma bardzo dużą pojemność, niewielka zmiana w napięciu spowoduje dużą zmianę w liczbie zgromadzonych na okładkach elektronów (czyli ładunku Q).
Jeżeli uda nam się rozdzielić dodatnie i ujemne ładunki na osobnych okładkach kondensatora, możemy to wykorzystać do wykonania pracy. Jeżeli następnie pozwolimy im wzajemne się przyciągnąć do siebie np. poprzez podłączenie kondensatora do obwodu, ładunki zaczną się przemieszczać, czyli w obwodzie popłynie prąd. Oprócz pracy związanej z przepływem prądu w obwodzie, ładunki te możemy wykorzystać także do specjalnych zadań np. do rozgrzania włókna żarowego w żarówce. Całkowita energia, którą można wydobyć z w pełni naładowanego kondensatora, jest związana z jego pojemnością i różnicą potencjałów pomiędzy jego okładkami,
E = 1/2 CVsquared
Cartoon showing how discharging a capacitor can turn on a light bulb.

## Do capacitors store charge?

Capacitors do not store charge. Capacitors actually store an imbalance of charge. If one plate of a capacitor has 1 coulomb of charge stored on it, the other plate will have -1 coulomb, making the total charge (added up across both plates) zero. If you short circuit the capacitor by connecting the two plates with a wire of negligible resistance, you’ll see a sudden rush of current (depending on the size of the capacitor, this can result in sparks) as the electrons on the -1 coulomb plate rush onto the +1 coulomb plate. This sudden rush of current releases all the energy that’s stored in the capacitor.
To help us understand parallel plate capacitors, consider this situation. Imagine you start with two metal plates with no difference of charge (Q= 0). You attach a battery, which at first adds a single electron to one side of the capacitor. The electron has an electric field that repels other electrons, and this field reaches through space and pushes on the electrons in the other plate, causing that plate to acquire an induced positive charge. Now your first plate has a charge of -1e, and the far plate has a charge of +1e, where e is the way we normally write the elementary charge of a single electron.
Cartoon showing the flow of electrons when charging a capacitor.
Now imagine repeating this process over and over, until a considerable amount of negative charge has built up on one plate and induced an equal positive charge on the other plate. At some point, the existing negative charge on the first plate will be so repulsive that it prevents you from adding any more negative charges to that plate. In this case the capacitor is fully charged. This maximum charge Q corresponds to the final voltage of the charged capacitor in the relation Q= C V.
But how does the shape of the capacitor affect this process?
• Distance: The further apart the two plates are, the less the free electrons on the far plate feel the push of the electrons that you’re adding to the negative plate, making it harder to add more negative charges to the negative plate. If the plates were infinitely far apart, you would just be adding negative charges to an already negative metal surface, which would be pretty hard. If the plates were very close to each other or even touching, you essentially would be making current flow through a short circuit, which would be easy. This means that the capacitance of a parallel plate must be inversely related to the plate separation.
Cartoon showing a large distance between two capacitor plates. Molecules on one plate are saying they cannot hear what the molecules on the other plate are saying to them because the distance is SO far!
• Area: It’s a lot easier to add charge to a capacitor if the parallel plates have a huge area. Two wide metal plates would give two repelling like charges a greater range to spread out across the plate, making it easier to add a lot more negative charge to one plate. Likewise, a very small plate area would cause the electrons to get cramped together earlier, making it harder to get a large difference in charge for a given voltage. From this we can guess that the capacitance of a parallel plate must be related to the plate areas.
Cartoon showing the difference between a positive and a negative plate. The positive plate is missing electrons.
These two principles can be expressed as the parallel-plate capacitor formula:
C = ɛ A/d
A is the area of the plates, and d is the distance between the plates. ɛ is a constant called the permittivity, which determines how easily the air between the plates allows an electric field to form. If a different insulating material is used inside the gap, this constant will have a different value, and so materials with a higher value of this constant generally make better capacitors.

## Consider the following… cardiac defibrillators

Sometimes the regular rhythm of your heart pumping blood around your body stops beating regularly. It turns out that the most effective way to make the heart start ticking regularly is simply to shock it with a giant capacitor. When a patient’s heart beats too fast or doesn’t beat in the correct sequence (called fibrillation), paramedics attach two electrodes to the patient’s chest. These electrodes are connected to a defibrillator, which consists of a battery and a giant capacitor. When paramedics use defibrillators, batteries slowly charge the capacitor by adding electrons to one plate and pulling an equal number of electrons off of the other plate. Once the capacitor is charged to the set voltage, paramedics rapidly discharge the capacitor through the electrodes on the patient’s chest in hopes of resetting the heart beat.

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