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aqa A-level physics Year 2 (yr13) capacitance: chapter 6
Definitions
Capacitance |
the charge stored per unit pd |
capacitor |
component that stores charge. composed of two parallel conducting plates with a dielectric between them |
dielectric |
an insulating material placed between the two plates of a capacitor in order to increase the amount of charge it can store |
time constant |
time taken for a capacitor to dishcarge 37% of its inital charge |
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it is equal to the product of capacitance and the resistance of a fixed resistor (that the capcitor is being discharged through) |
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intro
- the positive side of the battery attracts electrons from one side of the initally uncharged plate
--> this causes the left plate to become positively charged
- the negative side of the battery repels these new electrons to the right of the parallel plates
--> causing the right to become positively charged
it can also be used to recity ac current by bring the current down gradually instead or sharply (? refer to graph)
these plates store these electrons as charge so if the circuit breaks connection with the battery a separate circuit connected to the capacitor can continue to operate with the capacitor acting as a battery until it runs out of charge
maximum stored charge = pd across the battery |
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Equations
capacitance |
Q/V (farad) |
V |
EQ |
energy stored in a capacitor |
1/2 QV |
(area under graph) |
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1/2 CV2 |
V/Vo (V over V inital) |
e -t/RC |
C |
Er Eo A / d |
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Er -relative permitivity of a dielectric/insulator between plates |
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Eo -relative permitivity of free space |
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A area of plates |
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d distance between plates |
- |
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in a capcitor half the energy is always lost to heat either in resistor or wires etc
(refer to energy = 1/2 QV - this is where the missing energy is going)
Capacitors in series and parallel
capacitor |
series |
parallel |
charge |
same |
2x |
pd |
split |
same |
C total |
1/Ct = 1/C1+1/C2 |
Ct = C1+C2 |
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Decay and Time constant
compared to the V-t graph of a charging capacitor (similar to x1/2) which changes to a curved exponential decreasing graph of I-t
the V and I-t graphs for a discharging capacitor are the same (same shape as charging I-t)
V/Vo = e-t/RC
r- resistance
c- capacitance
when t = RC we get e-1 which is 0.37 (37%)
therefore when the time equals the resistance, we get 37% of the original voltage
this is why RC is our time constant - tc |
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Capacitance and dielectrics
if you were to increase the distance between the two plates the capacitance would decrese
two things can follow from that:
1. if the battery was connected - you have a constant v
as E = 1/2CV2
the energy would decrease
2. if the battery was disconnected - you have a constant Q
as E = 1/2Q2/C
energy increases
(2 makes sense as if you try to separate two charged plates that are attracting each other then you are putting energy into the system to do this) |
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