capacitors Flashcards
capacitance
the amount of charge its able to store per unit potential difference
measured in farads
capacitance equation
C = Q / V
capacitor set up
an electrical components that can store electrical charge
made up of two electrical conducting plates and a dielectric between them
when a capacitor is connected to a D.C.
Charge builds up on each plate, one plate becomes negatively charged, the other positive
The dielectric makes sure no charge travels across the plates so a potential difference builds up between the plates
voltage rating
the voltage rating of a capacitor is the maximum potential difference that can safely be put across it
relationship between potential difference and charge
CV = Q
capacitance is constant so charge is directly proportional to potential difference
capacitors set up
can onlt store relivitely small amounts of charge and provide power for short amounts of time
useful as it can store charge until its needed and discharge it all in a fraction of a second
it can be very dangerous though
uses of capacitors
camera flash
ultracapacitors - back up power supplies
energy stored
when a capacitor is charged, one becomes negative, the other positive, this means the plates are being forced together which requires energy which is supplied by power source and and stored as electric potenctial as long as the charge is held
when the charge is released, the eletric potential energy is released
p.d. - Q graph
proportional to eachother
area under equal to energy
3 enegy equations
E = 0.5QV
E = 0.5CV^2
E = 0.5 Q^2 / C
Where does current flow
positive to negative
where does electrons in current flow
negative to positive
permittivity
a measure of how difficult it is to generate an electric field in a medium
higher the permittivity of a material. the more charge is needed to generated an electric field of a given size
relative permittivity
AKA dieletric constant
ratio of permittivity of a material to the permittivity of free space
relative permittivity equation
εr = ε1 / ε0
properties of capacitors that can change how much charge it can store at a given voltage
- the dielectric material separating the two conducting plates
this changes the capacitance as different materials have different relative permittivity
polar molecules
permittivity can be experienced by motion of molecules inside the dielectric
imagine a dielectric made up of polar molecules ( positive end / negative end )
when no charge is being stored, no electric field is being generated and molecules are aligned randomly
when a charge is applied, and electric filed is generated, negative end attracted to positive plate and vice versa
molecules rotate and align antiparalell to field
polar molecules relationship with larger permittivities
each molecule has their own field opposing the applied field of the capacitor
the lareger the permittivity, the larger the opposing field
This reduces the overall eletric filed between the parallel plates reducing the p.d. needed to transfer a given charge to the capacitor so the capacitance increases
capacitance equation with area
C = Aε0εr / d
capacitance depends on
dimensions of the capacotor
dieletric
charging a capacitor
when a capacitor is connected to a d.c. power supply, a current flows until the capacitor is fully charged
eletrons flow from - terminal of supply onto the plate connected to the capacitor so a negative charge builds up on the plate
eletrons then flow from other plate to positive terminal of supply making that plate positive
These eletrons are repelled by the negative charge on the negative plate and attracted to positive terminal of supply
current change when capacitor is charging
initially the current is high
as charge builds up on plate, electrostatic repulsion makes it harder for more electrons to be deposited
when the p.d. across the supply equals the p.d. across the capacitor the current falls to 0 and the capacitor is fully charged
charhging through a fixed resistor
the resistance affects the time taken to charge the capacitor
as current starts to flow, p.d across the capacitor is zero so there is no p.d opposing the current
the p.d of a battery causes an initially high current to flow (V/R)
as p.d across capacitor increases and p.d across resistor decrease and current drops
I-T graph
capacitor through a fixed resistor
1 / x^2
starts at I0
V-T and Q-t graph
capacitor through a fixed resistor
starts at Q0 and V0
x^2 graph, cut in half
charging equation
Q = Q0 (1- e^-t/RC)
V = V0 (1- e^-t/RC)
I = Io e^-t/RC
What does Q0 / V0 / I0 mean
value when fully charged
initial current
how to discharge through a fixed resistor
to discharge through a capacitor, take out the battery and reconnect the circuit
discharging through a fixed resitor
the p.d drives a current through a circuit
this current flows in the oppsote direction from the charging current
current is initially high too
capacitor is fullt discharged when the p.d across the plates and the current falls to zero
I-t / Q-t / V-t graph
all 1 / x^2
discharging equations
Q = Q0 e^-t/RC
I = I0 e^-t/RC
V = V0 e^-t/RC
time taken for capacitor to charge/ discharge depends on
- capacitance affect the amount of charge that can be transferred at a given voltage
-resistance of a circuit ( larger resistance the longer)
time constant
RC
time taken for charge on a discharging capacitor to fall to 1/e (roughly 37%) of initial value or charge to rise to about (63%) of full charge
when t = RC
Q / Qo = 1/e = 0.37
time taken to fully charge/discharge
in practice 5RC
Time to half equation
0.5 = e^-t/RC
T0.5 = 0.69RC
