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capacitor
device that stores electrical charge and therefor electrical energy

capacitor consists of
two conductors placed near each other but not touching

parallel plate capacitors are separated by
an electrically charged insulating material called a dielectric

one capacitor plate is
positively charged the other is negatively charged

electric potential of positive plate exceeds that of the negative plate by an amount
V

when the magnitude of the charge on each plate is doubled the electric potential is
 doubled
 Q is proportional to V
 Q=CV where c is capacitance and is a constant





capacitance
the charge stored per unit potential difference across a capacitor

initially the flow of charge , current , to an uncharged capacitor is
high as time passes the rate reduces as the charge from the cell must overcome the build of of charge on the plate

on charging electrons flow from
negative terminal of cell to one end of plate (which becomes negative) and then from the other end of the plate (which becomes positive) to positive terminal of cell

it isn't possible to store more and more charge by applying an ever increasing pd across the capacitor
eventually the pd becomes too large for the insulating material between the plates . electrical breakdown then occurs and conduction takes place across the gap

various dielectrics are used to
increase the capacitance , the material used and its thickness determine the max working pd of the capacitor

for a Q VS pd graph the gradient is
C

.... must be done to charge up a capacitor therefor
 work
 electrical potential energy is stored as a result

the amount of energy stored depends on
charge stored by the capacitor and the pd across it

when a capacitor is being charged
charge flows on to the capacitor

the battery has to
transfer energy to do work against the repulsive force from the charge already on the capacitor

work done in moving charge through a pd is
W=QV

... across a capacitor isn't constant
pd

average pd is
0.5pd (pd increases from 0 to max pd when capacitor is fully charged)

work done in charging a capacitor is therefor
0.5QV

energy stored by the capacitor is therefor
0.5QV

Q=CV so energy stored also =
0.5CV^{2} or 0.5Q^{2}/V


draw a V vs Q graph
what's the gradient
what does the area under the graph represent
 1/C
 work done in charging a capacitor , energy stored by a capacitor 0.5QV

capacitor discharge circuit

charging through a fixed resistor
when an uncharged capacitor is placed in a circuit to be charged the initial current I_{0} depends on the
 emf of the battery and the resistance of the circuit
 I_{0} = V_{0}/R

as charge accumulates on the capacitor the
pd across it increases .

the pd opposes that of the battery and it becomes
increasingly difficult to push charge on to the capacitor and the charging current drops

eventually the pd across the capacitor is
equal but opposite to that of the battery and the charging current drops to zero

as the capacitor charges the pd across the resistor
gets smaller because the pd across the capacitor gets bigger and so the current drops

Q ∞ V sp Q vs t graph is the same as V vs T graph
draw these graphs for charging through a fixed resistor

the rate at which the current drops depends on
resistance and on the capacitance of the circuit

the larger the resistance
the lower the current the capacitor therefor takes longer to charge

a large value of capacitance
also increases the charging time since it takes more charge to fill the capacitor

the product RC is known as
the time constant for the circuit

draw an I vs T graph for charging through a fixed resistor

time constant is the time
it takes for current to drop to 1/e of its original value

draw a V vs T graph for charging across a fixed resistor showing curves for pd across capacitor and pd across resistor
 where :
 A = across capacitor and
 B = across resistor
 Vc + Vr = EMF

exponential decay curves
have the property that they always take the same time to decrease by a given fraction

to discharge a capacitor
take out the battery and reconnect the circuit

when a charged capacitor is connected across a resistor the pd
drives a current through the circuit

the current flows in the
opposite direction from the charging current

the capacitor is fully discharged when
the pd across the plates and the current in the circuit are both zero

draw the three vs T graph for discharging through a fixed resistor

the I vs T graph is the same as the one for charging
the current starts off relatively high and gradually decreases to zero . this is because initially when a charged capacitor is connected across a resistor the pd drives a current through the circuit but the pd across the resistor decreases as the charge on the capacitor decreases




time constant is the
 time taken for charge/voltage/current on a discharging capacitor to fall to 0.37Q_{0}/V_{0}/I_{0}
 its's also the time taken for voltage/charge on a charging capacitor to rise to 0.63V_{0}/Q_{0}
 it's also the time taken for current on a charging capacitor to fall to 0.37I_{0}


capacitors discharge energy quickly so they can be used in
applications where a lot of energy is required rapidly , a taser is an example . Filters also use capacitors to smooth electrical signals

if we have two capacitors in parallel the voltage of each capacitor has to be the same because
the capacitors are in parallel

if we have two capacitors in parallel the final charge in each capcitor is
 capacitor A
  x total charge
 total capacitance
 and the same goes for B
 total charge is Q=CV for capacitor that is being charged
 voltage can be worked out in the same way but you will find the voltage is the same for both capacitors as discussed in previous question

if we have two capacitors in parallel the final energy stored in each capacitors is
E = 0.5CV^{2} where v is the final pd across the capacitor

why is there a loss of energy stored
because battery has to transfer energy to do work against the repulsive force from the charge already on the capacitor so energy is wasted and hence less is stored

battery has more energy because
pd in battery is constant so E=QV

