Chapter 21 Cappacitance Flashcards
What is a capacitor , and what is it made of
A cappator is an electrical component that is designed to STORE charge, seperating electrical charge into +Q and -Q
Thus it stored energy in the form of EPe in electric field , and thus can be used later once charged
2 made out of two metal plates and an insulator in between simplest, can be a sphere too with isolated charge
What is definition for capacitance
The amount of charge that can be stored based on voltage applied
Thus charge is PROPORTIONAL TO VOLTAGE,
How does a capacitor work
Voltage is turned on and a current js driven from positive plater to the first plate of cappator
- here electrons build up and a negative charge is formed here
- due ti a build up of negative , and as it can cross due to insulation, by induction it REPELS electrons from other plate, causing them ti move around the circuit and eventually be deposited at the negative plate again
- AS CHARGE MUST BE CONSERVED , the positive plate charge is = to neagtive plate but positive
THUS charge stored is separated to +Q and -Q
Due TO CHARGE = ELECTRIC FIELD AND POTENTIAL FORMED , potential difference formed between the charged
This causes it to DRIVE ITS OWN CURRENT , but now in the OPPOSITE WAY
- as a result the net current in the circuit begins to drop as the capacitor is charging
- once the current out= in , the current is at 0
This can only occur once the pd of the capacitor = to the pd of the supply for them to both generate same current
So when fully charged, current is at 0 and the PD of captor = PD of the power supply!
Storing charge , charge conserved but split into Q+ and -
What actually going on - Whars charge in all of cappator vs plate
The total charge stored across the capacitor is = just Q
Think of one plate storing Q, leave the lomg thoughts, or just that it stores charge of Q
Basically total charge stored by cappator is 0, but charge in each plate is stored with magentiude if Q
Why are rules for swries and parallel what they are
IMPORTANT
SERIES
1) in series no matter what, the TOTAL CHARGE is stored the same by EACH CAPPACITOR
- however the VOLTAGE IS SPLIT (based in capacitances)
Parallel
1) voltsge going into each capacitor is the SAME
- but the charge is split
So different
WHY IS THE TOTAL CHARGE GONNA BE STORED BY ALL THE CAPPATOR IN SERIES
(So all if them have the same why?)
- how charge still conserved
- and does this mean you split charge equally amongst all 3 or what?
Because , the plates the wires are actually connected to become charged of equal and opposite magentiude, and then by induction and movement of electrons so are the ones in the middle
Thus the charge stored by each is the same, but net charge still 0 so charge is CONSERVED
NO THEY ALL HAVR THE SAME CHARGE = TO TOTAL CHARGEEEE
How to prove CHARGE IS THE SAME FOR SERIES
2) using multimeter set to cappacscitsnce TO TEST RULES?
Badicsllt for series , you know the cappscitsnces hopefully, run a current through them and attach to voltmeter
And then based in voltages and capapctsnces work out charge, should find out to be the same
2) here, csn use the multimeter to find the capacitances if them separately , and then use them to find them together by measuring the COMBINATION
- should see the series follows The rules confirming they are true
What are any discrepancies in experimental values for charge same across series due to
Inaccuracies due ti manufactured capacitance readings and voltmeters
CORREVT way ti derrive seires and parallel equations, even for electricity?
1) write down the Variable that isn’t constsnt
2) divide by variable that IS CONSTANT
Rearrange the formula to fit what you want
Proof that energy is stored in a capacitor can be seen fi you disconnect cappacitor connect to flashbulb and it lights up
BUT WHERE DOES THIS ENERGY COME FROM
Basically , when the plate is already negatively charged and other is positively chwrged
Work is done to add MORE electrons to the negative side which is repelling them, and REMOVE electrons from the positbe side, which is attracting them
Thus work is done on the electrons, and this work is provided by the EXTERNAL POWER SUPPLY
Thus energy comes from the power supply
Where do energy equations come from
Basically when we have potential , we know energy is potential x charge / mass
So draw a charge against voltsge graph, gradient is capacitance, and area = work done
Thus work done = 1/2QV
And rearrange ti find other equations
Why do we charge and discharge through a resistor bith times?
This is because if we didn’t the discharge and charge would happen so fast can’t measure anything
What is circuit for discharge
What are INITAL condtions
What happens when wire detached for discharge
- current
-charge
Pd across capacitor
Pd across resistor
1) di ruin is cappator connected to supply, connected to resistor in parallel and voltmeter
2) T=0, the voltage across capacitor = V due to it BEING FULLY CHARGED, voltsge across REISTANCE also v as is it is parallel . Current in resistance and circuit = V/R
3) when wire detached, supply detached, so capacitor takes place,
- as it has a potential difference, it has a current, so electrons begin to flow to resistor, and thus CHARGE IN CAPACITOR BEGINS TO DROP
- AS CHARGE BEGINS TO DROP, SO DOES PD
- as Charge continued to drop, SO DOES CURRENT IN CIRCUIT
These are ALL EXPONENTIAL Decreases
Summary for what happens to current charge PD capacitor and resistor and why during discharge
Pd is from capacitor now
- current drives, so charge begins to drop
-charge begins to drop, so PD begins to drop
- charge begins to drop then current begins to drop
And pd froM RESISTOR is dependent on SUPPLY , which is cappacitor, it’s new master, so as that drops so does resistor pd
Equations for exp decrease + graohb
V = V0 e ^-t/RC
Graph is it starts at max and goes to zero, tends to zero so must go down and curve in
What is time constsnt and what does it represent for discharge and how to find out
Time constsnt is RC , and represents time taken for anything to decrease to 0.37% of origanl value
Sun in RC for time
Explain circuit for cappacitor charging from resistor
Also edplantaiton better to why voltage in resistor decreases
1) power supply connected to a reisdotr and cappacitor, initally turned off
2) as soon as switch turned on, thr current in system is MAX = V/R, and all the voltage js given to the resistor so it’s at V0
- but then as time continues, and charge builds up on the capacitors, a potential difference there, so own current drives back
- this goes against current, as a RESULT CURRENT DECREASES
- as the voltsge in the cappacitor increases, by Kirchhoff second law the voltage in the resistor MUST DECREASE
- as the charge builds up on cappacitor CHARGE INCREASES AND VOLTSGE INCREASES
At any point the sum of voltages in cappacitor and redid ore must = emf
So as one exp decrease other exo increases
2) better explanation is that as current decreases and REISTANCE fixed, it’s voltsge devreased too, better than just saying it does because of 2nd law
What will graphs for voltsge if reidtor and capacitor look like
Always mirror opposite, capacitor is exp increasing ti v max and resistor is exp decreasing to 0
At all times this adds to V0 SO MAKE SURE THIS WORKS ON ALL GRAPHS
When charging a capacitor what does time constsnt mean for something exp increase
It comes from subbing in, time twine to charge to 0.63% of orignal vslue
If you want a faster discharge / vs charge
Faster discharge , make time constsnt smaller (less time needed to get to 0.37)
Faster charge, time constsnt smaller, less time taken
When cappacitor fully charged, is the energy in capacitor the same as energy from supply?
NO if total energy = QV, and energy at capacitor 1/2 QV
it means capacitor gets half the energy ALWAYS, whereas rest of circuit the rest or it’s lost
What is the useful thing about capacitors given they can’t store thst much energy
Yh they can’t store that much energy in a given volume
But they can DISCHARGE it in very small times giving rise to HIGH POWER OUTPUTS
Thus for anything that required high power, like cameras, emergency flashlights, capacitors are used
Difference between capacitor and rechargeable batteries then?
Capacitors can be recharged over wnd over again no problem, hence used for emergencies
Rechargeable batteries degrade over time with changing snd in general
Two reasons to have capacitors!
Camera = needs high power in small time
1) when high powers needed
2) TO SMOOTH AC CURRENT INTO DC
How to smooth ac into dc what exact components and circuit needed and whyb
1) DIODE
- didode means only positbe cycles or whatever one way cycles of dc is used
2) resistor + CAPPACITOR
- need capacitor and resistor so it charges in between ac going to peak and discharged when it goes to other peak
- resistor so it discharges SLOWLY
What are the ripples when smoothing out
Rippled are like the minimum voltsge it goes to when discharge, as it doesn’t discharge to max
So how to REDUCE RIPPLE
Think CAREFULLY
2) what value should your time cinstsnt be roughly to make it nice and smooth
look, you want the discharge to be AS SLOW AS POSSIBLE, so it barely loses any voltsge and it becomes almost direct and constant
THEREFORE , need the time constsnt to be as big as POSSIBLE
If make it bigger then time period then hopefully the ac smooths at Nicole’s
