Chapter 21 CAPACITANCE

Question 1

What is a capacitor made out of

Answer 1

Two metal plates, with some sort of insulation between the, known as a dielectric

Question 2

What does a capacitor basicallt do

Answer 2

There separate electrical charge and store it on both plates

Question 3

How does it work
How and when is it fully charged basicslly

Answer 3

First a potential difference externally drives a current which transfers electrons to one end of the plate .

Then by induction, as they can’t go through, the build up of electrons creates a charge which then repels electrons on the other plate, causing it to become positively charged, and this electrons move around the circuit.

As charge is conserved these plates both have a -Q and +Q charge. As a result there is a POTENTIAL DIFFERENCE BETWEEN THEM TOO

This causes current to start going the other way, opposing the direction current INITALLy went .

The current falls to 0 in the circuit when the same current going in = the current pushing against by capacitor. This must thus occur only if they have the SAME potential difference. As a result, the capacitor is now MAXIMUM and fully charged, and has the same potential difference as the thing that charged it

Here pd across capacitors = emf across cells!

Question 4

Equation for capacitance

Answer 4

Is defined as the amount of charge / voltage across it

C =Q/V

The more charge , thr more voltage, = they are proprtinsl, and this works out!)

Question 5

Rules for capacitance SERIES AND PARALLEL

Answer 5

In series = parallel rule for electricity (just like spring )

In parallel = series rule for electricity (like spring)

Question 6

Why is series cappator like parallel and parallel like series?

Answer 6

In series, the charge stored by each cappator is the SAME (even if they have different capacitance), but voltage is split

I’m parallel the total charge is sum of indicual charges stored by cappator , but the voltage the same

(Thin about it, in series, same attraction and repulsion like a chain effect, in parallel the charge is i Dukakis and free to do what it wants)

Question 7

What IMPORTSNT thing to re,e,bed about series capacitance charge!

how to prove in a circuit?

Answer 7

No matter what, it’s always the same, the furthers two plates will get equal and opposite charge, and then middle plates too by induction

Can prove this by putting two known cappatiacnes in , voltmeteres around them and safer rejector and read the voltmeteres. Now yiu can Calculate the charge, and should find it’s THE SAME!

Question 8

If you disconnect cappator circuit once charged and connect to lightbulb, it will flash, showing energy stored in cappator

But where does this energy come from?

Answer 8

An electron going ti negative plate would naturally by repelled by already negative charge, but it still goes because of EXTERNAL WORK from power source basically. Work done to the charge !

Similarly electron leaving positive would be attatratced to it, but external work is done to push it away

Basicslly thr energy stored by these charged on cappator originally came from battery itself!

Question 9

How ti derrive 3 equations for energy stored by charge in capacitor?

Answer 9

Well if v = J/C, J= VC
- so for area of VC graph = energy
- this triangle, so energy stored = 1/2QV
And subbing in c =Q/V get two more equations

W= 1/2Cv2
W= 1/2Q2/c

Question 10

3 energy equations (basically if you have Q,CV yiu can

Answer 10

W = 1/2 QV

W = 1/2 CV2

W = 1/2 Q2/C

Question 11

What happens as a capacitor is discharged through a resistor and how ti set this up

Answer 11

Basically charge the capacitor through external voltage source, same voltage will be given to resistor

Now when you remove the switch, the cappator will discharge into the resistor.
The more charge that leaves, the lower the pd, and thus lower the current.

Eventually once fully discharged, the current, voltage and charge will be 0

This happens in exponential decay

Question 12

What is exponential decay again

Answer 12

Where for every equal time interval the ratio of decrease is constsnt

This is evident when the change in one property is dependent on the amount of property you had before

Question 13

Voltsge , current, charge are all exponentially decay

What equations and what does growth look like

Answer 13

Graph = e ^-x, where y intercept is INITAL priority

V = V0 e^-t/RC
I = I0 e^-t/RC
Q = Q0 e^-t/RC

Question 14

What does RC represent

So what if you want voltsge to discharge quicker? What we need to do for RC

Answer 14

The time constsnt, which is the time taken for the property to decrease to 37% of orig al value (sub in RC )

Thus if you want something to decay quicker, you want RC to be less

Question 15

How to find INITAL current voltsge and captains g

Answer 15

Current = V/R, so V0/R

Capacitance = Q/V, Q0= Cx V0

Question 16

How to deal with v = v0 e ^-t/RC for graphs

Answer 16

Ln both sides, we know we can only measure voltsge change with time, and can find gradients and intercepts

Question 17

Bruv to find the time constsnt if all you have is R AND C?😂

Answer 17

Just multiply them lol

Question 18

We learned what happened when capacitors is DISCHARGING to a resistor, but what about when it’s CHARGING through a resistor (circuit with resistor sietch and capptor)

Answer 18

-When turn switch in, INITALLy current is MAX
- all the voltage available by 2nd law is used by component that can. So the resistor gets all the VOLTAGE

-however as time continues, the cappator is getting charges similar to before, generating , creating its own pd and current. As a result the PD IF CAPPATOR IS INCREASING , while the CURRENT IN CIRCUIT DECREASES

• currents is gonna decrease exponentially fine .
• as the resistance in resistor fixed that means the voltage will also decrease exponentially of the resistor and that’s fine
• by 2nd law, the total voltage v0 in the circuit is the duke of VR and VC. So as VR decreases VC increases

As total charge in circuit is given by Q0 = QR + Qc, as Q c is increasing QR gonna decrease (as current decreases there too!)

Question 19

As a result whats all equations for when a cappator is charging through a resistor IMPORTSNT

Answer 19

-Current = exponentially decrease = I = I0 e ^-t/RC
-if current here exp decreases, voltage in resistor exp decrease = V = V0 e^-t/RC

BY 2ND LAW, V0= VR + VC. THUS VC = V0-VR = V0- V0e^-t/RC
= v0 (1-e^-t/RC)

And similar for charge, as the charge in resistor decreases and charge in cappator increases

Question 20

So what’s difference between capptor charging vs discharging

Answer 20

Discharge= voltage, current and charge all exp decrease

Charge = current exp decreases, and voltage at resistor exp decreases
- but voltage at cappator exp increase, and charge exp increase too

Question 21

What do the graphs look like for exp increase

Answer 21

When time is the lowest, the decrease is largest, and so when time increase, decreases levels off

Thus starting at 0, it increases at a decreasing rate , and levels off at max V/Q

Question 22

How else can you find charge after time without using charge equation

Answer 22

As callatiance constsnt, you can find voltage using voltage equation and then Q=CV

Question 23

When charging capacitor, what does the time constsnt equal now in terms of percentage
So if you want a faster charge?

Answer 23

The time taken to charge the cappator to 63% of its max charge / voltage

So if you want quicker charge, make the time constsnt bigger !

Question 24

Remember when drawing graph questions with two capacitors and voltage change, what to make sure!!!

Answer 24

By 2nd law these must add up to make total V , so make sure one is the subtraction of the other by total v

Question 25

Why did both of those capacitors get the same voltage

Answer 25

Well as in series, the charge now must be the same remember, so it will split evenly, and as they had same dwpstiwcne, it will have same voltage at the end

The first capptor discharged to 5, and the second charged ti 5, Kirchhoff satisfied, the graphs are add up to 10!

Question 26

Why is girl equipment good for experiment?

Answer 26

Because look at the time taken for the decreases to be less than the resolution. If you can get like 10 readings before this happens that’s okay cuz you’ll have enough to plot graph

Now look if you can actually measure the ,Adium current, by finding it, if you can then that’s good too

And now say how the resolution fi time pretty good

Overal, it was adequate

Question 27

Two uses of capacitor

Answer 27

1) sources of high power output (release small energy but in very small time = high power)
2) smooth ac voltsge to dc

Question 28

Why cappator produce high power outputs

Answer 28

Can’t store a lot of energy but will discharge very quickly, so high power

Here this js seen in camera flashes for example,

Question 29

How does ac voltage become smoothed into almost dc

Answer 29

Household appliances need dc

A circuit containing a DIODE, resistor and capacitor can smooth out the ac voltage which goes form positive to negative

• here the diode removes the negative voltage
• the cappator smooths out the output voltsge by discharging stored energy

Question 30

How can the ripples of the “dc voltage” become smaller

THINK CAREFULLY
what should time CONSTSNT be roughly for good ripple

Answer 30

If you make the time constsnt SLOWER, then dischsrge happens LONGER, so it maintains its voltsge and the voltsge added is quite high

If time CONSTSNT fast then it will go down too quick and the ripple to big

So to rescue ripple ensure time CONSTSNT ad big ss possible and preferably beijger than period of the ac so it never gets to discharge thst much !!

Question 31

IMPORTSNT to tell difference, when a cappator is changing, is thr energy charged the same as energy removed from battery?

Answer 31

No

Question 32

Charge stored by capacitor is what compared to plates

Thus how is charge cinserved

Answer 32

As it’s +Q and -Q

The net charge is 0, so charge is conserved , but in Esch plate itd Q

Basically only charge that exists is in circuitd

Question 33

When pulling and pushing capacitor what to make sure stays cinstsnt and why

What equations to be used and what happens to energy logically speaking

Answer 33

CHARGE ALWAYS CONSTANT : this because the electrons haven’t actually GONE anywhere, so charge on plates the same

If you do C = EA/D, equation, you’ll see the permitivity and area are constsnt, thus the CAPPACITANCE must change with distance

Multiply distanc by 2 = by 1/2

And if c is 1/2 but Q is cinstsnt then V must double

And if V doubles and D doubles then ELECTRIC FIELD IS CONSTSNT

2) think about energy wise, pulling apart, work is being done to separate them so potential will increase and energy too

3) all equations linked are Q=CV, C = EA/D, V=ED

Question 34

So what are the constants when pulling pushing plates

Answer 34

Charge always and electric field too

Think about if electrons moving and use 3 equations

Question 35

If the capacitor are in parallel, what must the voltsge become and why

Answer 35

Must become the same as the upper and bottom plates are of common potential, meaning the common POTENITAL DIFFENCE across both plates for each cappacitor must be the same

And in general voltsge in parallel is equal

Question 36

In an ambiguous situation how ti tell if it’s in parallel and if it’d in desired

Answer 36

If plates touch each other then it MUST BE PARALLEL,

If they don’t and only one does then it’s series

Question 37

In a case where the cappacitors are said to be in parallel and you know the voltage must be the same , how to find the COMMON voltage

Is Kirchhoff conserved?

Answer 37

Must do total charge / total cappacitance parallel setup

Not really but maybe, since the emf “reduces” to half, and the pd increases then I guess net in thr loop is 0

But it’s not to say that it MUST equal what the emf was BEFORE!