Capacitance Flashcards
1
Q
What is a capacitor’s use
A
to store charge/cause a current for a specific time
2
Q
What is the circuit symbol for a capacitor
A
–| |–
3
Q
Structure of capacitor
A
two parallel metal plates with a small gap between
Most capacitors consist of two strips of aluminium foil separated by a layer of dielectric, all rolled up and put into a casing making the capacitance as large as possible because the area A is as large as possible and the spacing d is as small as possible.
4
Q
What happens when a capacitor is connected to a battery in terms of electric flow
A
When a battery is connected to the plates, electrons from the negative terminal of the battery move onto the plate connected to that terminal. At the same time, electrons move from the other plate to the positive terminal of the battery leaving this plate with a positive charge. The two plates store equal and opposite amounts of charge
5
Q
For a capacitor, storing a charge of Q means
A
+Q on one plate and –Q on the other
6
Q
Uses of capacitors:
A
back up power supplies (which take over if the mains supply is interrupted), tuning circuits, touchscreen technology, camera flash
7
Q
Work done in a capacitor =
A
W=QV
8
Q
Why is the work done different to to the energy stored
A
Only half of energy transferred from battery (W = QV) is stored in capacitor.
The rest is wasted due to the resisitance in the circuit and is dissipated in the surroundings.
9
Q
Doubling the charge does what to the energy stored
A
doubling the charge will double the voltage and as energy = 0.5CV^2 the stored energy will increase by a factor of 4
10
Q
Describe the energy stored in a thundercloud
A
ground and cloud act like parallel plates d apart, ground positive, cloud negative, strong electric field of strength, E, between the two. Pd between cloud and ground V=Ed. Energy stored = 0.5QV = 0.5QED, higher clouds have more energy since work is done by the force of the wind overcoming the attraction between cloud and ground
11
Q
How can you make the rate of charge/discharge slower
A
use a resistor
12
Q
RC is the time constant (units = s) and occurs when
A
any of the quantities Q, V or I falls to 0.37 = 1/e of its initial value
13
Q
Take taken for the initial value of V, Q or I to halve =
A
0.69RC
14
Q
If the gap between the two parallel plates of a capacitor is filled with a dielectric, then
A
the capacitor can store more charge and has a higher capacitance
15
Q
A dielectric is
A
Dielectrics are electrically insulating materials that increase the ability of a parallel-plate capacitor to store charge when it is placed between the plates of the capacitor e.g. Polythene
16
Q
Give examples of dielectrics
A
polythene and waxed paper
17
Q
What happens to each molecule in a dielectric
A
they become polarised
18
Q
What happens to the electrons of the molecule in a capacitor
A
pulled towards positive plate
19
Q
Negative charge is attracted to
A
the surface of dielectric facing the positive plate
20
Q
Why is the surface of the dielectric left positively charged
A
The surface of the dielectric facing the negative plate loses negative charge and some positive charge is left on its surface
21
Q
The relative permittivity, or dielectric constant of the dielectric, epsilon r =
A
The charge stored with dielectric, Q / The charge stored without dielectric, Q0 = Q/Q0 =C/C0
Relative permitivity = charge stored by a parallel-plate capacitor when the space between the plates of the capacitor is completely filled with the dielectric substance, and Q0 = charge stored at the same pd when the space is completely empty. C, C0 also works.
22
Q
For a parallel plate capacitor with dielectric filling the space between the plates, its capacitance C
A
e0 * er * A / d
d=plate spacing
A=surface area of plate/common area of the plates
er = dielectric constant
e0 = 8.85x10^-12 (F/m)
23
Q
For large capacitance, what is needed:
A
Large A
Small d
Dielectric with large εᵣ
24
Q
What are polar molecules
A
Molecules in a dielectric substance that are already polarised, but lie in random directions
25
When polar molecules are placed between the two charged plates, what happens and what does this cause
These molecules turn when the dielectric is placed between the charged plates because their electrons are attracted slightly to the positive plate. The surface of the dielectric near the positive plate gains negative charge, and the other surface gains positive charge
As a result, more charge is stored on the plates because the positive side of the dielectric attracts more electrons from the battery onto the negative plate and the negative side of the dielectric pushes electrons back to the battery from the postitive plate
26
In an alternating electric field, at low frequencies, the polarisation is...
bur as the frequency increases, polarisation... because of
In an alternating electric field, at low frequencies, the polarisation is in phase with the field, but as the frequency increases, polarisation ceases to work due to the inertia of the particles involved and the resistive forces that oppose the motion of the dipoles.
27
Give an example of a use of capacitor discharge through a fixed resistor
any electronic timing circuit or time-delay circuit
28
What do dielectrics do
increase the charge stored in a capacitor for any given pd across the capacitor terminals i.e. its effect is to increase the capacitance of the capacitor
29
For a parallel plate capacitor with dielectric filling the space between the plates how is a large capacitance achieved
making the area A as large as possible, making the plate spacing d as small as possible, filling the space between the plates with a dielectric which has a relative permittivity as large as possible.
30
Charge discharge circuit
Capacitor centre with two way switch to the left
Battery above with voltmeter
Bulb with joulemeter below
Switch towards battery for charge, switch towards bulb for discharge through resistor?
Resistor is used to slow charge/discharge down but must be put in right place for each different type
Energy is released from the capacitor as shown in the above diagram.
The capacitor is charged by the battery.
It is then discharged through the bulb.
This energy can be measured using a joulemeter across the bulb
31
A couple consists of
two conductors insulated from each other
32
Graph of charge against voltage is
Q=CV
y=mx
straight line
33
When a capacitor is charged, how is energy stored
energy is stored in it because electrons are forced onto of its plates and taken for the other plate. The energy is stored in the capacitor as electrical potential energy
34
Energy stored in a capacitor =
0.5QV = 0.5CV^2 = 0.5Q^2/C = area under charge against pd graph
35
A joulemeter is used to
measure the energy transfer from a charged capacitor when the capacitor discharged. Measured before and after and the difference is the energy transferred from the capacitor during the discharge process.
36
Milli m
Micro mu
Nano n
Pico p
Milli 10^-3
Micro 10^-6
Nano 10^-9
Pico 10^-12
37
Why cannot a steady dc current pass through a capacitor
Because the dielectric is an insulator
38
Capacitance unit =
Farad (F)
39
Relative permittivity, er is usually between
2 and 10 but is 1 for air/vacuum
40
Capacitors in parallel and series
Parallel: Ct = C1 + C2
Series: 1/Ct = 1/C1 + 1/C2
41
The time for Q, V and I to fall to half their original values is given by
RC*ln2
42
Between the plates of the capacitor...
no charge flows
43
Charge –Q flows onto the plate connected to the negative terminal of the supply and
flows off the place connected to the positive terminal of the supply, leaving it with charge +Q
44
Why is the total charge of a capacitor actually zero, and why is there energy
As the capacitor plates have equal amounts of charge of the opposite sign, the total charge is actually zero. However because the charges are separated they have energy and can do work when they are brought together
45
The amount of energy stored in a capacitor depends on its
the amount of charge on the capacitor plates. The voltage required to place this charge on the capacitor plates, i.e. the capacitance of the capacitor.
46
The time constant represents
time it takes for the charge on a capacitor to fall to 1/e of its initial value when a capacitor is discharging. The time it takes for the charge on a capacitor to rise to 1-1/e of its final value when the capacitor is charging
47
Give two reasons why a capacitor is not a suitable source for powering a cordless telephone
capacitor would be impossibly large (to fit in phone), capacitor would need recharging very frequently, capacitor voltage would fall continuously while in use
48
Charging capacitor, what happens from t=0 until fully charged in terms of electron flow
net electron flow is round the circuit from right hand side of capacitor clockwise to left hand side. Rate of electron flow or current decreases as time increases (repulsion from electrons already on left hand side makes flow decrease), current ceases when pd across the capacitor = emf, current decreases exponentially
49
Charging capacitor, what happens from t=0 until fully charged in terms of potential differences across the capacitor and resistor
pd across capacitor increase, pd across resistor decreases, sum of pd of resistor and capacitance = emf, capacitance increases exponentially with time to the emf, resistor voltage decreases exponentially with time to 0V
50
Conducting sphere in a capacitor with P1 the positive plate, p2 the negative plate why does the sphere shuttle between the two plates
sphere gains electrons (or is charged –ve) at p2 and is repelled by p2 (or attracted by p1 or experiences correct force in field), sphere loses electrons at (or negative charge) P1, explanation of return of sphere from p1 to p2, sphere reaches same potential as plate on contact
51
Gradient of Q against t curve =
Current as Q/t = I
52
Discharging capacitor graphs against time for
Current
Voltage
Charge
All exponential with decreasing gradients from y axis tending towards zero cutting the y axis at maximum value
53
Charging capacitor graphs against time for
Current
Voltage
Charge
Current is same as discharging, decreasing gradient from y axis tending to zero
Voltage and charge is inverted, starts from zero and asymptope at supply charge/voltage
time constant occurs when V rises to 0.63 of its initial value
54
Explain the shape of the current time graph
As capacitor is charged there is more charge so Q increases. It is then harder to find places to store charge so electrons do not flow as fast. So current equals charge flowing per second decreases and the amount of rate that charge is added to the capacitor decreases
55
Charging equations
```
V = Vₒ(1-e^-t/RC)
Q = Qₒ(1-e^-t/RC)
I = Iₒ(e^-t/RC)
```
56
Discharging equations
```
V = Vₒ(e^-t/RC)
Q = Qₒ(e^-t/RC)
I = Iₒ(e^-t/RC)
```
57
Charging capacitor energy/time exponential
-1/x
58
When t=RC the charge falls to
37% of its initial value or 63% of its final value
59
The time taken to discharge by over 99% is equal to
t=5RC
60
Equipment for charging a capacitor at constant current
Ammeter, switch, high resistance voltmeter, variable resistor (to keep current constant)
61
Capacitor discharge equipment
voltmeter, resistor, switch, capacitor
62
Define capacitance
Capacitance = charge stored per unit potential difference = ratio of the magnitude of the charge on one plate to the potential difference across the capacitor = Q/V
63
What is the role of a capacitor
to store energy/charge and release it/cause a current when needed
64
What is an advantage to the capacitor over batteries
they charge much better
65
What is the composition of capacitors
two metal plates separated from each other by an insulating, dielectric material. A wire from each plate connects the capacitor to the circuit
66
Why are the two metal plates in a capacitor separated by a dielectric material
so electrons do not flow between them
67
What is meant by permittivity
How hard it is for an electron to pass through it
68
What reduces the strength of an electric field and what does this mean
Materials reduce the strength of the electric field meaning more charge can be stored
69
What happens when another material is put in between the plates of a capacitor
the capacitance charges. Since the dipole field in the dielectric tends to partially cancel the capacitors field, the net field is reduced.
70
When a charge of Q coulombs is transferred to the capacitor, it means that
one capacitor plate will have a charge of +Q coulombs while the other plate has charge –Q coulombs. The charge stored by the capacitor is Q coulombs
71
Dielectric action in the capacitor, or capacitance, is equal to Ae0er/d where d is the perpendicular diameter, er is the dielectric constant =
permittivity of the dielectric material in between the plates, e0 is permittivity of free space and A is the area of the smallest capacitor
72
Why does the voltage across a capacitor decrease with time
Electrons slow down due to repulsion so the rate of flow decreases therefore the voltage across the capacitor decreases with time
73
What way do electrons flow around a capacitor
positive terminal to negative terminal
74
Explain the Voltage time graph for a charging capacitor
asymptope at batteries voltage
75
Define the volt
energy per unit charge so 1V = 1J/C
76
When a capacitor is fully charged the pd =
Vs
77
When a capacitor begins to charge the pd across the plates is
zero
78
Derivation of 0.5QV = E
Q on x axis, E=QV, area under graph = total energy = 0.5Qv
79
The rate at which electrons leave the capacitor is dependent on
how many electrons on the capacitor
80
At which point during the discharging process is the capacitor losing charge
at them smallest rate: when the pd across R is least
81
Explain why there is an increase in the energy stored by the capacitor when er is reduced
Energy increases because in the polar dielectric molecules align in the field with positive charged end toward the negative plate and so work is done on the capacitor separating the positively charged surface of the dielectric from the negatively charged plate (or vice versa)
82
Charging circuit equipment
battery, switch, capacitor, voltmeter, resistor, rectangle with battery on the left, switch at top, capacitor on right, resistor on bottom and voltmeter in parallel to capacitor.
83
Discharging circuit
resistor moved in between the capacitor and voltmeter
84
Explain the charging capacitor circuit
As soon as the switch is closed towards the battery, the battery is connected across the capacitor, current flows, and the potential difference across the capacitor begins to rise but, as more and more charge builds up on the capacitor plates, the p.d. across the capacitor equals that of the supply voltage. The capacitor is then fully charged.
85
Charge discharge circuit how they are changed to each other
battery on the left, capacitor in the middle, resistor on the right. For charging: switch above capacitor towards the battery to the left while for discharging the switch is towards the resistor to the right
86
Explain the discharging capacitor circuit
As soon as the switch is put to the resistors side, a large current starts to flow and the potential difference across the capacitor drops. As charge flows from one plate to the other through the resistor the charge is neutralized and so the current falls and the rate of decrease of potential difference also falls. Eventually the charge on the plates is zero and the current and potential difference are also zero – the capacitor is fully discharged. Note that the value of the resistor does not affect the final potential difference across the capacitor – only the time it takes to reach this value. The bigger the resistor, the longer the time taken
87
VIQ /t graphs asymptopes and axes
Current - zero
Charge - discharging = 0, charging = Qs
Voltage - discharging = 0, charging = Vs
VQ charging cuts at zero
IVQ charging cut at IVQmax
88
Explain the shape of the current time graph for a capacitor
When a capacitor discharges through a fixed resistor, the discharge current decreases gradually to zero. The pd across the capacitor decreases as it loses charge so the current decreases gradually. Because the resistors connected directly to the capacitor, the resistor current decreases as the pd decreases
89
Quantity decreases by the same factor in equal intervals of time e.g. if the charge is Q0 after t seconds then it is ... after nt seconds
x^nQ0
90
In an alternating electric field what happens to dipoles
the polar dipoles rotate and the non-polar dipoles oscillate one way then the opposite way as the field strength increases and decreases
91
At low frequencies what happens to dipoles in an alternating electric field
At low frequencies, the three polarisation mechanics alternate in phase with the field at low frequency. However, as the frequency increases, each mechanism ceases to work due to the inertia of the particles involved and the resistive forces that oppose the motion of the dipoles.
92
The mass of the particles being moved by the field determines
which mechanism ceases first as the frequency increases.
93
The greater the mass of each particle
the greater its inertia is, and so the frequency at which ceases first as the frequency increases, then ionic polarisation, then electronic polarisation
94
When a dielectric is placed between two oppositively charged parallel plates connected to a battery what happens and what is its implication
each molecule of the dielectric becomes polarised. This means that its electrons are pulled slightly towards the positive plate so the surface of the dielectric facing the positive plate gains negative charge at the expense of the other side of the dielectric that faces the negative plate. The other surface of the dielectric loses negative charge so some positive charge is left on the surface
95
What is the voltage in the circuit at any instant
| What is the initial current
instant during the charging process, the source pd V0 = the resistor pd + the capacitor
Hence V0 = IR + Q/C at any instant.
The initial current I0 =V0/R assuming the capacitor is initially uncharged
96
Explain why the vt curve for a charging capacitor is shaped like that
* When a capacitor is charged by connecting it to a source of constant pd, the charging current decreases as the capacitor charge and pd increases.
* When the capacitor is fully charged, its pd is equal to the source pd and the current is zero as no more charge flows in the circuit.
* The capacitor charge builds up until the capacitor pd V is equal to the source pd V0.
97
The current at any stage is equal to
the rate of change of charge
| Therefore the current is given by the gradient of the charge-time graph and so it decreases exponentially.
98
Explain the shape of a charge time graph for a charging capacitor
In a DC circuit a capacitor functions by the removal of some electrons on one plate and the addition of electrons on the other plate. The electrons are moved through the wire attached to the plates, and this is driven by a battery or a DC power supply. As more and more electrons are moved, it becomes harder and harder to move more, and the maximum charge that can be placed on each plate is approached over time. Once "charged" in this way, a capacitor stores energy in the electric field between the plates, and this energy can later be used in many different ways as the capacitor is discharged.
99
Why does a capacitor allow AC current but not DC current
Direct current can't jump the gap between plates, because it would take a massive amount of voltage to force the electron to jump the gap between plates. The electrons hit the plate and stop.
Alternating current, on the other hand, is moving the electrons back and forth in place -- so the plate on one side of the capacitor is constantly having electrons pushed in and then pulled back out. This motion creates a small electric field which induces the same alternating current in the other plate, because electric fields can jump the gap between plates.
100
Permitivity of free space
8.85*10^-12 F/m
