Unit 4.1 - Capacitance Flashcards
Capacitor
Any two conductors that are separated by an insulator
What happens when a capacitor is connected to a battery?
A small current flows for an instant as the emf of the battery “pumps” electrons around the circuit
What do the electrons do when a capacitor is connected to a battery?
The flow of electrons collect on the negative plate and leave the other plate positive
What is the total charge on a capacitor and why?
Zero
The capacitor carries an equal but opposite charge
Where are electrons drawn to and where are electrons repelled from?
Drawn to: the end to the positive terminal
Repelled by:the emf from the negative terminal
What is the total charge on a capacitor and why?
Since the total negative charge on one end is equal to the positive charge on the other end
What is the potential difference equal to when the capacitor is only just connected to the battery?
Equal to the battery charge
What do we say capacitors have on them when we discuss them?
Charge Q
Charge on a capacitor at a higher potential
Charge +Q
Charge of a capacitor at a lower potential
Charge -Q
What do we mean when we talk about the charge on a capacitor?
The separated charge
Describe the charge is if 1C of charge has been pulled from positive to negative on a capacitor?
The total charge isn’t 2C, it’s just 1C that’s been separated
What could a capacitor be considered to be?
A deceive for storing charge
How could the capacitance of a capacitor be considered metaphorically?
Capacitor - a bucket storing water
Capacitance - the volume of the bucket
Capacitance
The ability of a component or circuit to collect and store energy in the form of electrical charge
How can a capacitor be constructed simply?
From two metal plates separated by air
What is needed to pump electrons from the positive plate to the negative plate in a capacitor and why?
A large emf
It isn’t easy to remove a charge from one plate to another
What do electrical charges do to each other and what is this according to?
According to electrostatic theory, electrical charges either attract or repel each other
What does the work done when something is charged depend on?
1.) whether the charges attract or repel
2.) the size of the charge
3.) the electrical properties and dimensions of the charged object
What is used as a measure of the energy required for work to be done when something is charged?
The electrical potential
Electrical potential
An object has a potential of 1V if 1J of work is done to bring 1 coulomb of positive charge from infinity to that object
Work done is the electrical potential is positive
More than 0
Work done if the electrical potential is negative
Less than zero
What is the effect of putting charge Q on an insulated object?
Raises its potential to V
What is V proportional to?
Charge
Equation linking charge and voltage
Q = CV
C in Q = CV
Capacitance
Unit of capacitance
The farad
How is the farad unit used more often than not?
Micro farad, nano farad or pico farad
What would a 1F capacitor be described as?
A super capacitor
Definition of a farad
If the result of placing 1 coulomb of charge on an object is to raise its’ potential by 1 volt, then the object is said to have a capacitance of 1 farad
What is the farad?
Unit of capacitance
Factors that affect capacitance
1.) the distance between the plates
2.) the surface area of the plates
Describe two different experiments that can be done to investigate the factors that affect capacitance
(For both)
Two parallel plates are placed a few cm apart. One plate each is connected to the positive and negative terminals
Then…
Distance between the plates is varied
Overlapping area of the plates is varied
Relationship between capacitance and the distance between the plates
Inversely proportional
What is capacitance inversely proportional?
The distance between the plates
Why is capacitance inversely proportional to the distance between the plates?
Distance increases = work done on system
Pd increases to become more than the battery
Q = CV, so capacitance decreases
What is capacitance directly proportional to?
The overlapping area of the plates
Relationship between capacitance and the overlapping area of the plates?
Directly proportional
Relationship obtained if combining both the experiments that vary the overlapping area of the plates of a capacitor and the distance between the plates
C ∝ A/d
How can we adapt the proportionality of C ∝ A/d to get an equation?
If air fills the gap between the plates, we can use the permittivity of free space (εo) to get the equation
C = εoA/d
Permittivity of free space symbol
εo
εo meaning
Permittivity of free space
General equation for a parallel plate capacitor and meaning of the symbols
C = εoA/d
C = capacitance
εo = permittivity of free space
A = area of overlap
d = separation of the plates
Why is εo used?
So that we get an equation rather than a proportionality. It’s a constant from the data book
How would the general equation for a parallel plate capacitor change?
If a dielectric were to be introduced
What would introducing a dielectric do?
Change the equation for a parallel plate capacitor
Dielectric
A material that doesn’t allow a current to flow
Under what situation is the general equation for a parallel plate capacitor unchanged?
If an air filled parallel plate capacitor, since the difference between air and a vacuum is negligible
Difference between air and vacuum as an insulator in a capacitor?
Negligible
What happens to the general equation for a parallel plate capacitor when a dielectric is introduced?
It’s changed by a factor of εr
Equation changes to…
C = εrεoA/d
εr
Relative conductivity - a property of the material
Relative conductivity symbol
εr
What does a dielectric do to the capacitance of a vacuum-spaced capacitor?
Increases it
Apart from the distance between the plates and the surface area of the plates, what does the general equation for a parallel plate capacitor show us that a capacitor is dependent on?
The permittivity of the material between the plates
Why is εo used for air in the general equation for a parallel plate capacitor?
The permittivity of the material (air) is virtually the same as a vacuum, and so using the permittivity of free space (εo) is sufficient
How could the capacitance of a material be increased?
By the introduction of a dielectric between the plates
How can we explain why the introduction of a dielectric increases the capacitance of a capacitor?
By thinking on a molecular level
Describe non-polar molecules
The centres of positive and negative charge coincide under normal conditions
What are the majority of molecules?
Non-polar molecules
Where is a dielectric placed when placed between the plates of a charged capacitor?
Inside an electric field
What happens within each molecule in the material when a dielectric is placed inside a capacitor (an electric field)?
The positive nuclei are pushed in one direction and the negative electrons are pushed in the opposite direction
What can’t electrons do in an electric field?
Drift
What happens as a result of positive nuclei being pushed in one direction and negative electrons being pushed in the opposite direction when a dielectric is placed in a capacitor?
The molecules become polarised and induced dipoles are formed
In which direction to electrons move compared to the direction of electrical fields?
The opposite direction
What do the dipoles formed in the molecules of a dielectric material placed in a capacitor do in the bulk of the dielectric?
Cancel out between neighbouring molecules
What happens when induced dipoles are formed in the molecules of a dielectric in a capacitor?
Has an effect on the surfaces facing the plates - there is a row of identical charges
Effect of the row of δ- in the molecules of a dielectric in a capacitor by the positive plate
Reduced the potential on that plate
Effect of the row of δ+ in the molecules of a dielectric in a capacitor by the negative plate
Reduced the potential on that plate
As the potential at each of the plates of a capacitor decreases with a dielectric, what happens to the potential difference across the plates?
Has reduced
What does it mean if the potential difference across the plates of a capacitor has decreased?
More electrons are moved from 1 plate and pumped to the other
When the potential difference across the 2 plates of a capacitor has decreased with a dielectric, what is this potential difference less than?
The potential difference across the supply
What needs to be done when the potential difference across the plates of a capacitor is less than the potential difference across the supply?
More charge needs to be placed onto the capacitor in order to balance the supply
What is the net effect of needing to place more charge onto the capacitor to balance the supply when the potential difference across the plates of the capacitor is less than the potential difference across the supply?
The capacitor stores more charge = increased capacitance
What does it mean if a capacitor has increased capacitance?
Stores more charge
Name for the factor by which the capacity of a capacitor is increased with a dielectric
The relative permittivity of the material or the dielectric constant
εr equation
Capacitance of capacitor with vacuum between plates / capacitance of capacitor with the dielectric in place
How is the capacitance equation adjusted when a dielectric increases the capacity by a factor of the relative permittivity of the material?
C = εrεoA/d
Polar molecules
Molecules that are polarised with the presence of an electric field
What type of molecules are more effective materials as dielectrics?
More polarised molecules
What are more polarised molecules more effective as?
More effective materials as dielectrics
What type of dielectric materials increase the capacitance of a capacitor the most? Why?
Materials that contain polarised molecules (more than non-polar materials)
The molecules physically line up in the field
Where does the energy required for polarised molecules to line up in the field come from? What does this mean for the capacitor?
The charging supply
The capacitor stores more charge
Why are dielectrics containing polarised molecules more effective at increasing the capacitance of a capacitor?
Polarised molecules physically line up in the field
The energy required for them to do this comes from the charging supply, and therefore the capacitor stores more charge
What material would make an excellent dielectric to increase the capacitance of a capacitor and why?
H2O (a polar molecule with εr of about 80) in its pure form
Highly polarised molecules
Advantages of a dielectric
1.) it increases the capacitance
2.) it acts as a “spacer” so the plates can be placed very close together
3.) it prevents sparking between the plates
Why does there exist a force field in a capacitor?
Since there is a force between the two plates (electromagnetic attraction)
What is a force field within a capacitor caused by?
The electromagnetic attraction between the two plates
How should we imagine the force field within a capacitor?
As a gravitational force field, where objects not in contact still exert a force on each other
Describe the force field on a capacitor
Uniform in all directions
What does the value of the electric field of a capacitor depend upon?
The potential difference and the separation between them
Equation to work out the electric field strength of a capacitor + define the symbols
E = V/d
E = electric field strength (Vm-1)
V = p.d between the plates
d = separation of the plates
What is the argument for the energy stored in a capacitor very similar to the argument for?
The energy stored in a stretched spring
What is there for a capacitor with capacitance C and charge Q on its plates?
A potential difference V between the plates (Q=CV)
If a small charge of ΔQ is moves across the plates of a capacitor, how does this affect the potential difference V?
Can approximate that it has no effect
Work done in moving a small charge of ΔQ + explanation
VΔQ
From the definition of the volt - energy per unit charge
Definition of the volt
Energy per unit charge
What does the voltage across the plates of a capacitor vary in direction proportional to with?
The charge Q on the capacitor
What happens for every extra charge ΔQ moved from plate to plate on a capacitor?
The area increases under the graph of V against Q
The work done therefore increases
How can we tell that the work done on a capacitor increases with a graph of voltage against charge?
Area under the graph increases
Total work done by a capacitor
∑VΔQ
What is work done, ∑VΔQ, equivalent to?
The area under a graph of voltage against charge
What does the area of a graph of voltage against charge give us?
Work done
The area under what type of graph gives us the work done by a capacitor?
Voltage against charge
How do we know that the area under a voltage against charge is equal to the work done by capacitor?
By looking at the units
V —> JC-1
Q —> C
So area underneath —> J
Unit of electrical work done
J
Equation for the electrical energy stored in a capacitor
U = 1/2QV
Useful equation to learn for the electrical energy stored in a capacitor + its derivation
U = 1/2QV
Q = CV
U = 1/2(CV)V
U = 1/2CV^2
What is the electrical energy stored in a capacitor equivalent to?
The electrical work done
What is the electrical work done by a capacitor equivalent to?
The electrical energy stored in a capacitor
Why can we always find a single capacitor with capacitance C?
It will be the direct equivalent of any combination of capacitors
What is the same for all capacitors in series?
The same charge on their plates
Why do capacitors in series all have the same charge on their plates?
The negative charge from the positive plate of C2 is placed on the negative plate of C1
Describe and explain the potential differences across the plates of capacitors in series
Since Q = CV and they all have the same charge on their plates, this means that that they will not have the same potential difference across their plates if their capacitances are different
Describe the total capacitance of a combination of capacitors in series
Always smaller than the smallest individual capacitance present
Describe the potential difference across the plates of capacitors in parallel
All have the same potential difference across their plates
Describe and explain the charges on the plates of capacitors in parallel
Capacitors in parallel all have the same potential difference across their plates
Since Q = CV, this means that they will not have the same charge not heir plates if their capacitances are different
Derive the equation for the total capacitance of capacitors in series
V = Q/V
Therefore Vtotal = Q/Ctotal, V1 = Q/C1, V2 = Q/C2 and V3 = Q/C3
So
Q = Ctotal + Q/C1 + Q/C2 + Q/C3
Dividing throughout by Q
1/Ctotal = 1/C1 + 1/C2 + 1/C3
Derive the equation for the total capacitance of capacitors in parallel
Qtotal = Q1 + Q2 + Q3
Since Q = CV
Q1 = C1V, Q2 = C2V, Q3 = C3V
therefore CtotalV = C1V + C2V + C3
Dividing through by V
Ctotal = C1 + C2 + C3
Describe the total capacitance of a combination of capacitors in parallel
Always larger than the largest individual capacitance present
Equation for capacitors in series
Ctotal + (1/C1 + 1/C2 + 1/C3)^-1
Equation for capacitors in parallel
Ctotal + C1 + C2 + C3
For what arrangement of capacitors do we just add up the value of each capacitor to get the total capacitance?
Capacitors in parallel
Working out total capacitance compared to working with resistors in unit 2
Complete opposite way around with the equations in series and parallel
What can’t a voltage do when it’s placed across capacitor terminals?
Can’t raise the potential instantly to the final value
Why can’t a voltage raise the potential instantly to the final value when placed across capacitor terminals?
As the charge builds on the plates, it tends to repel any addition of charge
What does the rate at which a capacitor can charge depend on?
1.) the capacitance of the capacitor
2.) the resistance of the circuit it is being charged (or discharged) through
What does the fact that the rate at which a capacitor can charge is dependent on the capacitance of the capacitor and the resistance of the circuit it is being charged or discharged through make a useful feature for?
Building timing circuits and clocks in computers
What is the emf supplied by when we discharge a capacitor through a circuit?
Supplied by the capacitor
Where does the current come from when a capacitor is discharging?
The capacitor
What is formed when a capacitor is discharging?
A current
Derive I = Q/RC and explain what this equation is for
V = IR and so I= V/R
Q = CV so V = Q/C
Substituting for V gives I = Q/RC
this is the equation for the current in the circuit
What is the current in a circuit where the capacitor is discharging equal to?
The rate of discharge of a capacitor
Write an equation that shows that the current in a circuit is equal to the rate of discharge of the capacitor
-I =dQ/dt
How do we discharge a capacitor?
Short circuit it
What does the rate of discharge of a capacitor depend on?
The amount of charge present
Explain how the rate of discharge of a capacitor depends on the amount of charge present
Its exponential and when there’s a lot of charge at the start, the rate of discharge is high
What does -I = dQ/dt mean and why is the sign negative?
That the current is equal to the rate of discharge of the capacitor
The negative sign indicates that the charge is flowing our of the capacitor
What does the negative sign in -I = dQ/dt indicate?
That the charge is flowing from the capacitor
What can we integrate using calculus to obtain Q = Qoe^-t/RC?
-Q/RC + dQ/dt
What does integrating -Q/RC = dQ/dt using calculus do?
Gives us Q = Qoe^-t/RC
R and C in Q = Qoe^-t/RC
R = resistance
C = capacitance
Why can we write V and I in the same format as Q = Qoe^-t/RC?
Since Q is proportional to V and I is proportional to V
Compare the curve of a charging capacitor with the curve of a discharging capacitor
The same curve only inverted
How do we get Q = Qoe^-1/RC?
It’s the same curve as discharging a capacitor (which uses the other equation) only inverted
What does Qo and Vo represent?
The charge/voltage from the supply
What’s significant about the equation Q = Qoe^-1/RC and its form with V?
The only equations with positive exponential growth
Why is the curve of charging a capacitor the same as the curve of discharging a capacitor only inverted?
Current flows in the opposite direction
Where does a capacitor charge fastest?
At the start
Where is a capacitor charging/discharging curve steepest and why?
T the start
Charges/discharges faster at the start
What type of graph would have the exact same shape for both the capacitor charging and discharging graphs with charge of capacitor against time? Why?
Since Q is proportional to Vm the graphs of pd against time would have the exact same shape for both
Describe how a graph of current from the capacitor or voltage across the capacitor would look compares to the capacitors charging and discharging graphs
If the y-axis were voltage across, or current from the capacitor, it would give the same curve shape as the capacitor discharging for both charging and discharging
Why would the graph of current of the capacitor against time be the same shape as a capacitor discharging (charge against time) graph for both charging and discharging? Explain
Because you would have the same current for both
Capacitor is empty = easier for current to flow
Capacitor is full = easier for current to flow
Describe the ease at which current flows in an empty/full capacitor
Easier to flow
When is the highest value of the current of a capacitor?
The initial current
What happens to the current of a capacitor as it empties?
Decreases as the capacitor empties
What happens to current as a capacitor empties?
Decreases
RC in equations like I = Ioe^-t/RC meaning
Time constant of the circuit
Time constant of the circuit symbol?
RC
Why is RC called the time constant of the circuit?
Since it governs the rate at which the capacitor discharges
In which direction is the force field always on a capacitor?
Always from positive to negative
What happens to the rest of the energy stored in a capacitor over time?
Becomes heat loss when heating the resistor
Equations for discharging a capacitor
V = Voe^t-RC
I = Ioe^t-RC
Q = Qoe^t-RC
Equations for charging a capacitor
Q = Qo(1-e^1/RC)
V = Vo(1-e^1/RC)
What do we do if asked to calculate a % remaining of voltage with a capacitor?
Use the usual method, but Vo is 100 and V is the % required
What do we do when using the charging equations for a capacitor and why?
Input the values of charge as they are without the corrections of the prefix to be in base units since (1-e-t/RC) is unitless and we need positive numbers so that the logs work
Gradient at the start of a charge against time graph
Initial current
Intercept of the gradient line on the x-axis on a charge against time graph
RC (time constant)
How do we work out the initial current on a charge against time graph?
Gradient at the start
What type of graph has the gradient at the start at the initial current?
Charge against time
How do we find RC (time constant) on a charge against time graph?
Intercept of the gradient line on the x-axis
What stays constant and when plates of a capacity are charges but are electrically isolated (when the power supply is disconnected from the capacitor)?
Constant charge
When are the players of a capacitor charged but electrically isolated?
When the power supply is disconnected from the capacitor
What happens to the plates of a capacitor when the power supply is disconnected from the capacitor?
The plates are charged but electrically isolated
Time constant (RC) unit
Seconds
Define capacitance
C = Q/V
Q = charge on each plate
V = pd between plates
Explain the charges on the plates of a capacitor
Same, one is positive one is negative
When do capacitors in series all have the same charge on their plates?
When joined to a common pd
Why does a capacitor store energy when a pd is applied to the plates?
Since the pd leads to charges on the plates and this set up can do work
Capacitance
Energy stored per unit potential difference
Capacitor
Two parallel metal plates separated by an insulator
What does the time constant represent for capacitors?
The time taken to become 50-75% charged/discharged (remember this if you have to draw one of those graphs)
