A Level Physics Revision: All of Capacitors (in under 21 minutes)
Summary
TLDRThis A-Level physics tutorial explores the fundamentals of capacitors, including their symbol, function, and the concept of capacitance. It explains how capacitors store electrical charge proportional to potential difference and introduces the formula for capacitance (C = Q/V). The tutorial covers charging and discharging processes, the role of electron flow, and how capacitors can serve as a power source. It also delves into series and parallel configurations, explaining the rules for calculating total capacitance in each case. The video further discusses the exponential nature of voltage and current changes during charging and discharging, introduces the time constant, and demonstrates how to derive it from graphs. Practical examples and calculations are provided to solidify understanding.
Takeaways
- 🔋 The symbol for a capacitor is two parallel lines, representing its function to store electrical charge.
- 🔌 Capacitors charge and discharge in a circuit, storing charge when connected to a power supply and releasing it when connected to a load like a light bulb.
- ⚡ The amount of charge a capacitor can store is proportional to the potential difference across it, with the constant of proportionality being the capacitance (C).
- ⚖️ Capacitance is defined as the amount of charge stored per unit of potential difference, measured in farads (F), where 1 F = 1 coulomb per volt.
- 🔄 When charging, electrons flow from the negative terminal of the power source to the negative plate of the capacitor, creating an equal and opposite charge on the positive plate.
- 🔌 In a parallel circuit with capacitors, the total capacitance (C_total) is the sum of individual capacitances (C1 + C2), and the voltage across all is the same.
- 🔗 In a series circuit with capacitors, the total capacitance is found using the reciprocal formula: 1/C_total = 1/C1 + 1/C2, and each capacitor experiences the same current.
- 📉 The voltage, current, and charge in a discharging capacitor decrease exponentially over time, following the formula V = V_initial * e^(-t/(CR)).
- 🕒 The time constant (τ) of a capacitor is the product of its capacitance and the resistance in the circuit, and it determines the rate of charge/discharge.
- 📈 The time constant can be determined from a graph of voltage, current, or charge over time, where the voltage drops to approximately 37% of its initial value after one time constant.
- 🔌 During charging, the voltage across a capacitor increases exponentially while the voltage across a resistor in series decreases, with the total voltage remaining constant due to Kirchhoff's second law.
Q & A
What is the symbol for a capacitor?
-The symbol for a capacitor is two parallel lines.
What is the fundamental purpose of a capacitor?
-The fundamental purpose of a capacitor is to store electrical charge.
How is the amount of charge stored on a capacitor related to the potential difference across it?
-The amount of charge stored on a capacitor is proportional to the potential difference across it.
What is the constant of proportionality between the charge and potential difference on a capacitor called?
-The constant of proportionality between the charge and potential difference on a capacitor is called capacitance, symbolized by 'C'.
What is the unit of capacitance and how is one farad defined?
-The unit of capacitance is the farad. One farad is defined as the amount of capacitance when one coulomb of charge is stored for one volt.
How can the charging of a capacitor be explained in terms of electron flow?
-During the charging of a capacitor, electrons flow from the negative terminal of the cell to the negative plate of the capacitor, causing excess electrons to gather on the negative plate and repelling electrons from the positive plate, leading to an equal and opposite charge on the plates.
How does the total capacitance change when capacitors are connected in parallel?
-When capacitors are connected in parallel, the total capacitance is the algebraic sum of the individual capacitances, expressed as C_total = C1 + C2.
What is the rule for calculating the total capacitance when capacitors are connected in series?
-For capacitors in series, the total capacitance C_total is calculated as the reciprocal of the sum of the reciprocals of the individual capacitances: 1/C_total = 1/C1 + 1/C2.
Why is the potential difference the same across all capacitors in a parallel circuit?
-In a parallel circuit, the potential difference is the same across all branches because the voltage of the source (e.g., a cell) is distributed equally across all parallel paths.
How is the charge shared in a parallel circuit with capacitors?
-In a parallel circuit, the total charge is shared among the capacitors, with the total charge Q_total being the sum of the individual charges Q1 + Q2.
What is the time constant in the context of capacitors, and how is it defined?
-The time constant, denoted by the Greek letter tau (τ), is the product of the capacitance and resistance in a circuit. It represents the time it takes for the voltage (or current) to reach approximately 37% of its final value during the charging or discharging of a capacitor.
How does the voltage across a discharging capacitor decrease over time?
-The voltage across a discharging capacitor decreases exponentially over time following the formula V = V_0 * e^(-t/(CR)), where V_0 is the initial voltage, t is the time, C is the capacitance, and R is the resistance.
What happens to the potential difference, charge, and current at time equals the time constant during capacitor discharge?
-At time equals the time constant, the potential difference, charge, and current will drop to approximately 37% of their initial values during the discharge of a capacitor.
How can the capacitance of a capacitor be determined from a discharge graph?
-The capacitance can be determined from a discharge graph by identifying the time constant from the graph, which is the time it takes for the voltage to drop to 37% of its initial value, and then dividing this time by the resistance in the circuit.
What is the relationship between the potential difference across a charging capacitor and the time since it started charging?
-The potential difference across a charging capacitor increases with time, following the formula V_C = V_0 * (1 - e^(-t/(CR))), where V_0 is the initial potential difference, t is the time, C is the capacitance, and R is the resistance.
How does the current in a series circuit change as a capacitor charges?
-As the capacitor charges in a series circuit, the current decreases exponentially over time, following the same formula as the potential difference across the resistor: I = I_0 * e^(-t/(CR)), where I_0 is the initial current.
Outlines
🔋 Introduction to Capacitors and Charging
This paragraph introduces the concept of capacitors in A-Level Physics, explaining their role in storing electrical charge. The symbol for a capacitor is depicted as two parallel lines. The paragraph details the process of charging a capacitor within a circuit, emphasizing the relationship between stored charge (q), potential difference (v), and the constant of proportionality, known as capacitance (C). The formula C = q/v is presented, along with the definition of capacitance as the charge stored per unit potential difference. The unit of capacitance, the farad, is also defined. The explanation of electron flow during charging is provided, describing how electrons move from the cell's negative terminal to the capacitor's negative plate, leading to the accumulation of charge and the development of an equal and opposite charge on the capacitor's positive plate. Additionally, the paragraph touches on the use of a capacitor as a power source in a circuit, explaining how a charged capacitor can power a light bulb and the resulting decrease in the capacitor's charge.
🔌 Adding Capacitors in Series and Parallel
This section delves into the principles of adding capacitors in both series and parallel configurations. For parallel connections, the total capacitance (C_total) is the sum of individual capacitances (C1 + C2), as demonstrated with two 300 microfarads capacitors totaling 600 microfarads. In contrast, for series connections, the total capacitance is calculated using the reciprocal formula: 1/C_total = 1/C1 + 1/C2, which is then inverted to find C_total. An example calculation for two 300 microfarads capacitors in series results in a total of 150 microfarads. The paragraph also discusses the misconceptions about capacitors in series and suggests a video in the playlist for further understanding. The rules for charging and discharging in series and parallel configurations are also highlighted, emphasizing that in parallel circuits, the voltage is the same across all components, while in series circuits, the current is the same through all components.
⚡ Understanding Capacitor Discharge and Exponential Decay
The paragraph discusses the process of discharging a capacitor through a resistor, illustrating the exponential decay of voltage over time. The voltage across the capacitor (v) is described by the formula v = v_naught * e^(-t/CR), where v_naught is the initial voltage, t is time, C is capacitance, and R is resistance. The paragraph provides an example calculation for a 500 microfarad capacitor discharging through a 500 kilo-ohm resistor, resulting in a voltage of 3.29 volts after 150 seconds. The concept of an exponential function is explained, emphasizing the constant property ratio in equal time intervals, indicating that the voltage decreases by the same factor over equal time periods. The paragraph also explains how to rearrange the exponential decay formula to solve for time (t) and introduces the concept of the time constant (τ), which is the product of capacitance and resistance and has units of time.
🕰 The Time Constant and Capacitor Charging
This section explains the significance of the time constant (τ) in the context of capacitor charging and discharging. The time constant is shown to be the time it takes for the voltage to drop to 37% of its original value, using the exponential decay formula. The paragraph demonstrates how to calculate the capacitance from a discharge graph, using the time constant and resistance values. It also discusses the charging process of a capacitor, where the voltage across the capacitor increases while the voltage across the resistor decreases exponentially. The relationship between the potential difference across the resistor (VR) and the capacitor (VC) is explained using Kirchhoff's second law, leading to the formula for the potential difference across the charging capacitor. The paragraph concludes with the formula for the current in the circuit during capacitor charging, which decreases as the capacitor charges due to the decreasing potential difference across the resistor.
🔚 Conclusion of Capacitor Concepts in A-Level Physics
The final paragraph wraps up the discussion on capacitors, summarizing the key points covered in the A-Level Physics specifications. It revisits the main topics, including the charging and discharging of capacitors, the calculation of capacitance, and the understanding of exponential decay. The paragraph encourages viewers to ask questions if they have any and thanks them for watching, indicating the end of the video script on capacitors.
Mindmap
Keywords
💡Capacitor
💡Potential Difference (voltage)
💡Capacitance
💡Electron Flow
💡Parallel Circuit
💡Series Circuit
💡Charge Sharing
💡Exponential Decay
💡Time Constant
💡Discharging
💡Charging
Highlights
Introduction to capacitors and their symbol representation in the A-Level Physics curriculum.
Explanation of a capacitor's function to store electrical charge proportional to the potential difference.
Definition of capacitance as the amount of charge stored per unit of potential difference.
The unit of capacitance, the farad, defined in terms of charge and voltage.
Describing the charging process of a capacitor in terms of electron flow.
Use of a capacitor as a power source in a circuit with a light bulb.
Calculating total capacitance in parallel circuits by simple addition.
Deriving the formula for total capacitance in series circuits and its relation to individual capacitors.
Common misunderstandings about capacitors in series and parallel circuits clarified.
The relationship between voltage, charge, and current in parallel circuits.
The counterintuitive nature of charge distribution in series circuits.
Discharging a capacitor through a resistor and the resulting exponential decrease in voltage.
The formula for voltage, charge, and current during capacitor discharge.
Application of the exponential decay formula to a practical problem involving a 500 microfarad capacitor.
The concept of an exponential function and its constant property ratio.
Rearranging the exponential equation to solve for time.
Introduction and explanation of the time constant in capacitor charging and discharging.
Calculating the time constant from a graph of voltage against time.
The charging process of a capacitor in a circuit with an EMF source and resistor.
The relationship between the potential difference across a charging capacitor and the resistor.
Current decrease in a series circuit as a capacitor charges.
Conclusion summarizing the capacitor portion of the A-Level Physics specifications.
Transcripts
hello physicists today we are going to
be looking
at all of the capacitors section on the
a-level physics
specification well let's get started
first of all the symbol for for a
capacitor is as
follows it is two parallel lines
now let's imagine that we put a
capacitor
and a little circuit in which we have a
cell
this capacitor here is going to start
charging
the idea of a capacitor is to store
electrical charge the amount of
charge that is stored on the capacitor
will be proportional to the potential
difference
v across the capacitor
and across the power supply that is
charging it
the constant of proportionality between
them
is known as the capacitance
and it is given the symbol
c rearranging for c
we get that c is equal
to q divided by v
and this leads us to our definition of
capacitance that
capacitance is the amount of charge
stored per unit of potential
difference the unit for capacitance is
known as the
ferret one farad is defined
as the amount of capacitance we would
get
when we have one coulomb of charge
that has been stored for one
volt can explain the
charging of a capacitor in terms of
electron flow
first off in a cell during the
charging of a capacitor we're going to
just connect this cell
to a capacitor as we can see over here
the electrons are going to flow from the
negative terminal of the cell
to the negative plate of
the capacitor there's going to be some
excess electrons that are going to
gather on the negative plate
and those are going to repel some
electrons
of the positive plate of the capacitor
which are going to move towards the
positive terminal of the cell overall
the plates are going to acquire an
equal and opposite charge
on the other hand we can also use a
capacitor
essentially as as a source of
power in a circuit for instance we can
take
a charged capacitor and we can connect
it to a
light bulb when we connect the capacitor
to this circuit the excess electrons are
going to flow
from the negative plate in this case
this will be clockwise to the
positive plate and the charge on the
capacitor
is going to be decreasing
let's go over adding capacitors in
series and parallel we're going to start
off with adding capacitors
in parallel first so if we have
capacitors in power
parallel for instance here we have two
capacitors of 300 microfarads which have
been connected in parallel you can see
the junctions
over here in parallel the total
capacitance i'm going to call that
c total c total
is equal to just the algebraic sum of
the two numbers
so that would be let's say c1 plus c2
applied to this problem above the total
capacitance
is going to simply be equal to
300 plus 300 micro farads so let's write
that 300 plus 300 which will be
equal to 600
microfarads
if the two capacitors are connected in
series the rule is as follows
1 over the total capacitance c total
will be equal to
1 over c1 plus 1 over
c2 it is best to input this into a
calculator by just finding the c
total as brackets one over c
one plus one over c two
then raise this whole expression to a
power of minus one
for instance the total capacitance in
this case will be equal to
one over three hundred plus
one over three hundred raise this whole
expression to a power of minus one
which is going to give us a hundred and
fifty micro farads
if you're wondering how to derive those
two rules or why they're exactly the
opposite to adding resistors
uh check out my video in the playlist of
my full online lessons
on capacitors which is in the
description
here are a couple of more commonly
misunderstood
facts about capacitors in a series
and in a parallel circuit let's start
off with
a parallel circuit first off because
this is a parallel circuit
the voltage or the potential difference
is exactly the same
across all the different parallel
branches
so the potential difference of our
source of emf in this case this is a
cell
it's going to be the same as the
potential difference over the
first capacitor when fully charged and
the potential difference
over the second capacitor when fully
charged
however because the current is actually
shared in a parallel circuit is being
added up
this also means that the charge
is going to be shared as well in
practice
this means that the total charge
q total will be equal to q1
plus q2 i mean if we wanted to
we could also write that c
total the total capacitance times
the potential difference will be equal
to c1
times v1 plus c2
times v2 however because the
potential difference is exactly the same
the voltage will be also
exactly the same and this is why we can
also see
that the rule for capacitance is that c
total is c1 plus c2
because all of the potential difference
is going to
be cancelled out
in a series circuit each capacitor
is going to experience the same current
so
this means that it will acquire the same
amount of charge
and this is really really important
because it's really counterintuitive
this will also be the total amount of
charge within the
circuit so q total will actually be
equal to q1 which will actually be equal
to q2 the pd
is shared by kirchoff's second law
and which says that the sum of the emf
so let's call that
v total will be equal to v1
plus v2 let's have a look at
a capacitor discharging for instance we
have this capacitor here that is
connected
across a resistor we're measuring the
voltage across this resistor and if we
did that
we are going to see that it will be
decreasing
exponentially the equation for the
voltage across a capacitor at a time
t after it begins to discharge that v is
equal to v
naught e to the minus t over c
r where v naught is the initial voltage
t is the time of interest c is the
capacitance and
r is the value of this resistor
because q is equal to cv and c is
constant this equation also applies for
the
charge so q is equal to q naught e to
the minus t over c
r additionally it will also apply for
the current which will also be
decreasing exponentially applied this
equation to a little problem over here
we have a 500 microfarad capacitor which
is charged up to
6 volts which is going to be our initial
voltage it is then discharged for a
500 kilo ohm resistor the value of the
resistance is quite large so i'm
expecting
the voltage to still be relatively high
and find the pd across the capacitor 150
seconds after it begins to
discharge okay well let's write down my
equation over here so i'm going to say
that
v is equal to v naught e to the
minus t divided by c r my initial
voltage v
naught is 6.0 volts
i'm going to multiply this by the
exponential of minus t
which is 150 seconds i'm going to divide
this
by cr which is 500
micro farad so it's time 10 to the power
of -6 farads
times my resistance which is 500 kilo
ohms that's 500 times
10 to a power of 3. when we carefully
input this into a scientific calculator
we're going to get 3.29
volts at time is equal to being equal to
150 seconds
after the beginning of the discharge now
let's have a look at what
actually makes a function an exponential
function
we need to know the constant property
ratio of
exponential in equal time intervals
the initial voltage over another one
let's call it v1 is going to be equal to
v1 divided by v2 is going to be equal to
v2
divided by v3 in practice this
means that in equal time intervals the
exponential
function will be decreasing by the same
factor for instance let's say that the
value decreases by a factor of a third
from v1 to v2
this would also indicate that the
function will also
decrease by another third from v2
to v3 this is the nature of the
exponential decay talking about
exponential functions
let's also remember how to rearrange
this equation
let's say for the amount of time
t so i'm just going to write over here
for practice we can
rearrange for
t the first thing that we're going to do
will be to
just rearrange for the exponential so v
over v naught will be equal to e to the
minus t over c r then i'm going to
take the natural log of both sides of
this equation
so i'm going to get that ln of v over v
naught is equal to the ln
of e to the minus t over cr
now remember the natural log and the
exponential functions
are inverse functions which means that
essentially they undo each other
so this would mean that ln of v over
v naught well that's not v okay there we
go
v over v naught will be equal to minus t
over c r
then what i'm going to do is i'm going
to multiply both functions
by the power of -1
so what i'm gonna get is that minus
ln of v over v naught is equal to
t over c r
the minus sign is actually going to
flip the natural log so
this would mean that this will be ln of
v naught
over v which is equal to t
over c r and finally all i need to do is
just rearrange
for the time i'm going to get that t
is equal to c r multiplied by the
natural log
of v naught over v
let's revise this property known as the
time constant next the charging and the
discharging of a capacitor depends
only on the resistance and the
capacitance
so we define this quantity which is
normally given the greek letter
tau as capacitance times resistance
this is actually a time let's show that
it has the
units of time so i'm just going to
multiply the two quantities
so c times r is going to equal
now because q is equal to
just going to write this on the side q
is equal to cv so this means the
capacitance is
q over v so i'm going to put that in
there
this will be q over v times resistance
which you
which is just v over i like so
those guys are going to cancel out
which means that i'm left with q
over i but remember q is equal to
i times t which means that time
is equal to q over i so this quantity
c times r actually has units of
time so this
time constant t is going to have the
units of time which
are seconds
what happens at time is equal to the
time constant this seems to be a special
time
so in fact let's calculate the
pd at time is equal to the time constant
so i'm just going to write down my
exponential equation v is equal to
v naught e to the minus t over
c r however rather than just time
i'm going to write the time constant
well let's see what happens v is equal
to
v naught e to the minus
now the time constant is just cr
so what i'm going to get is cr divided
by
cr and as we can see no pun intended
those two guys are going to cancel out
which will lead us
to the fact that v is v naught
e to a power of minus one
now e to a power of minus one we could
just put this
into a calculator and what we're going
to get
is that v will be 0.37 up to two
significant figures
times the original voltage v naught and
in fact this is the
very definition of the time constant
that a time equal to a time constant the
pd
will drop to 37 of its original value
so will the charge and so will the
current we can often figure out the time
constant directly
from a graph this is quite an obvious
example but the principles of it can be
applied to
most graphs of potential difference or
current or charge against time
for instance we have the exponential
decrease in pd
in a circuit in which a capacitor is
discharging for a five
kilo ohm resistor we can use this
graph to figure out the capacitance of
the capacitor first off if we have this
graph
we have the time constant because
the voltage is initially 100 then drops
down to
37 volts which is 37 percent of its
initial value
in 25 seconds this would mean that the
time constant t
is equal to 25 seconds
however remember that the time constant
is the product of the capacitance
times the resistance which would mean
that our capacitance
will be equal to our time constant
divided by the resistance
which will be 25 divided by 5 kilo ohm
resistors going to be 5 times 10 to the
power of 3
and if we put that into a calculator
this will
just give us five times
ten to a power of minus three farads
finally let's have a look at the
charging of a capacitor in order to do
so let's imagine a
circuit of emf v node that we've
connected to a resistor r
and a capacitor which is initially not
charged as soon as this circuit is
connected
this capacitor will start charging
now as the capacitor starts charging
the voltage across the capacitor will
increase
so this guy over here will start
increasing
and the voltage across the resistor
will start decreasing exponentially
in fact the pd across the resistor will
be decreasing
exponentially so vr will be equal to
v naught e to the power of minus t
over c r you can kind of think of it as
as
soon as this circuit is switched on vr
is equal to v naught and this guy is
equal to zero
and then vc increases while vr
decreases exponentially we can use
kirchhoff's
second law the sum of the emfs in this
case we only have one emf which is
v naught the potential difference across
the cell
will be equal to v r
plus v c which is the voltage across the
capacitor
and what we can do is just
write down that v naught is random vr
i'm gonna write v naught e to the minus
t
over c r plus vc
i can rearrange for the pd across the
capacitor
and i'm going to get that vc will be
equal to
v naught minus v naught e to the
minus t over c r we can take a factor of
v naught and what we're going to get is
that the potential difference across
the charging capacitor will be equal to
v
naught 1 minus
e to the minus t over
c r like so which is a formula for the
pd across this
capacitor like so the formula for the pd
across the resistor is given
here the same formula
also applies for the charge across the
capacitor
because q is equal to cv so what we can
write over here is that
q across the capacitor equal to
q naught 1 minus e to the minus
t over c r this will give us the charge
across the capacitor
at a time t however if we wanted to find
the
current in this circuit notice that the
current
will be dropping down in this series
circuit
as the capacitor is charging this is
because the pd
across the resistor is going down so
what i'm going to say
is that the current in the circuit will
be decreasing
as the capacitor
is charging
and will be decreasing by the same
factor
as the potential difference across the
resistor
and in fact in this circuit i will be
equal to
the initial current which will be the
highest e to the
minus t over c r when the capacitor
has stopped charging and has reached the
maximum potential difference then the
current will be
dropped to zero okay folks well this
was the vast majority of the
capacitor portion of the a-level physics
specifications
hopefully you have found this useful if
there are any questions please leave a
comment
and thank you very much for watching
Weitere ähnliche Videos ansehen
Plus Two Physics | Electrostatic Potential & Capacitance | Sure Questions
Proses pengisian dan pengeluaran daya pada kapasitor
Chapter 2 - Fundamentals of Electric Circuits
What are Branches, Nodes, and Loops with Series and Parallel Components? | Basic Electronics
(1 of 2) Electricity and Magnetism - Review of All Topics - AP Physics C
Electric Current & Circuits Explained, Ohm's Law, Charge, Power, Physics Problems, Basic Electricity
5.0 / 5 (0 votes)