Class 12 Exam > Class 12 Videos > L14 : Numericals - Capacitor & Capacitance, Physics, Class 12
L14 : Numericals - Capacitor & Capacitance, Physics, Class 12 Video Lecture
FAQs on L14 : Numericals - Capacitor & Capacitance, Physics, Class 12 Video Lecture
| 1. What is a capacitor and what is its role in an electrical circuit? |  |
Ans. A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. Capacitors are used in electrical circuits for various purposes, such as filtering out noise, smoothing voltage fluctuations, and storing energy.
| 2. How does capacitance affect the performance of a capacitor? | |
Ans. Capacitance is a measure of a capacitor's ability to store electrical charge. It is determined by the surface area of the plates, the distance between them, and the type of dielectric used. Higher capacitance means the capacitor can store more charge, resulting in a higher energy storage capacity. Capacitance also affects the reactance of a capacitor, influencing its behavior in AC circuits.
| 3. What factors determine the capacitance of a capacitor? | |
Ans. The capacitance of a capacitor depends on several factors. These include the surface area of the plates, the distance between them, and the type of dielectric material used. The capacitance is directly proportional to the surface area and the permittivity of the dielectric, and inversely proportional to the distance between the plates.
| 4. How can I calculate the capacitance of a parallel-plate capacitor? | |
Ans. The capacitance of a parallel-plate capacitor can be calculated using the formula C = ε₀A/d, where C is the capacitance, ε₀ is the permittivity of free space (a constant value), A is the surface area of the plates, and d is the distance between the plates. By plugging in the values of A and d, you can determine the capacitance.
| 5. Can the capacitance of a capacitor be changed? | |
Ans. The capacitance of a capacitor is a fixed value determined by its physical properties. However, it is possible to change the effective capacitance in a circuit by connecting capacitors in series or parallel. When capacitors are connected in series, the effective capacitance decreases, while in parallel, it increases. This allows for flexibility in designing circuits with specific capacitance requirements.
Text Transcript from Video
hello friends this video on capacitors
and capacitance part 14 is brought to
you by exam feel calm no more fear from
exam please make sure that you have
watched all the videos to part 13 before
going ahead with part 14 this problem
states that a spherical capacitor has an
inner sphere of radius 12 centimeters
and an outer sphere of radius 13
centimeters so now it is talking about
the spherical capacitor noise and in the
videos we have learned oh he will
ferrell think capacitor we didn't talk
about spherical capacitor so let us look
at vertical capacitor when solving these
problems we recover so and if a
capacitor as well as we the tremendous
problem as when the outer sphere is
earth and the inner sphere is given a
charge of 2.5 microcoulombs
the space between the consecutive assets
fears is filled with a liquid of
dielectric constant into that means the
there are two protecting slabs instead
of the conducting plates who now have
inductance years and instead of this
slab between the plates you have this
liquid of dielectric constant which is
placed between the two spheres you have
to calculate the capacitance of the
capacitor and a potential of the Inner
Sphere and well as the comparing the
capacitance of this capacitor with that
of an isolated sphere of radius 12
centimeters okay we will solve them
later but let let us look at this very
health capacity let us suppose this is
mine spiracle capacitor okay so instead
of going through this problem directly
first let us look at how will we
approach a spherical capacitor
let us suppose that the radius of the
inner sphere is Rd and the radius of the
outer sphere is given by RB okay we say
and the outer sphere is earthed let us
suppose the outer sphere is Earth
the inner sphere is given a charge of
2.5 microcoulombs in this question but
otherwise later suppose some charge plus
Q is given in this inner sphere so it
has some charge now because of this
positive charge negative charges will be
induced on the inner surface of the
outer sphere right so here all you will
have negative charge is induced because
of which there will be positive charges
outside but since the outer side is
grounded therefore the positive charges
will directly go to the ground and get
utilized right so here you will have the
same pattern positive charges negative
charges so electric field will set so
electric field will set up and the
direction of the electric field will be
outward so this is how the electric
field will be set so now what would be
the value of electric field for all this
capacitance for the smaller capacitor
right when we are talking about the
smaller capacitor the electric field
inside the capacitor will be equal to
zero because electric field inside any
conductor is zero right the electric
field for radius greater than R D so
electric field outside the sphere will
also be zero so electric field will
exist only in this portion so the
electric field will basically exist only
in this portion that is the portion
between enclosed between the two
conductors so here we will have electric
fields okay so what did we see that
electric field exists between these two
spheres and it is radially outward so
electric field exists for any R which is
greater than R game but less than R B so
it exists only in this region and that
direction is radially outward right now
we know the direction of electric field
let us try to calculate the potential at
all at sphere a first we will calculate
potential ax fear
then you factor a potential X P and V
and then we calculate the potential
difference will be env so what would be
the potential on sphere a it would be
nothing but KQ by add a KQ by a day
because of the smaller sphere and - pay
cube by Rd because of the sphere because
this smaller sphere has plus Q and this
bigger sphere has - - right so it will
be minus K Q divided by R P so this
becomes K Q into RT minus RA divided by
r e RB so this is the potential at a now
what would be the potential for sphere V
potential for sphere V will be equal to
0 why because sphere B is Earth it is
art therefore its potential is 0 right
therefore the potential difference
between a and B potential difference
between E and V will be equal to VA
minus VB VB is anyway 0 so this will be
K Q into RB minus RT divided by R right
therefore the capacitance C will be
equal to Q minus V so Q my Q divided by
V so Q divided by this you will get it
as 1 by K into RB minus RA divided by RB
you are you so this would be the
capacitance of a spherical capacitor so
remember this the capacitance for a
spherical capacitor is 1 by K if you are
t minus R divided by r 18 RT C basically
you saw that the approach is still the
same we have to calculate the potential
difference between the two they'll be
the calculating the potential difference
between the two plates here we were we
are calculating the potential difference
between the two spheres
so once the potential difference is
calculated then we
straight away finding out the
capacitance now let us look at the
question so the first part of the
question asks us to calculate the
capacitance of this capacitor so that
for capacitance we can directly put
values in this formula now what are the
values given in the problem radius of
the smaller sphere is given as 12
centimeter that is 12 into 10 to the
power minus 2 meters radius of the
larger sphere is given as thirteen
centimeters that is equal to 13 into 10
to the power minus 2 meters charge on
the smaller sphere that is Q is given as
2 point 5 into 10 to the power minus 6
coulombs
what is this feel like open friends let
me tell you one thing that specifically
the K which I have been using in this
expression for potential is the key
which we used before the capital K that
is the constant which was 9 into 10 to
the power 9 right it is that key but
here as after we started dielectrics we
are also using K for dielectric constant
so this is not that dielectric constant
King right so this is your our previous
key so here after in this problem
wherever I use dielectric constant I
will use this K for dielectric constant
and this C for our previous wants to be
design into 10 to the power 9 okay so
that you don't get confused so in the
first part let us calculate the
capacitance C this will be just by 2 1
by 10 to the power 9 into 10 to the
power 9 into RV that is 30 into 10 to
the power minus 2 minus R a that is 12
into 10 to the power minus 2 divided by
RA into RB and extremely sorry I have
calculated the capacitance expression in
an incorrect way if you see here
capacitance is Q by V right so this
should happen the opposite RB into RA
divided by RB minus 1 similarly here it
should have been RB into Rd divided by
RB minus RT right so here also this will
be R a into RB divided by RB minus RA I
am sorry for that
so on calculating this you find the
value as 5 point 5 into 10 to the power
minus 9 balanced so this comes out to be
the capacitance of this spherical
capacitor so let us calculate the second
part now the second part of the question
asks what is the potential of the Inner
Sphere that means we have to calculate
the value of D a we have already
calculated this calculated this while
deriving the capacitance this was the
value of the potential of the Inner
Sphere let us take you with you RB minus
RA divided by RA RB so this was a Q Rd
minus RA divided by RB into r8 so again
we have all the values so K is 10 9 into
10 to the power 9 into Q is 2 point 5
into 10 to the power minus 6 RB minus RA
that is 30 into 10 to the power minus 2
minus 12 into 10 to the power minus 2
divided by 13 into 12 into 10 to the
power minus 4 so this value comes out to
be 4 point 5 into 10 to the power 2
volts right so this is one way of
calculating you can also calculate the
potential on e using this that potential
is equal to Q that is the charge on e
divided by capacitance C so charge on a
is given as 5 5 and C is also given so
you will also get the same value using
this this also will give you same value
right now let us look at the third part
so what is the third part it says
compare this with the capacitance of
isolated sphere so first of all let us
calculate the capacitance of an eye-full
a big sphere so let us consider a big
sphere so what may happen images of an
isolated sphere and suppose this is the
sphere so what would be the potential
due to this sphere let us calculate the
potential for the isolate
scale that will be equal to pH Q divided
by R if R is the radius of the sphere so
what would be the potential on the
surface of the sphere it would be 8 Q
divided by R 3 so when I have to
calculate the capacitance that is C so C
is equal to Q divided by V therefore
this is equal to Q divided by KQ by L
will cancel this will be equal to R by P
so the capacitance will become equal to
I by K what is this K the constant K was
nothing but 9 into 10 to the power 9
that is 1 by 4 pie epsilon-not
K is equal to 1 by 4 pie epsilon not
so this capacitance can be written as 4
pie epsilon-not beauty on so the
capacitance of an isolated sphere is 4
pie epsilon not R so we have to
calculate this value so calculate it you
get R divided by K so what is our R of
an isolated sphere is given in the
problem guide isolated sphere of radius
12 centimeters so your RL is 12
centimeters divided by K is 9 into 10 to
the power 9 so this comes out to be 1
point 3 3 into 10 to the power minus 11
France so now compare the capacitance
with the capacitance of the spectacled
capacitor what do you see the
capacitance of isolated sphere is lesser
why is it so now the question asks you
why is the capacitance of isolated
sphere latest market as I isolated
sphere so what do you see we see that
capacitance of isolated sphere is lesser
than the capacitance of the spherical
capacitor can you tell logically why is
it so that's because in case of the
spherical capacitor the outer sphere is
earthed by Earthling the outer sphere we
are increasing the potential difference
between the two snares as a result more
charge can be stored in the
and therefore the capacitance increases
whereas in some isolated sphere there is
no our team of any other conductor there
is only a single conductor
so there could its capacitance is
comparatively less thank you please
visit exam viacom to watch free
educational videos try 3 online tests
get the best quality study materials
study from the best tutors and mentors
and much moon thank you once again
and capacitance part 14 is brought to
you by exam feel calm no more fear from
exam please make sure that you have
watched all the videos to part 13 before
going ahead with part 14 this problem
states that a spherical capacitor has an
inner sphere of radius 12 centimeters
and an outer sphere of radius 13
centimeters so now it is talking about
the spherical capacitor noise and in the
videos we have learned oh he will
ferrell think capacitor we didn't talk
about spherical capacitor so let us look
at vertical capacitor when solving these
problems we recover so and if a
capacitor as well as we the tremendous
problem as when the outer sphere is
earth and the inner sphere is given a
charge of 2.5 microcoulombs
the space between the consecutive assets
fears is filled with a liquid of
dielectric constant into that means the
there are two protecting slabs instead
of the conducting plates who now have
inductance years and instead of this
slab between the plates you have this
liquid of dielectric constant which is
placed between the two spheres you have
to calculate the capacitance of the
capacitor and a potential of the Inner
Sphere and well as the comparing the
capacitance of this capacitor with that
of an isolated sphere of radius 12
centimeters okay we will solve them
later but let let us look at this very
health capacity let us suppose this is
mine spiracle capacitor okay so instead
of going through this problem directly
first let us look at how will we
approach a spherical capacitor
let us suppose that the radius of the
inner sphere is Rd and the radius of the
outer sphere is given by RB okay we say
and the outer sphere is earthed let us
suppose the outer sphere is Earth
the inner sphere is given a charge of
2.5 microcoulombs in this question but
otherwise later suppose some charge plus
Q is given in this inner sphere so it
has some charge now because of this
positive charge negative charges will be
induced on the inner surface of the
outer sphere right so here all you will
have negative charge is induced because
of which there will be positive charges
outside but since the outer side is
grounded therefore the positive charges
will directly go to the ground and get
utilized right so here you will have the
same pattern positive charges negative
charges so electric field will set so
electric field will set up and the
direction of the electric field will be
outward so this is how the electric
field will be set so now what would be
the value of electric field for all this
capacitance for the smaller capacitor
right when we are talking about the
smaller capacitor the electric field
inside the capacitor will be equal to
zero because electric field inside any
conductor is zero right the electric
field for radius greater than R D so
electric field outside the sphere will
also be zero so electric field will
exist only in this portion so the
electric field will basically exist only
in this portion that is the portion
between enclosed between the two
conductors so here we will have electric
fields okay so what did we see that
electric field exists between these two
spheres and it is radially outward so
electric field exists for any R which is
greater than R game but less than R B so
it exists only in this region and that
direction is radially outward right now
we know the direction of electric field
let us try to calculate the potential at
all at sphere a first we will calculate
potential ax fear
then you factor a potential X P and V
and then we calculate the potential
difference will be env so what would be
the potential on sphere a it would be
nothing but KQ by add a KQ by a day
because of the smaller sphere and - pay
cube by Rd because of the sphere because
this smaller sphere has plus Q and this
bigger sphere has - - right so it will
be minus K Q divided by R P so this
becomes K Q into RT minus RA divided by
r e RB so this is the potential at a now
what would be the potential for sphere V
potential for sphere V will be equal to
0 why because sphere B is Earth it is
art therefore its potential is 0 right
therefore the potential difference
between a and B potential difference
between E and V will be equal to VA
minus VB VB is anyway 0 so this will be
K Q into RB minus RT divided by R right
therefore the capacitance C will be
equal to Q minus V so Q my Q divided by
V so Q divided by this you will get it
as 1 by K into RB minus RA divided by RB
you are you so this would be the
capacitance of a spherical capacitor so
remember this the capacitance for a
spherical capacitor is 1 by K if you are
t minus R divided by r 18 RT C basically
you saw that the approach is still the
same we have to calculate the potential
difference between the two they'll be
the calculating the potential difference
between the two plates here we were we
are calculating the potential difference
between the two spheres
so once the potential difference is
calculated then we
straight away finding out the
capacitance now let us look at the
question so the first part of the
question asks us to calculate the
capacitance of this capacitor so that
for capacitance we can directly put
values in this formula now what are the
values given in the problem radius of
the smaller sphere is given as 12
centimeter that is 12 into 10 to the
power minus 2 meters radius of the
larger sphere is given as thirteen
centimeters that is equal to 13 into 10
to the power minus 2 meters charge on
the smaller sphere that is Q is given as
2 point 5 into 10 to the power minus 6
coulombs
what is this feel like open friends let
me tell you one thing that specifically
the K which I have been using in this
expression for potential is the key
which we used before the capital K that
is the constant which was 9 into 10 to
the power 9 right it is that key but
here as after we started dielectrics we
are also using K for dielectric constant
so this is not that dielectric constant
King right so this is your our previous
key so here after in this problem
wherever I use dielectric constant I
will use this K for dielectric constant
and this C for our previous wants to be
design into 10 to the power 9 okay so
that you don't get confused so in the
first part let us calculate the
capacitance C this will be just by 2 1
by 10 to the power 9 into 10 to the
power 9 into RV that is 30 into 10 to
the power minus 2 minus R a that is 12
into 10 to the power minus 2 divided by
RA into RB and extremely sorry I have
calculated the capacitance expression in
an incorrect way if you see here
capacitance is Q by V right so this
should happen the opposite RB into RA
divided by RB minus 1 similarly here it
should have been RB into Rd divided by
RB minus RT right so here also this will
be R a into RB divided by RB minus RA I
am sorry for that
so on calculating this you find the
value as 5 point 5 into 10 to the power
minus 9 balanced so this comes out to be
the capacitance of this spherical
capacitor so let us calculate the second
part now the second part of the question
asks what is the potential of the Inner
Sphere that means we have to calculate
the value of D a we have already
calculated this calculated this while
deriving the capacitance this was the
value of the potential of the Inner
Sphere let us take you with you RB minus
RA divided by RA RB so this was a Q Rd
minus RA divided by RB into r8 so again
we have all the values so K is 10 9 into
10 to the power 9 into Q is 2 point 5
into 10 to the power minus 6 RB minus RA
that is 30 into 10 to the power minus 2
minus 12 into 10 to the power minus 2
divided by 13 into 12 into 10 to the
power minus 4 so this value comes out to
be 4 point 5 into 10 to the power 2
volts right so this is one way of
calculating you can also calculate the
potential on e using this that potential
is equal to Q that is the charge on e
divided by capacitance C so charge on a
is given as 5 5 and C is also given so
you will also get the same value using
this this also will give you same value
right now let us look at the third part
so what is the third part it says
compare this with the capacitance of
isolated sphere so first of all let us
calculate the capacitance of an eye-full
a big sphere so let us consider a big
sphere so what may happen images of an
isolated sphere and suppose this is the
sphere so what would be the potential
due to this sphere let us calculate the
potential for the isolate
scale that will be equal to pH Q divided
by R if R is the radius of the sphere so
what would be the potential on the
surface of the sphere it would be 8 Q
divided by R 3 so when I have to
calculate the capacitance that is C so C
is equal to Q divided by V therefore
this is equal to Q divided by KQ by L
will cancel this will be equal to R by P
so the capacitance will become equal to
I by K what is this K the constant K was
nothing but 9 into 10 to the power 9
that is 1 by 4 pie epsilon-not
K is equal to 1 by 4 pie epsilon not
so this capacitance can be written as 4
pie epsilon-not beauty on so the
capacitance of an isolated sphere is 4
pie epsilon not R so we have to
calculate this value so calculate it you
get R divided by K so what is our R of
an isolated sphere is given in the
problem guide isolated sphere of radius
12 centimeters so your RL is 12
centimeters divided by K is 9 into 10 to
the power 9 so this comes out to be 1
point 3 3 into 10 to the power minus 11
France so now compare the capacitance
with the capacitance of the spectacled
capacitor what do you see the
capacitance of isolated sphere is lesser
why is it so now the question asks you
why is the capacitance of isolated
sphere latest market as I isolated
sphere so what do you see we see that
capacitance of isolated sphere is lesser
than the capacitance of the spherical
capacitor can you tell logically why is
it so that's because in case of the
spherical capacitor the outer sphere is
earthed by Earthling the outer sphere we
are increasing the potential difference
between the two snares as a result more
charge can be stored in the
and therefore the capacitance increases
whereas in some isolated sphere there is
no our team of any other conductor there
is only a single conductor
so there could its capacitance is
comparatively less thank you please
visit exam viacom to watch free
educational videos try 3 online tests
get the best quality study materials
study from the best tutors and mentors
and much moon thank you once again
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Dec 02, 2024 Last updated |
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