 Today we’ll examine this worked example on
a potentiometer circuit. We have a uniform length of wire a-b and It is one point two meters long it has a diameter of zero point four millimeters,
and it’s resistance is zero point it is eight homes and We are required to find the EMF of cell X according to this question, but These are some of the conditions. They’ve given us in the question we have two
switches in this potentiometer circuit We have K 1 and we have K 2 when K 1 is open and K 2 is closed the balance point is 83 point
two centimeters and when K 1 is closed and K 2 is open The balance point is 67 point five centimeters
now Remember that this is the driver cell, and
it is the one that is providing the current that is going through this Primary circuit so in this current that is
being provided going through the goes to the primary circuit and K 1 is closed When switch K 1 is closed when this current
is coming here It will It won’t go through the 3 ohm resistor, so
if we closed switch K 1 this current will definitely pass via that
route, and it won’t go through the resistor because the resistance E. Is definitely higher So it means that in our calculations when
K 1 is closed? the 3 ohm resistor will be ignored it will
act as though it is not existent because Current is not flowing through it, but when
switch K is open, then it means that the current that is incoming has no option but to Go through the resistor and so in our calculations We will have to include the consider the 3
ohm resistor in all our calculations this is the dry-cell in the secondary circuit When this switch is closed it means that this
circuit this down repeat the circuit is incomplete We calculate as though this is Not in the circuit because it is broken, but
if switch cato is closed It means now this 10 ohm resistor has come
into the circuit so in our calculations that re that are relating with this circuit down the secondary circuit will have to consider
that as well now for us to be able to find the EMF of this cell so X First of all know that we are going to move
this jockey along this where it be when we Move that jockey along that where it be there’s
going to be a position where this Joker will be? In such that no current is going through when
the current through the galvanometer IG is equal to zero that is what we are holding
the ballast put point and when that balance point is reached It means that the potential difference across
AJ is going to be the same as the potential difference across The sail X or and that would be a MF of the
cell ex or non open circuit So the first thing we need to know we need
to find the PD PD per unit length of this wire this way as
the length of 1.2 meters so in minutes for us to find that
PD per unit length of this wire it means we need to find That is PD pilot length V is going to be equal
to I the current That is going through this which is going
to be the driver current times the resistance Pilot length the resistance per unit length
is the same as simply getting we get the resistance of the whole wire divide it by The length of the wire to get the resistance
by net length Now for us to get the EMF of cell X it means
that the EMF of cell X is going to be the EMF or the potential difference across the balance
point and point a When this resistor is out of the circuit? so for us to get that it means that we need
to first get the PD per unit length of This we know this is 1.2 meters So you need to get the PD per unit length
after getting the PD pioneer length Then we get the resistance per centimeter
so that when getting the PD Across AJ will be V is going to be equal to
the current that is going through this primary circuit Multiply that by the resistance pilot centimeter or pilot meter or PI unit length,
but the balance point when Cattle is open that is when the 10 ohm resistor
is not in the circuit is here When cattle is open and k1 is closed? It’s going to be sixty seven point five centimeter
and remember when k1 is closed it means that Current coming in is looping this 3 ohm resistor,
so this 3 ohm resistor is not Going to be considered in our calculations
so in CUC 4 let’s first get the PD pilot length it begins with getting the resistance per centimeter this AJ is remember is a hundred and Twenty centimeters so to get the resistance
per centimeter means that it’s going to be eight divided by than twenty centimeters Which will be give us eight over 120 ohm per
centimeter, which is one over fifteen on per centimeter? This is the resistance for centimeter now Let’s look we find the amount of current that
is going through the potentiometer the amount of current going through the potentiometer
V over R the EMF there is to be Three and So remember that now V over R the resistance we need to get the effective resistance in
this whole circuit But remember we are considering the amount
of current that is provided by this when K 2 is K 2 is open and K 1 is closed So when K 1 is closed it means that the amount
of current coming in will just pass via that side and go and so meaning the current won’t go through the few
ohm resistor since the current that is coming will opt to pass via a direction of a path of least resistance So it means for us to get our effective resistance,
we will be considering this resistor Which is the resistance of the wire which
we already know as 8 ohms? Then we shall also be? Considering the internal resistance of the
cell and we won’t consider the resistance of 3 ohms So it means that here away effective resistance
is going to be since this is in series with that resistance So it’s going to be 8 plus 1 ohm So I effective resistance will be 8 plus 1
ohm and We shall get our answer as 3 over 9 which
will give us 1 over 9 amperes and That would be our amount of current the Drava
current in the primary circuit IP So after getting that it means you can now
get our resistance per unit length oh I mean the pig define it length so our PD
pilot length is going to be equal to the resistance per unit length of the resistance per centimeter time’s the current
so PD Pass centimeter is going to be equal to Resistance per centimeter multiply that by a current I Our resistance per centimeter has 1 over 15
and our current is 1 over 9 ampere, so it’s going to be Our PT for units every day is 1 over 15 volts
per centimeter after getting our PD per centimeter we know that this balance point is achieved
when when K 2 is open and K 1 is closed when K 2 is open it means that
the balance point between a and J will be the same as the EMF across that cell
and That is achieved when the balance point is
at seven point five centimeters since we know our PD per centimeter here We have already gotten it as 1 over 45 volts
per centimeter so to get that the EMF is going to be the PD across via James so EMF EMF of surge a is going to be equal to of
the cell x is going to be equal to the PD across edge, and that’s going to be PD per centimeter Multiplied that by the balanced length, let’s
call the balanced length L. The PD per centimeter will go as 1 over 45 volts per centimeter Multiplied that by the balanced length which
is 67 Point five centimeters, and so it means that
our EMF for that cell is going to be 125 volts now Our next question is asking us to find the
internal resistance of the cell The internal resistance of cell X it means
that we are going to consider both We are going to look at the balance point
when both when K 2 is closed meaning that this thing
is in the circuit and when K 1 is Open when K 1 is open it means that? We have introduced three ohm resistor into
the primary circuit and introducing the 3 ohm resistor into the primary circuit means That our peopie net length is going to change
so it means you’re supposed to first calculate for the new PD pilot length then after getting the PD pilot length, then
we are able to get the potential difference across the balance point and a when 10 ohms is also been included in the
circuit cause when you close this K 2 we include the 10 ohm resistor in the circuit so the balance point of the PD occurs the
this the balance point and point a will be equivalent to They affect the PD across the effective resistance
of this cell and the 10 ohm resistor And it is from this that we shall be able
to compute the internal Resistance of the cell we derived this the
formulas in our previous example So we shall proceed with the working So let’s find the amount of current that is
flowing in the lower circuit Now when this thing is closed, and this one
is open It means that the 3 ohm resistor has been
introduced into the upper circuit, and when this skirt is closed it means that The 10 ohm resistor has been introduced into
the this lower circuit so we find the amount of current that is flowing
through this lower circuit and We also get the new P. Definitely. Let’s first get the new PD PI in its centimeter
in the upper circuit PD per centimeter Is going to be equal to resistance per centimeter Multiplied that by the current the driver
current IP now The resistance per centimeter we already obtained
it. It was 1 over 15 ohms per centimeter multiplied that by The current the driver current current is
going to be equal to V over our Current in the in the primary circuit is going
to be the total voltage reaches 3 volts over now the effective resistance the effective
resistance here is going will have changed because we have closed k1 I Mean we have opened k1, so it means that the
effective resistance well considering the 8 ohm Zia the 3 ohms And then they’ve one ohm resistor, so it means
the effective resistance in the primary circuit When k1 is open is going to be 8 ohms plus
3 ohms plus 1 ohm So it’s going to be 8 plus 3 Plus 1 and that will be 1 over 15 ohm per centimeter multiply that by 3 over 12 And RPD per centimeter will be 1 over 60 volts
per centimeter We have gotten our new PD per centimeter when
k1 is open and K2 is closed But remember when k1 is open and k2 is closed
the balance point shows eighty three point three centimeters Now the PD that is represented by the balance
point which is eighty three point three centimeters is equivalent to an APD that is Across the effective resistance of this lower
circuit so meaning that this eighty three point three centimeters We multiply this by the new PD per unit length Which you have just gotten before that must
be equal to the potential difference across This resistance down so meaning that V Our PD is going to be equal to The piece D per centimeter multiplied that
by the balanced length Our PD per centimeter is going to be we got
it as one over sixty volts per centimeter Up there, and it means we are supposed to
multiply this by our new balance length Which is going to be eighty three point three
centimeters? The potential difference that is oppressed
the effective resistance down So likewise if the idea is going to be equal
to this also that pity which is this? Is equal to the effective resistance in the
secondary circuit which we solve for pi times R the amount of current that is flowing in the
secondary circuit I the secondary circuit here has got current
that is being supplied by this This cell this cell has got an EMF it has
got the internal resistance of it’s the internal resistance We are looking for so it’s going to be e EMF E to get the current we know that EMF
is going to be equal to I into R plus R So to get making Ida subject of the formula
we know that our current. I is going to be e over R Plus R. Now this is the expression for the
amount of current that is flowing in the lower circuit So it’s going to be this current times the
effective resistance in this lower circuit So I is going to be equal to e over R plus
R multiply that by our What is a EMF the EMF of that cell we got
it before as 1.5 So it’s going to be 1 point 5 volts we got
it in our previous calculation divide that by R. Plus R Our capital R. Is 10 ohms plus our FFT resistance,
which we know our internal resistance, which you do not know Multiply that by 10 that’s going to be V.
AJ now we already got V. AJ as 1.3 But so it’s going to be one point three eight
eight is Going to be equal to that so when we make
the are the subject of the formula here I shall end up with our internal resistance
as Brings us to the end of this video. Thank you for watching somebody out there
needs to watch this video Don’t forget to like and share for more videos
simply subscribe to the same Baqubah me, otherwise. I’ll catch you in the next video Folks Tim Walker Amy this is an old drunk
economy