motion in the substance.

The root mean square 32

CURRENT ELECTRICITY
speed of these electrons in a conductor is the order of
5 -1
" The branch of physics in which we study about charge in 10 m s . But when we put this conductor is an electric
motion is called current electricity." field . Than all the electrons now starts to move or drift in
Q:- Define electric current. the direction just opposite to the electric field with very
-4 -1
Ans:- Generally we can say electric current is a flow of less velocity of the order of 10 m s . In this condition
charge. Numerically, "The amount of charge that flow these free electrons collides with immovable positively
through the cross section of a conductor in one second charged atoms.
is called electric current". " The average velocity of a free electron between any
Or two successive collision [with positively charged
"The rate of flow of electric charge through the cross particles], when it is placed in an electric field is called
section of a conductor with respect to time is called drift velocity " & is denoted by vd, and the time taken
electric current ." by an electron between two such successive collision is
If Q be the charge flows through a conductor is t sec, then called relaxation time and is denoted by .
Let the electric field is E so the force on an electron will
electric current will be,
be F qE eE But F ma
I= Q/t
eE
It is scalar quantity (actually it is tensor quantity ) because it So m a qE or a
m
does not follow the rules of vectors but direction matters. Its
Now maximum velocity between two successive
SI unit is ampere (A) & dimensional formula is [M0L0T0A],
collision for an electron will be -
The direction of electric current is always from positive to v1 u1 a 1
negative or in the flow of positive charge or in the direction
similarly v2 u2 a 2
just opposite to the flow of electrons or from a body at
similarly v3 u3 a 3
higher potential to the body at lower potential.
Q:- Define current density. similarly v4 u4 a 4
. . .
Ans:- The amount of electric current passing through a
. . .
conductor of unit cross section is called current density.
. . .
Or
similarly vn un a n
The amount of electric current passing per unit are a of
Now the average velocity will be -
cross section of a conductor is called current density.
If I be the electric current passing through a conductor of
bu 1 a 1 g bu a g 2 2

area of cross section A, current density will be, vd

bu 3 a 3g. . . . . . . . . b u n a n g
I n
It is a vector quantity , Its direction is from J
A
positive to negative i.e. in the direction of current. Its S.I. vd
bu1 u2 u3 ....... un g ab 1 2 3 ...... n g
n
unit A m-2 & dimensional formula is [M0L-2T0A].
Q:- Explain drift velocity & relaxation time. vd
bu1 u2 u3 ....... u g ab
n 1 2 3 ...... g
n

n n
Ans- We know that all the substances in this universe are
But u1 u2 u3
u 4 ........... un
made by atoms. Only some of the substances show conductivity uav 0
n
which are called conductors because they have free
So v d
a 1 b2 3 ...... n g
electrons (free electrons are those electrons which are free n
But average relaxation time
to move all over the substance like air molecule in a
1 2 3 ...... n
container). These free electrons show random & zig-zag
n
Physics for you
So eE the conductor, E be the electric field developed 33
vd a
m in the conductor than it is obvious that the intensity of
V
Q- Establish a relation between current density & drift electric field will be - E
l
velocity Or establish a relation between electric current& Now, electrostatic force act on a free electron will be-
drift velocity. F = q. E = e E
Ans- Let us consider a conductor of area of cross section. Where, e is the charge on an electron. Now, by the newton's
A & length l then it is obvious that. 2nd law. We know that,
Volume of conductor = A.l
Force = Mass Acceleration
Let n be the number of free electron in the unit volume of
Or F = m.a
conductor. Than total number of free electron in conductor
will be, N = n.A.l So, ma=eE
eE
Let e be the charge an electron .Than total charge on Or a
m
conductor will be, Q = n.A.l .e. On putting value of E we get,
When we apply an electric field across the conductor eV
a
current will flow through the conductor and the current will ml
be, Q n A le
I Let be the mean free path (i.e. distance between any
t t
But , l / t = vd (drift velocity of free electron ) two successive collision) and be the relaxation time,
So I = n.e. A. vd then by the 1nd equation of motion we know that,
1 2
This is a relation b/w electric current & drift velocity, s ut at
2
We know that the current density,
1 eV 2 eV 2
I neA vd So 0
J nevd 2 ml 2 ml
A A
Now drift velocity is the average velocity between two
This is relation between current density & drift velocity. successive collision
Q- State Ohm's law. eV 2
Ans- According to George Simon Ohm, 2 ml eV
vd
" If all physical condition like temperature, pressure, strain 2 ml

etc. remain unchanged for a conductor, the potential Now, we know that by the relation between electric
difference across the conductor is directly proportional current & drift velocity .
I = n e A vd
to the strength of electric current pass through it".
On putting value of vd we get,
Let V be the potential difference applied across a conduc-
eV ne 2 A V
tor & the current flowing through the conductor be I .Than I neA
2ml 2ml
according to ohm's law- V 2ml
Or
V I I ne 2 AV
Or V=RI
It is obvious from this equation, if all the physical
Where R is proportionality constant and is known as resistance
conditions remain constant & there is no change take
of the conductor.
place in any dimension of conductor, the quantity in right
Q- Give a derivation for Ohm's law on the basis of free
hand side of above equation remains constant, i.e.
electron theory.
Ans- Let us consider a conductor of length l & area of cross V / I = constant
section A. Let, the conductor has n number of free electrons in i.e. V I This is Ohm's law
its unit volume. When we apply a potential difference V across
Physics for you
Q- What do you mean by resistance of a conductor? Write called conductance of the conductor, i.e. 34
the factors on which the resistance of a conductor depends. 1
Conductannce(G)
Ans- By derivation of Ohm's law by free electron theory, Resistance(R)
we know that, V 2 ml The conductance is a scalar quantity & is denoted by G. Its
I ne 2 A S.I. unit is 'mho' { -1 } or seimon (S) & its dimensional
V formula is [ M-1L-2T 3A 2 ]. The conductance of a
and we know that R
I conductor depends on following factors :
2 ml (1)On the length of conductor :- The conductance of
So R
ne 2 A conductor is inversoly proportional to its length, i.e.G 1 l
By above equation we can say that the resistance of a In other words we can say that the conductance of a long
conductor depends on following factors : wire is lesser than that of conductance of a small wire.
(1)On the length of conductor :- The resistance of (2)On the area of cross section :- The conductance of a
conductor is directory proportional to its length, i.e. R l conductor is directly proportional to the area of cross
In other words we can say that the resistance of a long wire section of conductor Or directly proportional to the square
is more than that of resistance of a small wire. of its radius. i.e. R A or R r2
(2)On the area of cross section :- The resistance of a Or in the other words we can say that the conductance of
conductor is inversely proportional to the area of cross thick wire is more than that of thin wire.
section of conductor Or inversely proportional to the square (3)On the temperature of conductor :- The
1 1
of its radius. i.e. R or R conductance of a conductor is inversely proportional to
A r2
Or in the other words we can say that the resistance of the temperature of conductor because when we increase
thick wire is lesser than that of thin wire. the temperature of conductor the kinetic energy of its free
(3)On the temperature of conductor :- The resistance electron will also increase & hence the relaxation time
of a conductor is directly proportional to the temperature will decrease so that the conductance decreases.
of conductor because when we increase the temperature 1
G
T
of conductor the kinetic energy of its free electron will also (4)On the nature of conductor :- The conductance of
increase & hence the relaxation time will decrease so that a conductor also depends upon its nature i.e. on the
the resistance increases. R T number of free electrons of the conductor, i.e. the
(4)On the nature of conductor :- conductance of a conductor is directly proportional to the
The resistance of a conductor also depends upon its nature number of free electron per unit volume containing the
i.e. on the number of free electrons of the conductor, i.e. conductor. Mathematically. G n
the resistance of a conductor is inversely proportional to Q- What is specific resistance or resistivity of a
the number of free electron per unit volume containing the conductor? Write the factors on which it depends ?
conductor. Mathematically. R
1
Ans - We know that the resistance of a conductor is
n
directly proportional to the length l of the conductor,
Definition :- The obstruction offered by a conductor in inversely proportional to the area of cross section A of
the flow of charge by itself is called resistance of the 1
the conductor. i.e. R l and R
conductor. Its S.I. unit is Ohm & is denoted by ' ' A
On combining both the equation we get.
(Omega), it is a scalar quantity & its Dimensional Formula l l
R or R
is [ML2T-3A-2] A A
Where is the constant of proportionality & is known as
Q- What is conductance? Write the factors on which the specific resistance or resistivity of the material of the
conductance of a conductor depends. conductor.
Ans- The reciprocal of the resistance of a conductor is If we put l = l m & A = m2 ; in above equation than,
Physics for you
 R= conductivity becomes infinite. In this condition
35
the conductor now behave just like a super conductor &
So,"The specific resistance of the material of a conductor
the phenomenon is called super conductivity & the
is numerically equal to the resistance of the conductor temperature on which a conductor converts into super
of unit length and unit area of cross section." {This is conductor is called critical temperature for the conductor.
also called the resistivity of the material of body} e.g. - critical temp. for mercury is 4.2 K.
Q - Explain the combination of resistors.
The resistivity of the material of a conductor is a scalar quantity
Ans - There are two types of combination of resistors :
& is denoted by . Its SI unit is Ohm meter ( m) & Series combination :- If different resistors are so
Dimensional Formula is [ML3T-3A-2]. connected that 2nd end of 1st resistor is connected to 1st
We know that the resistance of a conductor is given by end of 2nd resistor. Similarly 2nd end of 2nd resistor is
2 ml connected to 1st end of 3rd resistor & so on.... A battery
following formula. R ................... ( 2 )
ne 2 A or a cell is connected across this combination then this
combination is called series combination of resistors. In
On comparing this equation 2nd with equation 1st we get, this combination all the resistor get same amount of current
2m but have different potential difference across there ends.
ne2 (i)Derivation for resultant resistance:- Let us
By this equation it is clear that the resistivity of the material consider three resistors of resistances R1, R2 & R3
of a conductor depends on following factors:- respectivaly are connected between points AB, BC &
CD. By a battery we apply some potential difference V
(1)On temperature :- The resistivity of material of
between A & D. So that I current flow through the
conductor is directly proportional to its temperature. combination.
(2)On nature of conductor :- The resistivity of material of A B C D
R1 R2 R3
the conductor is inversely proportional to number of free I I
E K
electrons containing per unit volume of it. + - ()
Q - Define conductivity or specific conductance. The P. d. across 1st resistor,
Ans - The specific conductance or conductivity of the VA - VB = R1I ........(1)
material of a conductor is the reciprocal of its specific Similarly P.d. across 2nd resistor,
resistance & is denoted , i.e. VB - VC = R2 I ........(2)
1
specific conductance (s) =
specific resistance (r) Similarly P.d. across 3rd resistor,
The conductivity of the material of conductor is a scalar
quantity Its S.I. unit is mho m-1 ( -1 m-1) or simon m-1 VC - VD = R3 I ........(3)
-1 -1 -3 3 2
(s m ) & its Dimensional Formula is [M L T A ] Let R be the equivalent resistance of the combination.Than
The conductivity of the material of a conductor depends on potential difference across whole combination will be-
following factors:-
VA - VD = RI ........(4)
(1)On temperature :- The conductivity of material of
On adding equation 1st, 2nd & 3rd we get,
conductor is inversely proportional to its temperature.
VA - VB + VB - VC + VC - VD = R1I + R2I + R3I
(2)On nature of conductor :- The resistivity of material of
the conductor is directly proportional to number of free VA - VD = R1I + R2I + R3I
electrons containing per unit volume of it. VA - VD = (R1 + R2 + R3) I
Q - Explain super conductivity. On putting value of VA - VD from eq. 4th we get
Ans- The concept of super conductivity is given by french
scientist Hei Ke Kamerling Onnes in 1911. RI = (R1 + R2 + R3) I
We know that, the resistivity of the material of a conductor is R = (R1 + R2 + R3)
directly proportional to its temperature, i.e. if we continuously Thus the equivalent resistance in the series combination of
decrease in the temperature of conductor, at ones its resistance
and resistivity becomes zero & hence conductance and resistor is equal to the sum of resistances of constituent resistors.
Physics for you
(ii)Derivation for paralled combination :- When two or Q - Explain electro motive force (emf) . 36
more than two resistors are so connected that there 1 ends Ans- The maximum potential difference between the two
st

are connected to each other & with one terminal of source electrodes of a cell is called e.m.f. of the cell while the cell
of current while 2nd ends are connected to each other & is open circuited.
with 2nd terminal of source of current. This combination is Or
called parallel combination of resistors . In this combination The potential difference developed across the terminal
all the resistors have same potential difference across there of the electrodes of a cell due to chemical reaction inside
ends. it is called e.m.f. of a cell while the cell should be in open
Derivation:- let us consider three resistors R1, R2 & R3 circuit. Or
connected parallely with a cell of P.d. V as shown in figure. The energy imparted by the cell to flow a unit charge in
I1 R1 the complete circuit, i.e. inside and in the external circuit is
I2 R2 called e.m.f. of the cell. Or
I3 R3 The work done by a cell in rotating a unit charge in
I complete circuit, i.e. inside and in the external circuit of
E K
+ - () cell is called e.m.f. of the cell .
It is obvious that when current I Or
reaches at point A, it will divide into 3 parts I1, I2 & I3 The work done by a cell shifting a unit positive charge
i.e. I = I1 + I2 + I3 ...............(1) from one terminal to another terminal of cell, when the
Let V be the potential difference across each resistor than cell is in open circuit, is called e.m.f. of the cell
value of current flow through each resister will be, It is denoted by e . It is a scalar quantity & its S.I. unit is
I1 = V / R1 ............(2) volt.
I2 = V / R2 ............(3) Q -Write difference between e.m.f. & potential
& I3 = V / R3 ............(4) difference .
Let R be the equivalent resistance of the combination Than Ans-
value of total current will be, e.m.f. Potential difference
I = V / R ............(5) i) e.m.f. is maximum potential i)The difference of potential

On putting the value of I1,I2 & I3 & I from equation 2nd, 3rd, difference between two poles of between terminals of a cell

4th & 5th in equation1st we get, a cell when cell is in open circuit. when cell is in close circuit is

V LM V V V OP called terminal voltage or

R NR 1 R3 R3 Q terminal p.d.of cell.
V
VM
L1 1 1O
P ii)e.m.f. word is used for electric ii)e.m.f. word is used for any
R NR 1 R3 R Q
3 sources like cell generator, pair of points in a closed cir-
1 1 1 1 battery &dynamo cuit.
R R1 R3 R3 iii)e.m.f. exists after circuit is iii)p.d. doesnot exist after

Thus the reciprocal of equivalent resistant in parallel borken. circut is broken.

combination of resistors is equal to the sum of reciprocals iv)e.m.f. does not depend on iv) p.d. depends on resistance

of resistances of constitulent resistors. resistance of circuit. between the two points.

Note: When the lenght of the conductor is increased v)Its value is always more than v)Its value is always less than

such that it is increased to n-times of its original lenght, p.d. when cell is discharging e.m.f. when cell is discharging.

then its new resistance will be n2 times of its original vi)It causes the flow of current vi)It is caused by the flow of

resistance. in a circuit conneted to the given current in a circuit .

cell.
Physics for you
Q. Explain Kirchoff’s law for an electric circuit. In one diagonal there is a cell and a taping key 37
nd
Ans. To study an electric circuit Kirchhoff gave two rules connected while in 2 diagonal a galvanometer is
called Kirchhoff’s law. connected.
Law 1 :[Junction rule / current Rule ]: According to this According to wheat stone, when bridge is balanced
rule, “ The algebraic sum of all current meet at any then the ratio of resistance of two arms of one side of
junction of an electrical circuit is always zero.” bridge is equal to the ratio of resistance of another two
Mathematically, I=0 I6 arms of other side of bridge, i.e. P R
e.g. I - I - I + I - I - I + I = 0 I7 I5 Q S
1 2 3 4 5 6 7

I1 I4 Proof:- Let us consider are four resistance P, Q, R &

I2 S are connected in the sides AB, BC, AD & DC of a
this rule is also show the conservation of charges. I3 quadrilateral ABCD as shown in figure. Let on pressing
Law 2 :[Loop Rule / Mesh Rule]: According to this rule, the key K; i be the current flow through circuit. When
“ In a closed mesh the algebraic sum of all e.m.f. is this current i reaches point A. It divides into two parts.
numerically equal to the sum of product of electric current Let i1 go through AB arm & i2 through AD arm. When
to the relative resistance.” i1 current reaches point B it again divides in to 2 parts.
Mathematically, for a closed mesh Let Ig flow through bridge arm & i3 (= i1 - ig) flow
E IR Or E IR 0 through BC arm. Similarly the current ig & i2 meet at
e.g. - Let us consider an electric circuit as shown in figure. junction C and form i4 ( = i2 + ig) current flowing through
I1 E1 R1
A B BC arm. Let G be the resistance of galvanometer.
I2 E2 R2 Now, at the junction B by junction rule,
D C
I1+I 2 R3
i1- i3- ig = 0
E F But in equilibrium conditon, ig = 0
For closed mesh, ABCD So, i1- i3 = 0 Or i1 = i3 ......(1)
-E1 + E2 = - I1R1 + I2R2 Similarly, at junction , D
i2 + ig - i4 = 0
Or E1 - E2 = I1R1 - I2R2
But at equilibrium conditon, ig = 0
For closed mesh, DCFE
So, i2 - i4 = 0 Or i2 = i4 ......(2)
- E2 = - I2 R2- ( I1+ I2 ) R3 Now, by applying mesh rule in closed loop ABDA
Or E2 = I2 R2 + I1 R3 + I2 R3 i 1 P + ig G - i 2 R = 0
For closed mesh, ABFE But at equilibrium conditon, ig= 0
- E1 = - I1 R1- ( I1 + I2 ) R3 So, i 1 P - i2 R = 0
Or i1 P = i 2 R .....(3)
E1 = I1 R1+ I1 R3 + I2 R3
Now, by applying mesh rule in closed loop BCDB
Q. Explain principle of Wheat stone bridge & prove it.
i3 Q - i4 S - igG = 0
Ans. Scientist Wheat stone arranged four resistance in the
But at equilibrium conditon, ig= 0
sides of a quadrilateral as shown in following figure.
So, i 3 Q - i4 S = 0
B
i3 Or i3 Q = i 4 S ......(4)
P ig
A Q C Now by diving equation 3 & 4th we get
rd

G
R S i1 P i2 R
i3 Q i4 S
i4
D
On putting the value of i1 & i2 from equation 1st & 2nd
we get,
Physics for you
 i1 P i2 R P R known resistance (R.B.) ‘R’ is put in 2nd gap XY 38
or
i1 Q i2 S Q S Hence proved Hence, we will have to interchange S by R in 1st formula,
P S
Q. Explain meter bridge. How can you find resistance & i.e.
Q R
resistivity of a conductor by using meter bridge.
Hence the formula for S will be,
Ans. Meter bridge is an instrument which is used to obtain Rl
S ..........(3)
the resistance & resistivity of a conductor . In this there is a (100 l )
wooden plank of about 1m long (little more). On this plank If L be the length of unknown resistance wire & r be the
two L shaped brass strip AM & YC are fitted and a straight radius of wire. Than we know that the specific resistance
brass strip NX is fitted between L shaped strips. A one meter of material of wire will be,
SA
long wire made up of constantan or magnine is fixed between L
the terminals AC on a meter scale as shown in figure. 2
Where ‘A(= r )’ is area of C.S.
So, specific resistance will be,
M N X Y S r2
..........(4)
L
l 100-l By using this formula we can obtain the specific resistance
of material of wire.
Principle and formula:- Process :
Meter bridge works on the principle of wheat stone bridge. (i) 1st of all we make a circuit as shown in figure and
According to it if four resistors are connected as the sides of check it.
a quadrilateral & in its one diagonal a cell is connected while (ii) Now we put the plug in key K so that current can be
on 2nd diagonal, a galvanometer is connected. Than in the drown through circuit & choose a definite value of
balance condition of bridge the ratio of resistances of any resistance R from resistance box & its plug is removed
two arms of one side of the bridge is equal to the ratio of from R.B.
resistance of other two arms on the 2nd side of bridge. If (iii) Now put the jockey on the wire near point A &
PQRS are such resistance than, observe the deflection in galvanometer. Now move it
P R towards C on putting it at different points of wire until we
......(1)
Q S get null point B.
st
If we put resistance box in 1 gap MN & unknown resistance, (iv) Now find the length of wire AB & BC, i.e. l & (100- l )
S is put in the 2nd gap XY. And let we get null point at point B. & on putting the values in formula we can obtain the
Let length of wire AB be l cm. Than it is obvious value of unknown resistance. Repeat the above procedure
that remaining length of wire (i.e. length of wire BC) will be for different value of R from R.B. about 4 or 5 times &
(100 - l ) cm. Let x be the resistance of the wire per unit calculate the value of S.
length .Than, (v) Now, repeat the above process by interchanging
P=lx & Q = ( 100- l) x the gaps for resistance box & unknown resistance S about
st
On using the formula 1 4 to 5 times and at last calculate the values for S and find
lx R l R its average value
Or
(100 l)x S (100 l ) S (vi) Now, find the length of the wire of unknown
R(100 l) ..........(2) resistance L & by meter scale and its radius r by screw
Or S
l gauge at different cross section. Hence, we can obtain
By using this formula we can obtain the value of unknown the value of specific resistance of material of wire of
resistance S. unknown resistance after putting the values in the
st
Similarly if unknown resistance S is put in the 1 gap MN & equation 4th.
Physics for you
Observation Table : Q. Establish a relation between e.m.f. & internal 39
A. For value of S : resistance of a cell.
Resistance box in first gap Ans. Let us consider E be the e.m.f. and r be the internal
value of R in balancing R(100 l)
from R.B. length l in cm (100 - l) cm S l
resistance of a cell. On connecting this cell with an electric
1 circuit of resistance R its terminal voltage become V &
2
electric current flow through the circuit be I. Than, it is
3
Resistance box in second gap obvious that,
aver-
value of R in balancing Rl age E = I ( R+ r ) ......(1)
from R.B. length l in cm (100 - l) cm S (100 l) S
& V = IR ......(2)
On dividing eq. 1st by 2nd we get,
E I(R r) E (R r)
or
B. For value of r : V IR V R
Or ER V (R r) VR Vr
reading of reading of R( E V )
main scale circular scale total reading Or Vr ER VR or r
V
1 LM E V OP RLM E 1OP
2
3
Or r R
NV V Q NV Q .....(3)

With the help of equation 3rd we can obtain value of r

Precautions :- Again on subtraction equation 2nd from 1st we get.
(i) The value of resistance R from resistance box should be E - V = I (R + r) - IR
so chosen that null point be get in the mid section of wire. E - V = IR + Ir - IR
(ii) Jockey must not be rub on the wire.
E - V = Ir
(iii) Shunt should be used with galvanometer.
E = V + Ir
(iv) The plug from key should be removed when the
instrument is in non working conditon. It is obvious from this eq. that the e.m.f. is more than that
Q. What is internal resistance ? Write the factors on which it of terminal voltage.
depends. Q. Explain potentiometer, its principle & uses.
Ans. The opposition offered by an electrolyte in the flow of Ans. Construction:- In a potentiometer, there is a
charge inside a cell is called internal resistance of the cell wooden plank of about 1 m in length & few cm in breadth.
& is denoted by r. On the wooden plank there are 6 -10 (mostly 10) wires
Following are the factors on which it depends : made of magnine or constantan fixed parallely and
(i) On the area of electrodes:- The internal resistance of connected to each other by some brass strips in series. A
a cell is inversely proportional to the area of its electrodes scale calibrated in cm is fixed on the plank & a sliding
dipped in the electrolyte. jockey is fitted in this instrument.
(ii) On the distance between the electrodes:- Internal Circuit diagram & principle :
resistance of cell is directly proportional to the distance
C
between its two electrodes.
(iii) On the density of electrolyte:- Internal resistance of a l
cell is directly proportional to density of electrolyte.
(iv) On the temperature:- Internal resistance of a cell is
inversely proportional to the temperature of electrolyte.
(iv) On the polarisation:- Internal resistance of a cell is C- Storage cell, K- Keys, Rh- Rheostat,
inversely proportional to the polarisation of cell. E- Experimental cell, J- Jockey r- internal resistance
Physics for you
1st we make a circuit as shown in figure. Now if we put the C-storage cell; K,K1,K2- keys; J-Jockey; 40
r- internal resistance; Rh-rheostat; G-galvanometer
jockey at point D’. It is obvious that if the potential difference
AB - resistance wire; E1, E2- Experimental cell,
between A & D’ is less than that of e.m.f. of experimental cell
Formula :- Let E1 & E 2 are the e.m.f. of two
& the deflection in galvanometer will be left ward. When
experimental cells l1 & l2 are the distances of null points
we put the jockey at D”, and if the potential difference
for these two cells & let K be the potential gradient of
between A & D ” is more than that of e.m.f. of experimental
instrument .Than, it is obvious that
cell, galvanometer will show the deflection right ward, So it is
E1 = K.l1 .......(1)
obvious that we can obtain a point D between D’ & D”
& E2 = K.l2 .......(2)
where the deflection in galvanometer be zero, i.e. potential
st nd
On dividing equation 1 by 2 we get,
difference between A & D is equal to the e.m.f. of cell.
E1 Kl1 l1
Let L be the length of wire AB & potential difference .............(3)
E2 Kl2 l2
between AB is V and I be the current flow through it by
with the help of eq. 3rd we can compare the e.m.f. of any
connecting it with storage cell C
two primary cells.
Let x be the resistance of unit length of wire
Procedure :
So, V=ILx ........(1)
(i) 1st of all make a circuit as shown in figure.
If distance from A to D be l than e.m.f. of cell will be,
(ii) Now insert plug in key K & than in K1 & put the
E = Ilx ........(2)
jockey near point A on the wire & move it towards point
On dividing eq’n 2nd by 1st we get,
B, by touching the jockey on the wire at different point
E Ilx E l
Or until we get null point and find the distance of this null
V ILx V L
FG IJ
V
point from point A (i.e. l1).
Or E
H K L
l (iii) Now, remove the plug from key K1 & insert in key
K2 and repeat the above process to obtain l2.
But V/L = K (potential gradient of instrument)
(iv) On putting all the values in formula we can compare
So, E = K.l
the e.m.f. of two cells.
with the help of this equation we can obtain e.m.f. of cell.
Observation table :
Uses :
balancing balancing E l
(i) To compare the e.m.f. of two primary cell. 1 1
length l1 in cm length l2 in cm E2 l2
(ii) To calculate the internal resistance of a primary cell. 1
(iii) To find the potential difference b/w any two point of an 2
3
electric circuit.
Precaution :
(iv) To calibrate voltmeter & ammeter.
(i) The e.m.f. of storage cell should be more than e.m.f.of
(v) To find temperature.
experimental cells.
Q. How can you compare the e.m.f. of two primary cell by
(ii) positive terminals of all the cells should be connected
using potentionmeter ?
with same terminal.
Ans. Circuit diagram:-
(iii) Jockey should not be rubbed on the wire.
CC r
(iv) Shunt should be connected with the galvanometer
& should be remove near null point.
(v) Plug from key K should be removed while the instru-
E1 K1 ment is not in working condition.
E2 Q. How can you find the internal resistance by using
K2
potentiometer of a primary cell ?
Physics for you
Ans. Circuit diagram : Q. Explain the combination of cells. 41
C r Ans. There are three such combination of cells are
possible :
(i) Series combination of cell:- In the series
combination we connect the negative terminal of 1st cell
to the positive terminal of 2nd cell. Than, negative terminal
R.B. of 2nd cell is connected to the positive terminal of 3rd cell
C - storage cell; K-keys; Rh - rheostat; J - jockey and so on. At last the combination is connected with a
r - internal resistance E- experimental cell, load R as shown in figure.
Formula:- We know that the internal resistance of a cell can be
given by following equation.
LM E 1OP
r R
NV Q
let l1 & l2 be the balancing lengths for e.m.f. & terminal Let n cells of e.m.f. E each & internal resistance r are
voltage of cell & K be the potential gradient of potentiometer, connected in series than,
then, E =K.l1 & V = K.l2 Total e.m.f. of combination across load = nE

So r R
LM K l 1OP
1
And total internal resistance,
N Kl Q 2 rS = r + r + r ............n times = nr

Or r RM
L l 1 OP
1
............(1)
And total resistance = nr + R
Nl Q
2 Now, current drawn through load -
By using this formula use can calculate the internal resistance total e. m. f . nE
I ................ (1)
total resis tan ce nr R
of a cell.
Case -1 When nr >> R
Method:
Than, from equation 1st
(i) 1st of all make a circuit as shown in figure. nE E
(ii) Now, put the plug in key K & without removing any key I ( current through one cell )
nr r
from resistance box put the jockey on the wire near point A & Case -2 When nr << R
move it towards point B on touching different points of the wire. Than, from equation 1st
Till we get null point and measure the balancing length l1 cm. nE E
I n n current throughonecell
(iii) Now, choose a resistance from resistance box & remove R R
Hence, “we can say that the series combination of
its plug and again find the balancing length l2 as above.
cells is fruitful when internal resistance is much less
(iv) On putting all the values in formula we can calculate the
than that of external load”.
value of r .
2. Parallel combination of cell :- In the parallel
(v) For different value of R from R.B. repeat the above process combination of cells positive terminal of all cells are
& calculate the value of r in each case & at last obtain the connected with one point while negative terminal with
average value or r.
2nd point. Now, these two point are connected with a
Observation Table :
load as shown in figure.
value of R from balancing balancing
resistance box length l1 length l2 r R
LM l 1OP
1

in in cm in cm Nl Q
2

1
2
3
Precautions:- Same as that of previous question.

Physics for you

Let, n cells of e.m.f. E each and internal resistance r each 1 1 1 1 1 m 42
........... m times
are connected in parallel combination with load R rp rs rs rs rs rs
Than, net e.m.f. across load will be = E 1 m Or nr
rp
let rp be the net internal resistance of the combination than, r p nr m
1 1 1 1 1 n Now, total resistance of the circuit
........... n times
rp r r r r r nr m R nr
R net R
r m m
Or rp
n Now, current drawn through load,
And the total resistance of combination Total em f nE
r I
Rtotal R Total resis tan ce mR nr
n m
Now, current drawn through load, nm E
total e. m. f . E nE Or I
I .....(2) mR nr
total resis tan ce r r nR
R It is obvious that for maximum value of I , (mR + n r )
n
Case -1 When r >> R should be small & for smallest value of (mR + nr),
2
Than, from equation 2nd we get, nr mR nr mR 2 nr . mR
nE E It is obvious from above equation that for minimum value
I n n current throughonecell
r r of (mR + nr)
Case -2: When r << R 2
nd
nr mR 0 or nr mR 0
Than, from equation 2 we get
nE E
I ( current through one cell ) Or nr mR Or nr mR
nR R
Hence, “we can say that the parallel combination mR nr
So r or R
of cell is fruitful only when internal resistance is much n m
greater than that of load R.” now the maximum value of current will be
(3) Mixed Combination :- In this combination we nm E nmE nE
I m ax
connect some cells in series and some such series are mR mR 2mR 2R
connected parallely and this combination is now connected nm E nm E mE
with a load as shown in figure. I m ax
nr nr 2 nr 2r
E rE r E rE r
Thermister:- The devices made by the oxides of
semiconducting materials, whose resistance decreases very
rapidely with increase in temperature. The temperature
coeficient of these material is very high and negative.
let e.m.f. of one cell, be E & internal resistance be r let n cells Ohm’s law in vector form:- We know that by the
are connected in one series & m such series are connected formula of drift velocity eV
vd
parallel with a load R 2 ml
Net e.m.f. of one series here vd is drift velocity; e is charge on an electron; V is
= E + E + E ........n times = n E potential difference across the conductor; is relaxation
Since, all the series are connected parallel Than, net e.m.f.of time; m is the mass of an electron and l is the length of
combination will also= n E conductor.
Let rS be the net resistance of one series & rp be the net but we know that by the relation between potential
internal resistance of whole combination. difference and intensity of electric field.
So, rS = r + r + r ......... n times = nr & V eE
E So vd
l m
Physics for you
but the current density can be written as 43
J= nevd
eE ne 2 E
So J ne
m m
but we know that
m 1
So J E Or E J
ne 2

Or in vector form E J or J E

To memorise the colour codding one from following lines

has to be remember.
1. B B ROY Grate Bretain Very Good Wife
2. Bye Bye Rosie Off You Go Brestal Via Grate Western.

Physics for you