CURRENT ELECTRICITY CBSE -...

CURRENT ELECTRICITY CBSE

Res: 249, Chotti Baradari Part-2, Near Medical College, Jalandhar #98152-15362 1

CURRENT ELECTRICITY

Electric Current : The current ‘i’ is same for all cross-sections of a conductor, even though the cross-sectional area may be different at different points. This constancy of electric current follows because charge must be conserved it does not pile up steadily or drone away steadily from any point in the conductor under the assumed steady state conditions.

The existence of electric field inside a conductor does not contradict E = 0 inside the conductor condition of electrostatics. In electrostatics we dealt with a static in which all net motion of charge had stopped and assumed that conductor was insulated and no potential difference applied across it. In this there is no such condition. The direction of current does not signify at all that current is a vector quantity because the current does not obey the rules of vector addition. Charge carriers can only move along the wire. They do not have any direction of their own.

We know that potential is the property which determines the direction of flow of current. If we have two bodies placed certain distance apart at different potential. If there is no connection between them their potential remains constant but once they are connected, charge (positive) flows from body at higher potential unless their potential becomes equal.

But this is an instantaneous process and completes in a very short interval of time. To maintain current flow in between two bodies continuously we have to connect them across with a source of emf which helps in maintaining potential difference between them and current is defined as the rate of flow of charge across a cross-section of the conductor.

T

QI =

This relation holds good for uniform charge flow. For non-uniform charge flowing across any cross section of the conductor the relation will be,

dT

dQI =

Units of electric current :

(i) In SI, the current flow is measured in Ampere and current is said to be one ampere if one coulomb of charge flows across any cross section in one second.

sec1

11

coulombampere=

(ii) In cgs (e.s.u.) system, the current flowing across any cross-section is measured in stat-ampere and

sec1

11

coulombstatamperestat

−=−



(iii) In cgs (electromagnetic unit) system, the current flowing through a conductor is said to be measured in ab-ampere.

sec1

11

arg echofemuampereab =−

Relation between units of current :

ampereabamperestatampere

coulombstatcoulombampere

−=−=

−==

10

11031

sec1

103

sec1

11

9

9

Conventional current :

By convention, the direction of flow of current is taken to be the direction of flow of positive charge. The electrons always flow in direction opposite to marked in circuit diagrams.

Charge carriers in Substances :

In Solids :

In solids the charge carriers are the free electrons. As we know that in certain substances outermost orbits are very loosely bound to nucleus due to their large distance from nucleus. Hence these electrons are assumed to be free electrons. When potential difference is applied across two ends of such a conductor electrons flow from lower to higher potential.

In Liquids :

Liquids are classified into two categories depending upon their electrical properties. Electrolytes are the liquids which conduct electricity and non-electrolytes are liquids which do not conduct electricity or we can say that liquid which can break into their ionic form are electrolyte or conductors and liquids which do not break into ionic form are insulators. The charge carrier in electrolytes are the positive and negative ions.

In Gases :

Gases are normally insulators and do not conduct due to absence of any kind of free charges in them. But when the gas gets ionised due to passage of X rays etc., the positive and negative ions carry the charges. In gases if X rays strike the gas atom it knocks out an electron from it. The electrons thus acts as negative ion and which loses electrons acts as positive ion.



Type of currents :

The electric current can be classified into the following categories :

(i) Steady current : The current whose magnitude remains constant or does not change with time is called steady current. As shown in figure curve [A] represents steady current

(ii) Varying current : The current whose magnitude does not change with time is called varying current. Alternating current is an example of varying current. Curve [B] and [C] represents varying current.

Drift Speed :

A conductor contains large number of loosely bound electrons which we call free electrons or conduction electrons. The remaining material is collection of heavy positive ions called lattice. These ions keeps on vibrating about their mean positions. The average amplitude of vibration depends upon temperature. Occasionally, a free electron collides interacts in some other fashion with the lattice. The speed and direction of electron changes randomly at each such event. As a result electrons moves in a zig-zag path. As there is a large number of free electrons moving in

random directions, the number of electrons crossing unit are S from side nearly equals the number crossing from other side in any given interval. The electric current through the area is therefore zero.

When there is an electric field inside the conductor, a force acts on each electron in a direction opposite to the field. The electrons get biased in their random motion in favour of the force. As a result the electrons drift slowly in this direction. At each collision electrons starts afresh in random direction with random speed but

gains an additional velocity v due to electric field. This velocity v increases with time and suddenly becomes zero as the electron makes collision with the lattice and starts afresh with random velocity. As a result time t between successive collisions is small, the electrons slowly and steadily drifts opposite to applied field. If the electron drifts a distance ‘l’ in long time t, we define drift speed as

tvd

1=

The average time between two successive collisions is called the relaxation

time. If is the relaxation time, average distance drifted during this period is

22

2

1

2

1

==

m

eEal

The drift speed is thus

====

m

ekwherekE

m

eEvd

22

1



The constant k depends upon the material of the conductor and its temperature. Consider a cylinderical conductor with area of cross-section ‘a’ and charge density (i.e. number of electrons per unit volume) be ‘n’. In time dt electrons will transverse a length equal to vddt.

The total number of charges in this length of conductor = n A vd dt

Total charge in this length = n e A vd dt = dq

dneAvdt

dq=

I = n e A vd

and current density

dnevA

ij ==

The direction of the drift velocity →

v of a positive charge is the same as that of

the electric field →

E and the direction of velocity →

v of negative charge is opposite to →

E . Thus even in a metallic conductor where moving charges are negative electrons

only and move in opposite direction to →

E , the vector current density →

J is in the

same direction as →

E .

Ohm’s Law :

It states that if physical conditions remain unchanged, he current flowing through a conductor is always directly proportional to the potential difference applied across conductor.

V I

V = IR

Where R is constant of proportionality called resistance of the conductor. Resistance is a quantity, which depends upon the nature of material and its dimensions. Although resistance id independent of V and I. For conductors, which obey Ohm’s law, V- I graph is a straight line as shown in the figure.

Units of resistance: mathematically resistance is the ratio of potential difference applied across conductor to the current flowing through it..

thus, its SI units are volt/ampere or commonly called ohm[].

1 ohm = ampere

volt

1

1

Thus, resistance of the conductor is said to be I ohm, when unit potential difference [i.e volt] applied across conductor results in unit current [i.e. 1 ampere] through it.



Cause of resistance: The resistance of conductor physically implies opposition to the flow of current. When potential difference is applied across the conductor the electros gets accelerated. But as they accelerate, they collide with other atoms and ions and their motion is opposed. This opposition is called resistance of the conductor.

Non- Ohmic Conductor: the conductor which don’t obey ohm’s law or which V-I curve is not a straight line are called non-ohmic conductors. Even for non-ohmic conductors relation = IR can be used but for such conductors, R will not be constant s in the case of ohmic conductors. For e.g. thermistors, thyristor, diode etc.

Failure’s Of Ohmic Law: The few cases where ohm’s law is not obeyed is

[a] Potential difference may vary non-linearly with current: When current flows through a conductor, the temperature of the conductor begins to increase due to heating effect of the current. As the temperature rises the resistance of the conductor increases. Increase in resistance with temperature results n V-I deviating from straight line.

[b] Variation of current with potential difference applied depends upon the direction of electric field inside the conductor: This happens generally in the case of semiconductor diodes which allow one way flow of current. When positive terminal of battery is connected with p type and negative with n type resistance is small and when connections are reversed resistance is large

Color coding of Resistance :

Commercial resistances available in market have their magnitude written in the form of color codes. The two color code systems used are:

(i) We associate a color with each digit, 0, 1, . . . . . ., 9

Black = 0, Brown = 1, Red = 2, Orange = 3, Yellow = 4, Green = 5, Blue = 6, Violet = 7, Gray = 8, White = 9

The three coloured bands on one side indicate its resistance. The first two bands [A and B] from one end indicate the corresponding digits while third band’s color indicate powers of ten with which number must be multiplied to get the resistance value in ohm.

In addition to three bands, fourth band gives us tolerance with silver band implying tolerance of ± 5% and gold band with tolerance of ± 10%. No fourth band indicates resistance of ± 20%. For example, if four bands are of yellow, red, blue and

gold then resistance will be (42 106) ± 5%

(ii) In second system, the body of the resistance is of one color, the end are given another color while a dot is marked over the body. A ring on one side determines tolerance. The colour code remains same.



Factors affecting the Resistance of Wire (Resistivity) :

The resistance of material depends upon nature of conductor, its shape and size. Simple considerations show that: Resistance of conductor is directly proportional to length and inversely proportional to the area of cross-section of conductor.

a

lRor

a

lR

=

where is the constant of proportionality called the resistivity of the material. Its value is constant for a given material, independent of shape and size of

the conductor. As =l

RA, therefore if length and area are changed resistance of the

conductor changes in such a fashion that the resistivity remains constant. The units

of are mohmm

m

l

RA−=

==

2

.

NOTE : As potential difference is applied across length of conductor, electrons move from lower to higher potential. In the process they collide with each other and their motion is retarded. Now, if the length of the conductor is increased it will experience greater number of collisions and hence the resistance increases.

Similarly, larger area of cross-section means large number of electrons will cross the cross-section of conductor in one second, thereby giving a larger current. Larger the value of current smaller will be the resistance (according to Ohm’s law)

Conductivity:

Conductivity is defined as the reciprocal of resistivity or specific resistance. Therefore large resistivity implies smaller conductivity and vice-versa. It is generally

denoted by .

1=

It is measured in ohm—1 m—1 or mho/m

Conductance :

The reciprocal of resistance of a conductor is called conductance. It is denoted by C. The conductance

RC

1=

It is measured in ohm—1 or mho. It is also measured in Siemens.



Origin of Electric Resistance :

When electric field is applied across the conductor, the electrons are accelerated but as they accelerate they collide with positive ions of crystal lattice which retards their motion. Thus, the electrons after some time acquires a constant velocity.

For a perfect crystal lattice with all positive ions fixed, regularly at specified positions it can be proved quantum mechanically that conduction electron moves freely through the lattice under action of external field. However, no metal is composed of perfect crystal lattice. In some instances the imperfection is due to impurities that replace some of the metal ions. In addition to ions are always vibrating as a result of thermal energy. Since vibrating as a result of thermal energy. Since ions do not vibrate in phase, the distances between ions fluctuate. This fluctuation is equivalent to imperfections in crystal lattice. The electron thus suffers numerous scattering as a result of these imperfections and sometimes even moves backwards. Therefore rather than picking up energy continuously from electric field, the electron transfers some energy to lattice. After a short period of time a steady state is reached where average velocity becomes constant.

Effect of temperature on Resistance :

It was experimentally found that resistivity is inversely proportional to the

relaxation time, because smaller value of will mean more frequent collisions and hence larger resistivity. The relaxation is dependent on temperature of the given substance. An increase in temperature will mean that ions and atoms are vibrating more vigorously about their mean position and thus the frequency of collision increases. Hence a rise in temperature for conductors result in increase in resistivity of material. For some substances the increase in resistivity is linear such that we can write,

t = 0 ( 1 + t )

where t and 0 are the resistivities at tºC and 0ºC.

The constant is defined by,

t

t

0

0

−=

is known as linear coefficient of resistivity. It can be defined as change in resistivity per unit original resistivity per degree rise in temperature.

Even for metals, resistivity increases as higher power of T for low temperatures. For insulators and semiconductors resistivity increases exponentially with decreasing temperature.

(T) = 0(T) eEg/kT



where Eg is forbidden gap energy and k is Boltzmann constant. For insulators or semiconductors resistance decreases with increase in temperature because of the number of charge carriers available for conduction. There is an exponential increase in number of charge carriers.

Semiconductors:

In semiconductors the number of charge carriers per unit volume ‘n’ increases rapidly with increasing temperature. The increase in ‘n’ for outweighs increase in ‘u’ and the resistivity decreases. At low temperatures, n is very small and resistivity becomes so large that molecule can be considered insulator.

The modern theory of super conductivity predicts that in effect at temperatures below the critical temperature the electrons moves freely throughout the lattice. The

mean free path then becomes very large and resistivity is very small.

Superconductivity:

We have seen that as the temperature of conductor decreases the resistance also goes on decreasing. It was found by Onnes that mercury possessed zero resistance at temperature of 42K i.e. mercury has become superconductor. Later it was found that all conductors had their resistivity decreased to zero at certain value of temperature called critical temperature of conductor. Thus critical temperature can be defined as the temperature at which resistivity falls to zero and the conductor becomes superconductor.

A body is said to be superconductor if current flowing through it, keeps on flowing for 1017 years without any decay.

The critical temperature of pure metals is very low therefore alloys are developed whose critical temperature should be high. In 1987 a ceramic yittrium, barium and copper oxide was found to have TC as 90K.

The cause of superconductivity is that at low temperature the electrons do not remain independent and move in coherent clouds. Ionic vibrations are unable to deflect cloud of electrons whereas they can defect single electrons. Now, why the clouds start behaving in coherent fashion at low temperatures is yet not known.

Uses of Superconductivity:

(i) It is used for generation of very strong magnetic fields.

(ii) It is used in cryogenic space technology.

(iii) It is used in very high speed computers.



Now, if some day we are able to manufacture superconductors at daily life temperatures (300K – 320K) they can be used to transmit power without energy loss.

Relation between Relaxation Time and Resistivity:

The average time between two collisions is called relaxation time. Consider a conductor placed in electric field, E. The force experienced by electrons present in

electric field is, →→

= EeF .

The acceleration of electrons m

Eea

→

=

The drift velocity, vd = u + at

m

eEatuvd =+=

Also, if A is the cross-sectional area of the tube then vd is given by

Vd = I/neA

m

eE

neA

I=

m

ne

EA

I 2=

Also E = l

V, Substituting the value we get

As RA/l is the resitivity of the material, thus the Conductivity and resistivity are given by

2

2

ne

m

m

ne

=

=

This relation implies that if we increases the temperature of the conductor, the mass number density and charge on electron are constant. But the collisions becomes more freqent. Thus the relaxation time decreases and resistivity increases.



Resistors in Series and Parallel:

Most electrical circuits consists not merely of single source and single external resistor but comprise of number of resistors of capacitors etc. interconnected in a complicated manner. Such a circuit is called a network.

It is always possible to find a single resistor that should replace a combination of resistors in given circuit and leave unaltered the potential difference between the terminals of the combination and the current in rest of the circuit. The resistance of this resistor is called equivalent resistance of the combination.

Series Combination

If we have number of resistors connected in SERIES combination, the current in each resistor must be same and equal to the line current I, but the potential difference across each resistor is different such that if V1, V2, V3 be the potential difference across R1, R2, R3 then potential difference across series combination is V such that,

V = V1 + V2 + V3

or IR = IR1 + IR2 + IR3 (I must be same)

R = R1+R2+R3

For a combination of n resistors

R = R1 + R2 + - - - - - - - + Rn

The equivalent resistance of any number of resistors connected in series equals the sum of their individual resistances.

PARALLEL combination:

Resistors are said to be connected in parallel if one end of all the resistors are connected at one point and the second end at the other point. As all the resistors are connected between the same two points therefore potential difference between the terminals of each must be same. If we have number of resistors in parallel then current in each must be,

nn

R

VI

R

VI

R

VI === ,,,

22

11

Charge is delivered at point a by line current I and removed from a by currents I1, I2, - - - - - , In such that

I = I1 + I2 + - - - - - + In



n

n

RRRRor

R

V

R

V

R

V

R

V

1111

21

21

+++=

+++=

Thus, for any number of resistors in parallel, the reciprocal equivalent resistance equals the sum of reciprocals of their individual resistances.

Current in Parallel Combination:

If I be the total current flowing in parallel combination of two resistors R1 and R2, then,

I = I1 + I2

where I1 and I2 are currents in individual resistors R1 and R2 respectively.

2

211

2

11

2

111 1

R

RRI

R

RI

R

RIII

+=

+=+=

21

21

RR

IRI

+=

Similarly, the current in the second resistance R2 is,

21

12

RR

IRI

+=

Kirchoff’s Rules:

These are the rules used for simplifying complicated electrical circuits.

Branch Rule or Junction Rule:

A junction point in a network is a point where three or more conductors are joined. According to this rule algebraic sum of currents towards a junction point is zero. That is,

I = 0

Sign Conventions:

The current metering a junction is said to be positive and current leaving the junction is said to be negative.

The point rule is an application of conservation of charge. Since no electric charge can accumulate at a branch point the total current entering is always equal to the total current leaving.



Loop Rule:

Loop is any closed path in an electrical circuit. According to the Loop Rule, algebraic sum of all the emf’s is always equal to the sum of product of current and emf i.e.

E = IR

Sign Conventions:

a. Choose any closed loop in the network and designate the direction (clockwise or anticlockwise) to transverse the loop applying Loop Rule.

b. Go around the loop in the designated direction, adding emf’s and potential differences. An emf is counted as positive when it is transversed from negative to positive and negative otherwise. Similarly, product of current and resistance is positive if the direction of current is same as the direction in which we are transversing the loop, otherwise it is negative.

These basic rules are used to solve variety of network problems. Usually in problems some of the emf’s currents and resistances are known and others are unknown. The number of equations obtained from kirchoff’s rule must always be equal to the number of unknowns, to permit solution of equations, the following principles should be followed carefully.

First all quantities known and unknown are labelled carefully, including an assumed sense of direction for each unknown current. Often one does not know in advance the actual direction of current but this does not matter. The solution is carried out using assumed directions the value of quantity will come out to be negative if actual direction is opposite to assumed direction. Hence kirchoff’s laws gives us correct value of unknown current and emf’s.

Ammeters:

An ammeter is the instrument used for measurement of current in a circuit. Ammeter is essentially a galvanometer which is inserted in the circuit in series so that the whole current in the circuit passes through it. The deflection produced in ammeter is measure of current flowing through it. Since the coil of ammeter has some resistance, so on connecting it in series the resistance of circuit increases and current flowing through it decreases. Therefore, current read by ammeter is less than actual current flowing in the circuit. Thus, resistance of ammeter should be as small as possible, so that connecting it in the circuit does not change the current appreciably. Suppose emf of the cell be E, when connected in circuit having resistance R, current flowing will be

1R

EI =

On connecting ammeter in series in the circuit, the resistance of circuit becomes (R1 + RA) where RA is the resistance of ammeter and current reduces to



ARR

Ei

+=

1

'

Therefore, deflection of the ammeter shows i although current to be measured was i. For converting galvanometer to ammeter a small resistance called shunt is connected in parallel in the circuit. The combined resistance of the galvanometer and shunt is less than the resistance of the galvanometer and shunt. Therefore, when it is connected in circuit it does not produce an appreciable change in the circuit.

Another advantage is that when shunt is connected in circuit most of the current tends to pass through shunt and only fraction of total current will pass through galvanometer. Since deflection of coil is proportional to current passing through it, the deflection is sufficiently reduced. Hence now there will be full scale deflection of the coil for much larger current in the circuit.

Let i be the current flowing in the main current circuit and ig through galvanometer then current through shunt will be,

igG = (i − ig) S

g

g

ii

GiS

−=

Thus, with shunt in circuit galvanometer of range ig is changed into ammeter of range i ampere.

Conversion of Galvanometer into Voltmeter:

Voltmeter is a device used for measurement of potential difference between two points.

Voltmeter is basically a galvanometer with high resistance connected in series with it and is connected across two points between which p.d. is to be measured. The deflection produced in voltmeter is the measure of p.d. between two points. Since however, it is connected across two points, the potential difference between those points is changed.

Suppose p.d. is to be measured between two points a and b, before connecting the cell. The current in the circuit is,

21 RR

Ei

+=

The potential difference between them is

21

22

RR

ERiRV

+==

On connecting voltmeter of resistance RV, the current becomes,



21

22

21 '

'''

''

RR

ERRiVor

RR

Ei

+==

+=

To eliminate error in calculation R2 = R2

VRRR

111

2

+=

01

=VR

or RV =

Thus, ideal voltmeter should have infinite resistance. Suppose a is the resistance of galvanometer and we connected high resistance R in series with it. Suppose on connecting it between points a and b of a circuit, a current ig flows through it. If potential difference between a and b is V.

Gi

VRGRiV

g

g −=+= )(

If current ig in the coil produces full scale deflection then there will be potential difference V between a and b. Thus on connecting R galvanometer of range ig is changed to a voltmeter of range V.

Wheatstone bridge :

Wheatstone bridge is a special electrical circuit used to determine the value of unknown resistance. It consists of four resistances P, Q, R and S connected across as arms of a parallelogram. In one diagonal a galvanometer is connected in other diagonal a cell. The current i flowing in the circuit gets divided into two parts at A

a) i flowing through P and (i − i1) flowing through R.

b) Similarly on reaching B, i1 gets divided with ig flowing through

galvanometer and (i − ig) through Q.

c) Current flowing in S will be (i − i1 + ig).

Writing loop equation for the loop ABDA,

i1 P + ig G − (i − i1) R = 0

Similarly, for the loop BCDB,

(i1 − ig) Q − (i − i1 + ig) S − ig G = 0

Change the value of variable resistance R till B and C are at same potential. Thus, no current will flow through galvanometer or ig = 0. Hence, two equation becomes,

i1 P − (i − i1) R = 0



and i1 Q − (i − i1) S = 0

or S

R

Q

P=

This is called balanced wheatstone condition. Knowing the value of three resistances, fourth resistance could be easily calculated. The bridge has maximum sensitivity when all the four resistances are of same order.

Unsuitability of Wheatstone bridge:

Four arm wheatstone bridges are best suited for measuring medium resistance. If the resistance are very much high, R1, R2, R3 and R4 should also be high, then current through galvanometer will be small and bridge will not be sensitive.

If the resistance to be measured is very low, then for bridge to be sensitive all the resistances shall be low. The galvanometer should also be of low resistance which itself is very insensitive. Further the effect of variable contact resistance becomes noticeable and the error due to them may be 0.1 percent or more. This is because, for reason intrinsic to the nature of bridge, the contact resistance being in series with arm resistors are included in measuring network.

Meter Bridge:

Meter bridge is a device used for determination of resistance using wheatstone bridge principle. It consists of 1m long manganin or constanton wire fixed along a scale on a wooden base. The area of cross section of the wire should be uniform throughout. The wire is connected between two copper strips. Another copper strip is fixed between two strips to provide two gaps. A resistance box is connected between one gap and unknown resistance in second gap. A galvanometer is connected to terminal D on one side and jockey on the other. The position of jockey is adjusted on the wire so that balance point is obtained and galvanometer shows no deflection. Let the length of resistance of

wire AB = kl. Resistance of wire BC = k (100 − l).

According to the principle of Wheatstone bridge,

X

R

Q

P=

−=

−==

l

lR

l

lkR

P

RQX

100)100(



Potentiometer:

Potentiometer is also a device used for measuring potential difference accurately.

Principle:

Whenever steady current passes through a wire of uniform area of cross-section, potential difference between any two points on the wire is directly proportional to the length of the wire between the points.

Proof:

Consider a wire of resistivity and uniform area of cross-section, therefore, resistance per unit length will be

Al

R ==

Resistivity of material is always constant if physical conditions remains unchanged, thus if area of cross section is also constant, we can say that resistance per unit length is constant, the potential difference per unit length is,

e = r I (if I is constant, e is also constant)

and the potential difference per unit length can be used to find potential difference between two points as

V = el or V l

which is the potentiometer principle.

Applications of Potentiometer:

Potentiometer can be used for three main purposes:

1. Finding EMF of a cell:

The circuit diagram for comparing emf is shown in figure. The auxillary circuit consists of a battery, a rehostat and a key. The cell whose emf is to be determined is connected with positive terminal at A and negative terminal connected with galvanometer. The other end of galvanometer is connected to a jockey which moves on the potentiometer wire AB.

As positive terminal of cell is connected to A so it will have the same potential as A. Now jockey is moved on the wire, the galvanometer shows deflection. At one particular point the galvanometer shows a null deflection. This is called null point. This will be achieved if emf of a cell is equal to the potential difference between the wire AN. If length of wire AN is l, then according to potentiometer principle,

l or = kl



where k is the potential difference per unit length.

2. Comparing EMF of cell:

The circuit diagram is shown in figure (B). The method of calculating emf of comparing emf is same. The only difference is that we have to attach two cells in place of one using two keys. First the emf of one cell is determined by inserting key

k1. If null point is obtained at a distance l1 from A then1 l1 or 1 = k l1

Similarly, null point is obtained for the second cell by inserting key k2. If null point is obtained l2 from A then

2 = k l2

or

2

1

2

1

l

l=

3. Determination of internal resistance of cell:

We know that internal resistance of a cell is given by

RV

VEr

−=

where E, V and R are emf, potential difference and external resistance of cell respectively. The value of emf and potential difference are determined using potentiometer circuit.

First keeping the key k open jockey is slided along the wire to get a balance point. If l1 is the length of wire giving the balance point at P, then emf of the cell is given by,

= k l1

where k is the potential difference per unit length.

The key is now closed and again balance point is obtained by sliding the jockey over the potentiometer wire. Let l2 be the length of wire giving the balance point in this case. This potential difference V across the terminals of the cell is,

V = k l2

Substituting for E and V,

Rl

llr

Rkl

klklr

−

=

−

=

2

21

2

21



Conceptual Questions

Q.1 Is there any change in drift velocity of the electrons with rise in temperature of the conductor?

A.1 Drift velocity of the conductor s directly proportional to the relaxation time for the conductor. With rise in temperature the collisions of electrons becomes

more frequent and thus relaxation time decreases. If decreases the drift velocity of the electron will decrease.

Q.2 Is Ohm’s law applicable to all conductors of electricity? A.2 No, ohm’s law is applicable to only to conductors for which V-I curve is a

straight line. Q.3 The connecting wires are made of copper. Why? A.3 The connecting wires are made of copper because the electrical conductivity of

copper is large or it has low value of specific resistance. Also copper is a diamagnetic material and it does not get magnetized on passing current through it.

Q.4 The specific resistance of copper is . It is stretched to double its length. What will be the new resistivity?

A.4 The new resistivity will be again as changing the dimensions of the wire never changes the resistivity of the material.

Q.5 What do you understand by the term electromotive force? What are its SI

units? A.5 EMF is the potential difference between the terminals of the cell when no

current is drawn from it [or it is an open circuit]. The SI unit for measuring emf of the cell is volt.

Q.6 Explain why I parallel combination the effective resistance of the combination

decreases? A.6 In parallel combination the cross-sectional area of the wires through which

given current has to pass increases. As resistance is inversely proportional to the area the resistance decreases on increasing the area.

Q.7 Is electric current scalar or vector quantity? Explain. A.7 Electric current has both magnitude and direction but for given quantity to be a

vector, it must obey the laws of vector addition but current add just like any scalar quantity.

Q.8 On increasing current drawn from the cell, the potential difference decreases.

Why?



A.8 As V = rR

ER

+, the current drawn can be increased by decreasing the external

resistance R. If value of R decreases the potential difference will also decrease. Q.9 Can terminal potential difference of the cell exceed its emf? A.9 Yes terminal potential difference can be greater than emf of the cell during

charging of the cell, as during charging they are related as V =E + Ir. Q.10 Why constantan and manganin are used for making standard resistance coil? A.10 Constantan and manganin are used for making standard resistance because of

their low value of temperature of resistance i.e. change in their resistance due to change in temperature is negligibly small. Moreover they are not affected by the change in atmospheric conditions like moisture etc.

Q.11 What is the order of number of free electrons in a metal? What is their

significance? A.11 The number of free electrons per unit volume in SI is 1029 m-3. The significance

of these electrons is that when potential difference is applied they constitute the electric current which flows through the metal.

Q.12 What is the significance of direction of electric current? A.12 Electric current always flows from higher to lower potential i.e. it is the

direction of flow of positive charges. Electrons flows in direction opposite to the direction in which the electric current is marked.

Q.13 Why current is not possible without applying source of emf? A.13 The motion of charge carriers in the absence of the electric potential difference

is random and can’t constitute a electric current. But, even if there is some initial potential difference between the two points but no source of emf this potential difference will reduce to zero if we connect the two points in fraction of a second.

Q.14 Is ohm’s law valid for all conductors? A.14 No, Ohm’ law is valid for only metallic conductors for which graph V-I is a

straight line. Q.15 What is the effect of temperature on relaxation time for electrons? A.15 Relaxation time for conductors is the average time between two successive

collisions of electrons. When temperature is increased the collisions becomes more frequent and the relaxation time decreases.

Q.16 Can we use the relation V = IR for non-ohmic conductors also? A.16 yes, we can use the same relation or ohmic as well as non-ohmic conductors.

For Ohmic conductors the resistance remains constant and for non-ohmic conductor resistance in relation is variable.



Q.17 What is the resistance of human body and what is the voltage, which can be dangerous for the human body?

A.17 The resistance of dry human body is 10 k. Any current above 0.01A can be dangerous for the human body thus voltage which can be dangerous is 100V or more than it.

Q.18 When we switch on the electric bulb it glows instantaneously although the drift

speed of the electrons is very small. Explain. A.18 When we switch on the electric bulb it begins to glow instantaneously, this

happens because although the drift speed of the electrons is small the electric field is established in the whole of the wire with the speed of the em waves i.e. 3 x 108m/s.

Q.19 Can we use six primary cells in series in place of 9V car battery to operate the

car? A.19 No, because although the emf will be same for both but primary cells have

large internal resistance. Thus although the emf is same the current which they can supply is far less as compared to the secondary cell.

Q.20 When cells are connected in parallel, what will be the effect on [a] current

capacity [b] emf of the cells? A.20 The current capacity will increase in parallel combination of the cells whereas

the effective emf in parallel combination is same as emf across any one cell. Q.21 Is it possible that there is no pd across the terminals of the cell? A.21 Potential difference across the cell will be zero if it is short circuited, as the emf

of the cell will be equal to potential drop across the internal resistance. Q.22 What are thermistors? What are its applications? A.22 Thermistors are substances whose resistance changes very rapidly with the

change in temperature. The temperature coefficient of resistance of thermistors can be positive or negative i.e. their resistance can both increase or decrease with temperature. Thermistors can be used to measure the small changes in temperature and also in temperature control units of industry.

Q.23 What are factors on which emf of a cell depends? A.23 EMF of the cell depends upon [a] nature of electrodes [b] temperature of

electrodes and electrolyte [c] nature and concentration of the electrolyte. Q.24 It is easier to start a car engine on a warm day than on a chilly day why? A.24 This is due to difference in internal resistance of the battery, on warm day

internal resistance of the battery is small and large current can be supplied to the engine relative to cold day when small current can be supplied to the engine.



Q.25 Why it is unsafe to switch on or switch off the light while taking bath? A.25 While taking bath if we try to switch on or switch off the light a layer of water

can be formed between the fingers and the current carrying wire which can result in shock.

Q.26 What are the factors on which the resistance of the conductor depends? A.26 Resistance of the conductors depends upon its length , cross sectional area ,

nature of the material and physical conditions under which the resistance is to be measured.

Q.27 Bends in pipe slow down the flow of water through it. Do bends in wire

increase electrical resistance? A.27 No, bends in wire can’t change the electrical resistance because the drift speed

of the electrons in a conductor is so small that bends can’t have any effect on it.

Q.28 State, factors on which the internal resistance of the cell depends. A.28 Internal resistance of the cell depends upon the [a] distance between the two

electrodes [b] area of the electrode plates immersed in electrolyte [c] nature of electrolyte and the electrodes.

Q.29 To reduce the brightness of the bulb should another resistance be connected in series or n parallel with it?

A.29 To reduce the brightness we should reduce the current flowing through the bulb which can be easily done if another resistance is connected in series with the bulb.

Q.30 Lights of the car are dimmed when the starter is operated. Why? A.30 When starter of the motor is operated it draws large current from the battery

for its operation. This result in decrease in voltage across the bulb and it gets dimmer.

Q.31 The resistivity of semiconductor and insulators decrease with increase in

temperature. Why? A.31 At low temperatures there are no charge carriers in semiconductors and

insulators. But when the temperature is increased bonds break which result in increase in number density an decrease in resistance and resistivity of the semiconductors and insulators.

Q.32 A wire becomes red hot when current flows through it, if half of it is immersed

in water, the other half becomes hotter. Why? A.32 When half of the wire is immersed in water its temperature falls, which results

in decrease in overall resistance of the wire. If pd remains same decrease in resistance means more current through the wire. Thus temperature of part which is not immersed in water increases further.



Q.33 When ends of the wire are connected to battery, the current in the wire decreases slowly till falls to steady value. Why?

A.33 This happens because initially the wire is at low temperature thus low resistance and large current. But when the temperature of the wire is increased the resistance increases and current decreases till it falls to steady value.

Q.34 What is superconductivity? A.34 the phenomenon o reduction of resistance of the conductor to zero when the

temperature falls to value equal to or less than critical temperature is called superconductivity.

Q.35 Does the value of temperature coefficient of resistance always positive? A.35 No, positive temperature coefficient of resistance implies that the resistance

increases with increase in temperature. But for semiconductors and insulators the resistance decreases with increase in temperature and their temperature coefficient f resistance is negative.

Q.36 What is the difference between static electricity and current electricity. A.36 Static electricity deals with the study of electric charges at rest whereas

current electricity is the branch of physics which deals with charge particle in motion.

Q.37 Is Ohm’s law, universally applicable to all current carrying elements? A.37 No, no ohm’s law can be applicable only for substances for which V-I curve is

a straight line or whose resistance remains constant with potential difference. For non- ohmic conductors like diodes ohm’s law s not applicable.

Q.38 Currents of the order of 0.1A through human body are fatal what causes

death: heating due to current o something else? A.38 When current flows through the body it has electromagnetic wave associated

with it. This can interfere with the wave connecting brain with body parts and can affect the functioning of heart. Cardiac arrest is the cause of death in most cases

Q.39 If electron drift speed is small, and the charge on electron is also very small,

how can we obtain large amount of current in the conductor? A.39 Large currents can be obtained due to large number density of charge carriers

inside the conductors, which is of the order of 1029 m-3. Q.40 A steady current flows through the cylindrical conductor is there any electric

field inside the conductor? A.40 Current flows inside the conductor when potential difference is applied across

the two ends of the conductor. Thus, if V is the potential difference applied and l is the length of the conductor then electric ield inside the conductor is E = V/l



Q.41 There is an impression among people that person touching a high power line

gets stuck with it. Is that true? Explain. A.41 No, a person will not get stuck to the wire. But when current flows through

the wire it affects the nervous system and snaps the connection between brain and body parts. It is the brain, which is not giving an order to the hand to move it.

Q.42 A wire is carrying current. Is it charged? A.42 No, flow of current only means that electron are moving in direction opposite

to the electric field intensity. But, number of electrons in the wire are always equal to the number of protons in the wire Thus wire as a whole is neutral.

Q.43 The electron drift speed is estimates to be few mm/s for current flow. How is

then current established almost instantly when the circuit is closed? A.43 When we close the circuit, potential difference and thus electric field is

established instantly in the wire with the speed of em waves. Thus, information for flow of current through the wire is transmitted through the wire with a speed of 3 x 108 m/s.

Q.44 Of metals and alloys, which have greater value of temperature coefficient of

resistance?

A.44 The value of is more for metals, as there is greater variation in resistance f metals with temperature as compared to alloys.

Q.45 What happens to the drift velocity of electrons and resistance R, if the length

of conductor is doubled [keeping potential difference unchanged]? A.45 Drift velocity is inversely proportional to the length for constant value of V

potential difference. Thus, if the length of the conductor is doubled drift velocity will be halved.

The resistance of conductor is directly proportional to the length of the conductor. Thus, if length is doubled resistance will also be doubled.

Q.46 A large number of free electrons are present in metals, why there is no

current in absence of potential difference? A.46 In absence of potential difference, the electrons are moving randomly and

keeps on colliding with each other. Thus, even if the thermal speed of the electrons is of the order of 106 m/s there drift drift velocity is zero due to Brownian motion of electrons.

Q.47 When electrons drift in a metal from lower to higher potential, does that

mean that all the free electrons of the metal are moving in the same direction?



A.47 No, electrons will have resultant drift velocity in the direction from lower to higher potential. But they still suffer collisions inside metal and with each collision the direction of motion of electron changes.

Q.48 The electron drift speed arises due to force experienced by electrons in the

electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?

A.48 The free electron in metal under the effect of electric field intensity accelerates due to electric field intensity. It experience deceleration due to the collisions. The resultant affect of these two is that electrons acquire steady drift speed, which is almost, half the maximum drift speed acquired by the free electron before collision.

Q.49 A steady current flows through wire of non uniform cross-section. Explain

which of these quantities is constant along the conductor: current, current density, electric field and drift speed?

A.49 Only current is constant along the length as other quantities are inversely proportional to the cross-sectional area which is variable.

Q.50 What does the no deflection position in the galvanometer of potentiometer

experiment tells us about the flow of current? A.50 When null point is obtained on the wire, then potential difference between

one end of wire and null point is equal to the emf of the cell to be measured. Thus current through galvanometer circuit is zero.

Q.51 When is Wheatstone bridge most sensitive? A.51 Wheatstone bridge is most sensitive when four resistances in the Wheatstone

bridge are of the same order or null point is obtained in the middle of meter bridge wire.

Q.52 On what factors, does the potential gradient of the potentiometer wire

depend? A.52 The potential difference per unit length of the wire depends on [a] current

through the wire [b] specific resistance of the wire. [c] area of cross-section of the wire.

Q.53 Why the current should not be passed through the potentiometer wire for

long time? A.53 For potentiometer to work properly, pd per unit length should be constant.

But if the current is passed through for a long time then the wire gets heated

up and its specific resistance and resistance per unit length [i.e. r = /A] becomes variable.

Q.54 Copper wire is not used for making potentiometer wires. Why?



A.54 Copper should not be used for making potentiometer wire because temperature coefficient of resistance for copper is large and when current flows through wire, its specific resistance and resistance per unit length begins to vary due to heat generation.

Q.55 What do you understand by sensitiveness of potentiometer and how can you

increase the sensitiveness of the potentiometer? A.55 Sensitivity of potentiometer is the minimum value of potential difference

which it can measure or p.d. across unit length of wire. It can be increased by [a] increasing the length of the wire [b] decreasing the current flow through the potentiometer wire.

Q.56 Can you interchange the positions of the battery in the auxiliary circuit and

cell whose emf is to b determined in potentiometer circuit diagram? A.56 No, battery and cell can’ be interchanged because the emf of the battery

should always be greater than the emf of the cell is to be measured. If the positions of two are interchanged there will be no null point on the wire.

Q.57 Why do we prefer to use potentiometer for measurement of emf rather than

the voltmeter? A.57 Potentiometer is preferred for measuring the emf of the cell because it uses

null deflection method for measurement, thus it draws no current from the cell whose emf is to be measured.

Q.58 The emf of the driver cell should always be greater than emf of the cell to be

measured. Why? A.58 If emf of the driver cell is less than the emf of the cell to be measured because

in that case fall of potential across the length of potentiometer will be less than emf of the cell to be measured

Q.59 Are Kirchoff’s law applicable to both a.c. and d.c? A.59 Yes, Kirchoff’s two laws are basically law of conservation of charge and law of

conservation of energy. Thus, they are equally applicable to both ac as well as dc.

Q.60 Why the jockey should not be pressed against the potentiometer wire? A.60 Jockey should not be pressed against the potentiometer wire because

pressing the jockey will change the cross-sectional area of the wire and thus resistance per unit length becomes variable.

Q.61 Can meter bridge be used for measuring very low resistances? A.61 Meter bridge can’t be used for measuring low resistances because in that

case we can’t neglect the resistance of connecting wires and copper strips.



Q.62 Why the connection between resistors in Wheatstone bridge or Meter Bridge are made of thick copper wires?

A.62 Connections are made of thick copper wires so that the resistance of copper wires is negligible as compared to other resistances used in the circuit.

Q.63 Why balance point should be near the middle point of the meter bridge wire? A.63 Meter bridge is based on the principle of Wheatstone bridge. When null point

is obtained in the middle the ratio arms resistances is of the same order and sensitivity of potentiometer is maximum.

Q.64 What happens if cell and galvanometer in Wheatstone bridge are

interchanged? A.64 there will be no change in the balance point condition of Wheatstone bridge

even if galvanometer and cell are interchanged. Q.65 In Wheatstone bridge method why do we break the galvanometer circuit first

and then the battery circuit? A.65 This is done to save the galvanometer from large current, which can flow due

to large induced emf in the circuit at the time of breaking the circuit.



NCERT Text Book Problems

Q.1 The storage battery of car as emf of 12V.if the internal resistance of the

battery is 0.4, what is the maximum current that can be drawn from the battery [Ans. 30A]

Q.2 A battery of em 10V and internal resistance 3 s connected to a resistor. If the current in the circuit is 0.5A, what s the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

[Ans. 17, 8.5V]

Q.3 Three resistors 1, 2 and 3 are connected in series. What is the total resistance of the combination? [b] If the combination is connected to a battery of emf 12V and negligible internal resistance, obtain the potential

drop across each resistor? [Ans. 6, 2V,4V,6V]

Q.4 [a]Three resistors 2, 4 and 5e connected in parallel. What is the total resistance of the combination? [b] if the combination is connected to battery of emf 20V and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery?

[Ans. 20/19 [b] 10A, 5A, 4A]

Q.5 At room temperature [270C] the resistance of the heating element is

100.What is the temperature of the element if the resistance is found to be

117 given that temperature coefficient of the material is 1.7 x 10-4/0C. [Ans. 10270C]

Q.6 A negligibly small current is passed through a wire of length 15m and uniform

cross section 6 x10-7m2 and its resistance is measured to be 5. What is the resistivity of the material at temperature of the experiment?

[Ans. 2 x 10-7 -m]

Q.7 A silver wire has a resistance of 2.1 a 27.50C and resistance of 2.7 at 1000C. Determine the temperature coefficient of resistance of the material. [Ans. 0.00394C-1]

Q.8 A heating element using Nichrome connected to 230V supply draws an initial current of 3.2A which settles after a few seconds t a steady value of 2.8A. what is the steady temperature of the heating element if the room temperature is 270C? temperature coefficient of nichrome averaged over the temperature range is 1.7 x 10-4/0C. [Ans. 867.80C]

Q.9 Determine the current in each branch of the network as shown in figure.

[Ans. I1 = 4/17A, I = 10/17A, I2 = -2/17A]



Q.10 [a] In a meter bridge the balance pint is found to be at 39.5cm from the end

A, when the resistor Y is of 12.5. Determine the resistance of X. why are connections between resistors in wheatstone or meter bridge made of thick copper strips? [b] Determine the balance point of the above if X and Y are

interchanged? [Ans.[a]8.16 [b] 60.5cm from A]

Q.11 A storage battery of emf 8V and internal resistance of 0.5 is being charged

by a 120V dc supply using a series resistor of 15.5. What is the terminal voltage of the battery during charging? What is the purpose of having series resistor in the circuit? [As. 11.5V]

Q.12 A galvanometer coil has a resistance of 12 and meter sows full scale deflection for a current of 3mA. How will you convert into a voltmeter of

range 0 to 18V? [Ans. Connect 5988 in series]

Q.13 A galvanometer coil has a resistance of 15 and the meter shows a full scale deflection for a current of4mA. How will you convert into an ammeter of

range 0 to 6A? [Ans. Shunt of 10m]

Q.14 In a potentiometer arrangement, a cell of emf 1.25V gives a balance point at 35cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63cm, what is the emf of the second cell? [Ans. 2.25V]

Q.16 The number density of conduction electrons in a copper conductor estimated is 8.5 x 1028m-3

. How long does it take to drift from one end of the wire 3m long to the other end? The area of cross-section of the wire is 2 x 10-6m2 carrying a current of 3A. [Ans. 7.57 hrs]

Q.17 Name the carriers of electric current in [a] a bar made of silver [b] hydrogen discharge tube [c] a voltaic cell [d] a lead acid accumulator [e] germanium semiconductor [f] a wire made of alloy nichrome [g] a super conductor.

Q.18 The earth’s surface has negative charge density of 10-9 C-m-2. the potential difference of 400kV between the top of atmosphere and the surface results in a current of 1800A over the entire globe. If there were no mechanism of sustaining atmospheric electric field, how much time would be required to neutralize the earth’s surface? [Ans. 283.3s]

Q.21 Two wires of equal length one of aluminum and the other of copper have the

same resistance. Which of the two wires is lighter? [al= 2.63 x 10-8m, cu =



1.72 x 10-8m, relative density of Al and Cu are 2.7 and 8.9 respectively] [Ans. Mcu=2.155MAl]

Q.22 A cell of emf 1.5V and internal resistance 0.5 is connected t a non-linear conductor whose V-I graph is as shown. Obtain graphically current drawn from the cell and its terminal voltage. [Ans. 1A, 1V]

Q.23 Two identical cells of emf 1.5V each are connected in parallel to provide

supply to an external circuit consisting of two resistors of 17 each joined in parallel. A very high resistance voltmeter reads terminal voltage to be 1.V.

what is the internal resistance of each cell? [Ans. 1.21]

Q.24 [a] Three cells of emf 2V 1.8V and 1.5V are connected in series. Their internal

resistances are 0.05, 0.7 and 1 respectively. If the battery is connected

to an external resistance of 4 via a very low resistance ammeter. What should be the reading of the ammeter? [b] if the cells above are joined in parallel, would they be characterized by definite emf and internal resistance ? if not, how will you obtain currents in different branches of the circuit? [Ans. 0.92A ]

Q.25 [a] Given n resistors each of resistance R, how will you combine them to get the maximum and minimum effective resistance? What is the ratio of maximum to

minimum resistance? [b] Given resistance of 1, 2, 3 how will you combine them to get an equivalent resistance of [1] 11/3 [2]

11/5 [3] 6 [d]6/11 [c] Determine the equivalent resistance of the networks shown in figure.

Q.26 Determine the current drawn from the12V battery with internal resistance

of 0.5 by the infinite network shown in figure. Each resistor has a resistance

of 1. [Ans 3.713A]

Q.27 A galvanometer with a coil of resistance 12 shows a full scale deflection for current of 2.5mA. how will you convert galvanometer into [a] ammeter of range 0 to 7.5A [b] a voltmeter of range 0 to 10V. Determine the resistance of the meter in each case. When an ammeter is put in the circuit does it read slightly less or more than actual current? When voltmeter is put in the circuit

does it read less than or more than the actual voltage drop? [Ans. 4 in

parallel, 3988 in series]



Q.28 You are given two resistors X and Y whose resistance is to be determined

using an ammeter of resistance 0.5 and voltmeter of resistance 20k. t is known that X is of the order of few ohms and Y is f the order of few thousand ohms. In each case which of the two connections you will use for resistance measurement?

Q.29 A battery of emf 9 and negligible internal resistance is connected to 3 k resistance. The pd across the part of the resistor [between points A and B in

fig] is measured by 20k voltmeter. [b]a 1k voltmeter. In [c] both voltmeters are connected across AB. In which case we will get the highest and lowest reading. Will the answers alter if potential drop is measured across the entire resistor is measured? What if the battery has non negligible internal resistance?

Q.30 Figure shows potentiometer circuit for comparison of two

resistances. The balance point with standard resistance R = 10 is found to be at 58.3cm, while that with unknown resistance at 68.5cm. Determine the value of X. What do you do if you fail to get a balance point with the given cell of emf E?

[Ans. 11.74]

Q.31 Figure shows a 2V potentiometer used for the determination of internal resistance of 1.5V cell. The balance of the cell in

the open circuit is 763cm. When resistor of 9.5 is used in the external circuit of the cell, the balance point shifts to 64.8cm of length. Determine the internal resistance of the cell.

[Ans. 1.68]

Q.32 A dc supply of 120V is connected to a large resistance X. a

voltmeter of resistance 10k placed in series in the circuit reads 4V. What is the value of X? What do you think is purpose in using a voltmeter instead of

ammeter to determine the large resistance X? [Ans. X =290k]

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