P. No. 1

CURRENT ELECTRICITY

1. ELECTRIC CURRENT :Electric charges in motion constitute an electric current. Any medium having practically free electriccharges , free to migrate is a conductor of electricity. The electric charge flows from higher potentialenergy state to lower potential energy state. Positive charge flows from higher to lower potential andnegative charge flows from lower to higher. Metals such as gold, silver, copper, aluminium etc. are goodconductors.

2. ELECTRIC CURRENT IN A CONDUCTOR :In absence of potential difference across a conductor no net current flows through a corss section.When a potential difference is applied across a conductor the charge carriers (electrons in case ofmetallic conductors) flow in a definite direction which constitutes a net current in it . These electrons arenot accelerated by electric field in the conductor produced by potential difference across the conductor.They move with a constant drift velocity . The direction of current is along the flow of positive charge (oropposite to flow of negative charge). i = nvdeA, where Vd = drift velocity .

3. CHARGE AND CURRENT :The strength of the current i is the rate at which the electric charges are flowing. If a charge Q coulombpasses through a given cross section of the conductor in t second the current I through the conductor is

given by I = Qt =Coulomb

ondsec =Qt ampere .

Ampere is the unit of current . If i is not constant then i = dtdq

, where dq is net charge transported ata section in time dt.In a current carrying conductor we can define a vector which gives the direction as current per unitnormal, cross sectional area.

Thus J = IS n or I =J S

Where n is the unit vector in the direction of the flow of current.For random J or S, we use I = J ds

4. RELATION IN J, E AND D :In conductors drift vol. of electrons is proportional to the electric field in side the conductoras d = Ewhere is the mobility of electronscurrent density is given as J = IA = ne d

= ne(E) = Ewhere = ne is called conductivity of material and we can also write = 1 resistivityof material. Thus E = J. It is called as differential form of Ohm's Law.

5. SOURCES OF POTENTIAL DIFFERENCE & ELECTROMOTIVE FORCE :Dry cells , secondary cells , generator and thermo couple are the devices used for producing potentialdifference in an electric circuit. The potential difference between the two terminals of a source when noenergy is drawn from it is called the "Electromotive force" or "EMF" of the source. The unit ofpotential difference is volt.

1 volt = 1 Amphere 1 Ohm.

P. No. 2

6. ELECTRICAL RESISTANCE :The property of a substance which opposes the flow of electric current through it is termed as electricalresistance. Electrical resistance depends on the size, geometery, temperature and internal structure of theconductor.

7. LAW OF RESISTANCE :The resistance R offered by a conductor depends on the following factors :

R L (length of the conductor) ; RAl

(cross section area of the conductor)

at a given temperature R = Al

.

Where is the resistivity of the material of the conductor at the given temperature . It is also known asspecific resistance of the material .

8. DEPENDENCE OF RESISTANCE ON TEMPERATURE :The resistance of most conductors and all pure metals increases with temperature , but there are a few inwhich resistance decreases with temperature . If R

o & R be the resistance of a conductor at 0C and

C , then it is found that R = Ro(1 +) .

Here we assume that the dimensions of resistance does not change with temperature if expansioncoefficient of material is considerable. Then instead of resistance we use same property for resistivity as = 0 (1 + )The materials for which resistance decreases with temperature, the temperature coefficient ofresistance is negative.

Where is called the temperature co-efficient of resistance . The unit ofis K 1 of C 1 reciprocal ofresistivity is called conductivity and reciprocal of resistance is called conductance (G) . S.I. unit of G isohm.

9. OHM'S LAW :Ohm's law is the most fundamental of all the laws in electricity . It says that the current through the crosssection or the conductor is proportional to the applied potential difference under the given physicalcondition . V = RI . Ohm's law is applicable to only metalic conductors .

10. KRICHHOFF'S LAW'S :I - Law (Junction law or Nodal Analysis) :This law is based on law of conservation of charge . Itstates that " The algebric sum of the currents meeting at a point is zero " or total currents entering ajunction equals total current leaving the junction . Iin =Iout. It is also known as KCL (Kirchhoff's current law) .II- Law (Loop analysis) :The algebric sum of all the voltages in closedcircuit is zero.IR +EMF = 0 in a closed loop . The closed loop can be traversedin any direction . While traversing a loop if higher potential point isentered, put a +ve sign in expression or if lower potential point isentered put a negative sign . V1V2 +V3V4 = 0. Boxes may contain resistor or battery or any other element (linear or non-linear).It is also known as KVL (Kirchhoff's voltage law) .

P. No. 3

11. COMBINATION OF RESISTANCES :A number of resistances can be connected and all thecomplecated combinations can be reduced to two different types, namely series and parallel .

(i) RESISTANCE IN SERIES :When the resistances are connected end toend then they are said to be in series . The currentthrough each resistor is same . The effective resistance appearing across the battery .R = R1 + R2 + R3 + ................ + Rn andV = V1 + V2 + V3 + ................ + Vn .The voltage across a resistor is proportional to the resistance

V1 =n21

1R.........RR

R V;V2 =

n21

2R.........RR

R V ; etc

(ii) RESISTANCE IN PARALLEL :A parallel circuit of resistors is one in which the same voltage is applied across all thecomponents in a parallel grouping of resistors R1, R2, R3, ........, Rn .CONCLUSIONS :(a) Potential difference across each resistor is same .

(b) I = I1 + I2 + I3 + .......... In .(c) Effective resistance (R) then

n321 R1

..........

R1

R1

R1

R1

.

(d) Current in different resistors is inversallyproportional to the resistance .

I1 : I2 : ........... In =n321 R

1:..........:

R1

:R1

:R1

.

I1 =n21

1G.........GG

G I , I2 =

n21

2G.........GG

G I , etc .

where G = RI

= Conductance of a resistor .

12. EMF OF A CELL & ITS INTERNAL RESISTANCE :If a cell of emf E and internal resistance r be connected with a resistance R the total resistance ofthe circuit is (R+ r) .

I =rR

E ; VAB = rR

E where

E = Terminal voltage of the battery .If r 0, cell is Ideal & V E .13. GROUPING OF CELLS :

(i) CELLS IN SERIES :Let there be n cells each of emf E , arranged in series.Let r be the internal resistance of each cell.

The total emf = nE . Current in the circuit I =nrR

nE .

If nr > R then I =

r

E Series combination should not be used .

P. No. 4

(ii) CELLS IN PARALLEL :If m cells each of emf E & internal resistance r be connected in parallel and if thiscombination be connected to an external resistance then the emf of the circuit = E .

Internal resistance of the circuit =m

r .

I =mrR

E = rmR

mE .

If mR > r ; I = RE Parallel combination should not be used .

(iii) CELLS IN MULTIPLE ARC :mn = number of identical cells .n = number of rowsm = number of cells in each rows .The combination of cells is equivalent to single cell of :

(a) emf = mE & (b) internal resistance =n

mr

Current I =n

mrRmE . For maximum current nR = mr or

R =n

mr = internal resistance of battery .

Imax

=

R2mE

r2nE .

WHEAT STONE NETWORK :When current through the galvanometer is zero (null point or balance

point) QP

=

SR

. When PS > QR; VC < VD & PS VD or

PS = QR products of opposite arms are equal. Potential differencebetween C & D at null point is zero . The null point is not affected byresistance of G & E. It is not affected even if the positions of G & E areinter changed. ICD (QRPS) .

14. POTENTIOMETER :A potentiometer is a linear conductor of uniform cross-section with a steady current set up in it. Thismaintains a uniform potential gradient along the length of the wire . Any potential difference which is lessthen the potential difference maintained across the potentiometer wire can be measured using this . The

potentiometer equation is2

1

2

1II

EE .

P. No. 5

15. AMMETER :It is a modified form of suspended coil galvanometer it is used to measurecurrent . A shunt (small resistance) is connected in parallel with

galvanometer to convert into ammeter . S =g

gg

II

RI

; An ideal ammeterhas zero resistance . whereIg = Maximum current that can flow through the galvanometer .I = Maximum current that can be measured using the given ammeter .

16. VOLTMETER :A high resistance is put in series with galvanometer . It is used to measure potential difference .

Ig = RRV

g

o

.R , Ideal voltmeter .

17. RELATIVE POTENTIAL :While solving an electric circuit it is convinient to chose a reference point and assigning its voltage aszero. Then all other potential are measured with respect to this point . This point is also called thecommon point .

18. ELECTRICAL POWER :The energy liberated per second in a device is called its power . The electrical power P delivered by anelectrical device is given by P = VI , where V = potential difference across device & I = current. If thecurrent enters the higher potential point of the device then power is consumed by it (i.e. acts as load) . Ifthe current enters the lower potential point then the device supplies power (i.e. acts as source) .

Power consumed by a resistor P = I2R = VI =R

V2 .

19. HEATING EFFECT OF ELECTRIC CURRENT :When a current is passed through a resistor energy is wested in over coming the resistances of the wire. This energy is converted into heat .

W = VIt Joule ; = I2 Rt Joule ;= tR

V2 Joule .

20. JOULES LAW OF ELECTRICAL HEATING :The heat generated (in joules) when a current of I ampere flows through a resistance of R ohm forT second is given by :

H = I2 RT Joules ; =2.4

RTI2 Calories .

If current is variable passing through the conductor then we use for heat produced in resistance in time

0 to t is: H = t

0

2RdtI

21. UNIT OF ELECTRICAL ENERGY CONSUMPTION :1 unit of electrical energy = Kilowatt hour = 1 KWh = 3.6 106 Joules.

P. No. 6

EXERCISE # I

Q.1 A current of 5 amp. is passing through a metallic wire of cross sectional area 4 106 m2. If the densityof the charge carrier in the wire is 5 1026/m3. Find the drift speed of the electrons.

Q.2 A uniform copper wire of mass 2.33 103 kg caries a current of 1 A, when 1.7 V is applied across it.Calculate its length and area of cross section. If the wire is uniformly stretched to double its length,calculate the new resistance. Density of Cu is 8.92 103 kg m3 and resistivity is 1.7 108 m.

Q.3 Figure shows, as function of time, the energy dissipated by current in a resistor. Rank the three letteredtime period according to (a) the current through the resistor and (b) the rate of dissipation in the resistor,greatest first.

Q.4 In the circuit shown, if the current in the vertical resistance is equal to I then what is the potential of thebattery ?

Q.5 In a electric circuit, a cell of constant E.M.F 6 V and internal resistance 2is connected in closed circuitwith an external resistance. The potential difference across the terminals of the cell is 5 volt. If theexternal resistance is doubled, the potential difference across the terminals of the cell is ________.

Q.6 The four terminal network shown in the figure consists of four equal resistors and is a part of a largercircuit. The points A, B & C are at same potential. The p.d. between A and D is 40 volts. The p.d.between O and D is

Q.7 A network of nine conductors connects six points A, B, C, D, E and Fas shown in figure. The figure denotes resistances in ohms. Find theequivalent resistance between A and D.

P. No. 7

Q.8 Find the current I & voltage V in the circuit shown.

Q.9 Find the equivalent resistance of the circuit between points A and B shown infigure is: (each branch is of resistance = 1)

Q.10 Find the current through 25V cell & power supplied by20V cell in the figure shown.

Q.11 If a cell of constant E.M.F. produces the same amount of the heat during the same time in two independentresistors R1 and R2, when they are separately connected across the terminals of the cell, one after theanother, find the internal resistance of the cell.

Q.12 In the circuit shown in figure, all wires have equal resistance r. Find theequivalent resistance between A and B.

Q.13 Find the resistor in which maximum heat will be produced.

Q.14 For what value of R in circuit, current through 4 resistance is zero.

Q.15 In the circuit shown in figure the reading of ammeter is the samewith both switches open as with both closed. Then find theresistance R. (ammeter is ideal)

P. No. 8

Q.16 If the switches S1, S2 and S3 in the figure are arranged such thatcurrent through the battery is minimum, find the voltage acrosspoints A and B.

Q.17 A battery of emf 0 = 10 V is connected across a 1 m long uniformwire having resistance 10/m. Two cells of emf 1 = 2V and 2 = 4Vhaving internal resistances 1 and 5 respectively are connected asshown in the figure. If a galvanometer shows no deflection at thepoint P, find the distance of point P from the point a.

Q.18 A potentiometer wire AB is 100 cm long andhas a total resistance of 10ohm. If thegalvanometer shows zero deflection at theposition C, then find the value of unknownresistance R.

Q.19 In the figure shown for which values of R1 and R2 the balance point for Jockey is at 40 cm from A. WhenR2 is shunted by a resistance of 10, balance shifts to 50 cm. Find R1 and R2. (AB = 1 m) :

Q.20 A part of a circuit is shown in figure. Here reading of ammeter is 5ampere and voltmeter is 96V & voltmeter resistance is 480 ohm. Thenfind the resistance R

P. No. 9

EXERCISE # IIQ.1(a) The current density across a cylindrical conductor of radius R varies according to the equation

J =

Rr1J0 , where r is the distance from the axis. Thus the current density is a maximum Jo at the

axis r = 0 and decreases linearly to zero at the surface r = R. Calculate the current in terms of Jo and the

c o n d u c t o r s c r o s s s e c t i o n a l a r e a i s A = R2.(b) Suppose that instead the current density is a maximum J

o at the surface and decreases linearly to zero at

the axis so that J = J0 Rr

. Calculate the current.

Q.2 What will be the change in the resistance of a circuit consisting of fiveidentical conductors if two similar conductors are added as shown bythe dashed line in figure.

Q.3 The current I through a rod of a certain metallic oxide is given by I = 0.2 V5/2, where V is the potentialdifference across it. The rod is connected in series with a resistance to a 6V battery of negligible internalresistance. What value should the series resistance have so that :

(i) the current in the circuit is 0.44(ii) the power dissipated in the rod is twice that dissipated in the resistance.

Q.4 A network of resistance is constructed with R1 & R2 asshown in the figure. The potential at the points 1, 2, 3,.., Nare V1, V2, V3 , .., Vn respectively each having a potentialk time smaller than previous one. Find:

(i)2

1RR

and3

2RR

in terms of k

(ii) current that passes through the resistance R2 nearest to the V0 in terms V0, k & R3.Q.5 A person decides to use his bath tub water to generate electric power to run a 40 watt bulb. The bath

tube is located at a height of 10 m from the ground & it holds 200 litres of water. If we install a waterdriven wheel generator on the ground, at what rate should the water drain from the bath tube to lightbulb? How long can we keep the bulb on, if the bath tub was full initially. The efficiency of generator is90%.(g = 10m/s2)

Q.6 In the circuit shown in figure, calculate the following :(i) Potential difference between points a and b when switch S is open.(ii) Current through S in the circuit when S is closed.

Q.7 A rod of length L and cross-section area A lies along the x-axis between x = 0 and x = L. The materialobeys Ohms law and its resistivity varies along the rod according to (x) =0 ex/L. The end of the rodat x = 0 is at a potential V0 and it is zero at x = L.

(a) Find the total resistance of the rod and the current in the wire.(b) Find the electric potential in the rod as a function of x.

P. No. 10

Q.8 An ideal cell having a steady emf of 2 volt is connected across the potentiometer wire of length 10 m.The potentiometer wire is of magnesium and having resistance of 11.5/m. An another cell gives a nullpoint at 6.9 m. If a resistance of 5 is put in series with potentiometer wire, find the new position of thenull point.

Q.9 An enquiring physics student connects a cell to a circuit and measures the current drawn from thecell to I1. When he joins a second identical cell is series with the first, the current becomes I2. Whenthe cells are connected are in parallel, the current through the circuit is I3. Show that relation betweenthe current is 3 I3 I2 = 2 I1 (I2 + I3)

Q.10 Find the potential difference VA VB for the circuitshown in the figure.

Q.11 A resistance R of thermal coefficient of resistivity = is connected in parallel with a resistance = 3R,having thermal coefficient of resistivity = 2. Find the value of

eff .

Q.12 In the primary circuit of potentiometer the rheostat can be varied from 0 to 10. Initially it is at minimumresistance (zero).

(a) Find the length AP of the wire such that the galvanometer shows zerodeflection.

(b) Now the rheostat is put at maximum resistance (10) and the switch S isclosed. New balancing length is found to 8m. Find the internal resistance rof the 4.5V cell.

Q.13 A galvanometer (coil resistance 99) is converted into a ammeter using a shunt of 1and connected asshown in the figure (i). The ammeter reads 3A. The same galvanometer is converted into a voltmeter byconnecting a resistance of 101 in series. This voltmeter is connected as shown in figure(ii). Its readingis found to be 4/5 of the full scale reading. Find

(a) internal resistance r of the cell(b) range of the ammeter and voltmeter(c) full scale deflection current of the galvanometer

Q . 1 4 A n a c c u m u l a t o r o f e m f 2 v o l t a n d n e g l i g i b l e i n t e r n a l r e s i s t a n c e i s c o n n e c t e d a c r o s s a u n i f o r m w i r e o f

l e n g t h 1 0 m a n d r e s i s t a n c e 3 0 . The appropriate terminals of a cell of emf 1.5 volt and internal resistance1is connected to one end of the wire, and the other terminal of the cell is connected through a sensitivegalvanometer to a slider on the wire. What length of the wire will be required to produce zero deflectionof the galvanometer ? How will be balancing change (a) when a coil of resistance 5 is placed in serieswith the a accumulator, (b) the cell of 1.5 volt is shunted with 5resistor ?

P. No. 11

EXERCISE # III

Q.1 In the circuit shown in the figure, the current through :(A) the 3 resistor is 0.50 A (B) the 3resistor is 0.25 A(C) 4 resistor is 0.50 A (D) the 4resistor is 0.25 A

[JEE98, 2]

Q.2 In the circuit shown, P R, the reading of the galvanometer is same withswitch S open or closed. Then( A ) I R = IG (B) IP = IG (C) IQ = IG (D) IQ = IR [JEE99, 2]

Q.3 The effective resistance between the points P and Q of the electricalcircuit shown in the figure is(A) 2 Rr / (R + r) (B) 8R(R + r)/(3R + r)(C) 2r + 4R (D) 5 R/2 + 2r

[JEE 2002 (Scr), 3]

Q.4 A 100 W bulb B1, and two 60 W bulbs B2 and B3, are connected to a250 V source, as shown in the figure. Now W1, W2 and W3 are theoutput powers of the bulbs B1, B2 and B3 respectively. Then(A) W1 > W2 = W3(B) W1 > W2 > W3(C) W1 < W2 = W3(D) W1

P. No. 12

Q.6 Arrange the order of power dissipated in the given circuits, if the same current is passing through allcircuits and each resistor is 'r' [JEE 2003 (Scr)]

(I) (II)

(III) (IV)

(A) P2 > P3 > P4 > P1 (B) P3 > P2 > P4 > P1 (C) P4 > P3 > P2 > P1 (D) P1 > P2 > P3 > P4Q.7 In the given circuit, no current is passing through the galvanometer. If

the cross-sectional diameter of AB is doubled then for null point ofgalvanometer the value of AC would [JEE 2003 (Scr)](A) x (B) x/2 (C) 2x (D) None

Q.8 How a battery is to be connected so that shown rheostat will behavelike a potential divider? Also indicate the points about which output canbe taken. [JEE 2003]

Q.9 Six equal resistances are connected between points P, Q and R as shownin the figure. Then the net resistance will be maximum between(A) P and Q(B) Q and R(C) P and R(D) any two points [JEE 2004 (Scr)]

Q.10 For the post office box arrangement to determine the value of unknown resistance,the unknown resistance should be connected between [JEE 2004 (Scr)](A) B and C (B) C and D(C) A and D (D) B1 and C1

Q.11 Draw the circuit for experimental verification of Ohm's law using a source of variable D.C. voltage, amain resistance of 100, two galvanometers and two resistances of values 106 and 103 respectively.Clearly show the positions of the voltmeter and the ammeter. [JEE 2004]

Q.12 In the figure shown the current through 2 resistor is(A) 2 A (B) 0 A(C) 4 A (D) 6 A

[JEE 2005 (Scr)]

Q.13 A galvanometer has resistance 100and it requires current 100A for full scale deflection. A resistor0.1is connected to make it an ammeter. The smallest current required in the circuit to produce the fullscale deflection is [JEE 2005 (Scr)](A) 1000.1 mA (B) 1.1 mA (C) 10.1 mA (D) 100.1 mA

P. No. 13

Q.14 An unknown resistance X is to be determined using resistances R1, R2 orR3. Their corresponding null points are A, B and C. Find which of theabove will give the most accurate reading and why?

[JEE 2005]

Q.15 Consider a cylindrical element as shown in the figure. Currentflowing the through element is I and resistivity of material of thecylinder is. Choose the correct option outthe following.(A) Power loss in second half is four times the power loss in first half.(B) Voltage drop in first half is twice of voltage drop in second half.(C) Current density in both halves are equal.(D) Electric field in both halves is equal. [JEE 2006]

Q.16 A resistance of 2 is connected across one gap of a metre-bridge (the length of the wire is 100 cm) andan unknown resistance, greater than 2, is connected across the other gap. When these resistances areinterchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is(A) 3 (B) 4 (C) 5 (D) 6 [JEE 2007]

Q.17 Figures shows three resistor configurations R1, R2 and R3 connected to 3V battery. If the powerdissipated by the configuration R1, R2 and R3 is P1, P2 and P3 respectively, then Figure :[JEE 2008]

(A) P1 > P2 > P3 (B) P1 > P3 > P2 (C) P2 > P1 > P3 (D) P3 > P2 > P1

Q.18 Statement-1 : In a Meter Bridge experiment, null point for an unknown resistance is measured. Now,the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point canbe obtained at the same point as before by decreasing the value of the standard resistance. [JEE 2008]Statement-2 : Resistance of a metal increases with increase in temperature.(A) Statement-1 is true, statement-2 is true ; statement-2 is a correct explanation for statement-1(B) Statement-1 is true, statement-2 is true ; statement-2 is NOT a correct explanation for statement-1(C) Statement-1 is true, statement-2 is false(D) Statement-1 is false, statement-2 is true

P. No. 14

QUESTION BANK ONONLY ONE OPTION IS CORRECT.

Q.1 Two wires each of radius of cross section r but of different materials are connected together end to end(in series). If the densities of charge carriers in the two wires are in the ratio 1 : 4, the drift velocity ofelectrons in the two wires will be in the ratio:(A) 1 : 2 (B) 2 : 1 (C) 4 : 1 (D) 1 : 4

Q.2 In a wire of cross-section radius r, free electrons travel with drift velocity v when a current I flowsthrough the wire. What is the current in another wire of half the radius and of the same material when thedrift velocity is 2v?(A) 2I (B) I (C) I/2 (D) I/4

Q.3 An insulating pipe of cross-section area 'A' contains an electrolyte which has two types of ions theircharges being e and +2e. A potential difference applied between the ends of the pipe result in thedrifting of the two types of ions, having drift speed = v (ve ion) and v/4 (+ve ion). Both ions have thesame number per unit volume = n. The current flowing through the pipe is(A) nev A/2 (B) nev A/4 (C) 5nev A/2 (D) 3nev A/2

Q.4 A current I flows through a uniform wire of diameter d when the mean electron drift velocity is V. Thesame current will flow through a wire of diameter d/2 made of the same material if the mean drift velocityof the electron is :(A) v/4 (B) v/2 (C) 2v (D) 4v

Q.5 A wire has a non-uniform cross-section as shown in figure. A steady currentflows through it. The drift speed of electrons at points P and q is vP and vQ.(A) vP = vQ (B) vP < vQ(C) vP > vQ (D) Data insufficient

Q.6 A uniform copper wire carries a current i amperes and has p carriers per metre3. The length of the wireis metres and its cross-section area is s metre2. If the charge on a carrier is q coulombs, the driftvelocity in ms1 is given by(A) i/sq (B) i/psq (C) psq/i (D) i/psq

Q.7 The current in a metallic conductor is plotted against voltage at two differenttemperatures T1 and T2. Which is correct(A) T1 > T2 (B) T1 < T2(C) T1 = T2 (D) none

Q.8 If X, Y and Z in figure are identical lamps, which of the following changes tothe brightnesses of the lamps occur when switch S is closed?(A) X stays the same, Y decreases (B) X increases, Y decreases(C) X increases, Y stays the same (D) X decreases, Y increases

Q.9 Read the following statements carefully :Y : The resistivity of a semiconductor decreases with increases of temperature.Z : In a conducting solid, the rate of collision between free electrons and ions increases with increase oftemperature.Select the correct statement from the following :(A) Y is true but Z is false (B) Y is false but Z is true.(C) Both Y and Z are true. (D) Y is true and Z is the correct reason for Y.

P. No. 15

Q.10 A piece of copper and another of germanium are cooled from room temperature to 80 K. The resistanceof :(A) each of them increases(B) each of them decreases(C) copper increases and germanium decreases(D) copper decreases and germanium increases.

Q.11 A storage battery is connected to a charger for charging with a voltage of 12.5Volts. The internal resistance ofthe storage battery is 1. When the charging current is 0.5 A, the emf of the storage battery is:(A) 13 Volts (B) 12.5 Volts (C) 12 Volts (D) 11.5 Volts

Q.12 Under what condition current passing through the resistance R can beincreased by short circuiting the battery of emf E2. The internal resistancesof the two batteries are r1 and r2 respectively.(A) E2r1 > E1 (R + r2) (B) E1r2 > E2 (R + r1)(C) E2r2 > E1 (R + r2) (D) E1r1 > E2 (R + r1)

Q.13 A battery consists of a variable number n of identical cells having internal resistance connected in series.The terminals of the battery are short circuited and the current I measured.Which one of the graph below shows the relationship between I and n?

(A) (B) (C) (D) (E)

Q.14 In previous problem, if the cell had been connected in parallel (instead of in series) which of the abovegraphs would have shown the relationship between total current I and n?

(A) (B) (C) (D) (E)

Q.15 In the figure shown, battery 1 has emf = 6 V and internal resistance = 1 .Battery 2 has emf = 2V and internal resistance = 3. The wires have negligibleresistance. What is the potential difference across the terminals of battery 2 ?(A) 4 V (B) 1.5 V(C) 5 V (D) 0.5 V

Q.16 The terminal voltage across a battery of emf E can be(A) 0 (B) > E (C) < E (D) all of above

Q.17 A circuit is comprised of eight identical batteries and a resistorR = 0.8. Each battery has an emf of 1.0 V and internal resistanceof 0.2. The voltage difference across any of the battery is(A) 0.5V (B) 1.0V(C) 0 V (D) 2 V

Q.18 Two batteries one of the emf 3V, internal resistance 1 ohm and the other of emf 15 V,internal resistance 2 ohm are connected in series with a resistance R as shown. If thepotential difference between a and b is zero the resistance of R in ohm is(A) 5 (B) 7 (C) 3 (D) 1

P. No. 16

Q.19 A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due tothe current, the temperature of the wire is raised by T in time t. N number of similar cells is nowconnected in series with a wire of the same material and cross section but of length 2L. The temperatureof the wire is raised by the same amountT in the same time t. The value of N is :(A) 4 (B) 6 (C) 8 (D) 9

Q.20 A cell of emf E has an internal resistance r & is connected to rheostat. When resistance R of rheostat ischanged correct graph of potential difference across it is

(A) (B) (C) (D)

Q.21 The battery in the diagram is to be charged by the generator G. The generator hasa terminal voltage of 120 volts when the charging current is10 amperes. The batteryhas an emf of 100 volts and an internal resistance of 1 ohm. In order to charge thebattery at 10 amperes charging current, the resistance R should be set at(A) 0.1 (B) 0.5 (C) 1.0 (D) 5.0

Q.22 A wire of cross-section area A, length L1, resistivity1 and temperature coefficient of resistivity1 isconnected to a second wire of length L2, resistivity2, temperature coefficient of resistivity 2 and thesame area A, so that wire carries same current. Total resistance R is independent of temperature forsmall temperature change if (Thermal expansion effect is negligible)(A) 1 = 2 (B) 1L1 1 + 2L2 2 = 0(C) L1 1 + L2 2 = 0 (D) None

Q.23 Resistances R1 and R2 each 60 are connected in series as shownin figure. The Potential difference between A and B is kept 120 volt.Then what will be the reading of voltmeter connected between thepoint C & D if resistance of voltmeter is 120.(A) 48 V (B) 24 V(C) 40V (D) None

Q.24 The resistance of all the wires between any two adjacent dots is R.Then equivalent resistance between A and B as shown in figure is :(A) 7/3 R (B) 7/6 R(C) 14/8 R (D) None of these

Q.25 Consider an infinte ladder network shown in figure. A voltage V is applied between the points A and B.This applied value of voltage is halved after each section.

(A) R1/R2 = 1 (B) R1/R2 = 1/2 (C) R1/R2 = 2 (D) R1/R2 = 3

P. No. 17

Q.26 In the given circuit the current flowing through the resisitance 20 ohms is 0.3ampere while the ammetre reads 0.8 ampere. What is the value of R1?(A) 30 ohms (B) 40 ohms (C) 50 ohms (D) 60 ohms

Q.27 A brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor.The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass discto that of the carbon disc is [ is temperature coefficient of resistance & Neglect linear expansion ]

(A)BB

CC

(B)CB

BC

(C)BC

CB

(D)CC

BB

Q.28 In the circuit shown, what is the potential difference VPQ?(A) + 3V (B) + 2V (C) 2V (D) none

Q.29 In the circuit shown in figure reading of voltmeter is V1 when only S1 isclosed, reading of voltmeter is V2 when only S2 is closed. The readingof voltmeter is V3 when both S1 and S2 are closed then(A) V2 > V1 > V3 (B) V3 > V2 > V1(C) V3 > V1 > V2 (D) V1 > V2 > V3

Q.30 One end of a Nichrome wire of length 2L and cross-sectional area A is attatched to an end of anotherNichrome wire of length L and cross-sectional area 2A. If the free end of the longer wire is at an electricpotential of 8.0 volts, and the free end of the shorter wire is at an electric potential of 1.0 volt, thepotential at the junction of the two wires is equal to(A) 2.4 V (B) 3.2 V (C) 4.5 V (D) 5.6 V

Q.31 In the diagram resistance between any two junctions is R. Equivalent resistanceacross terminals A and B is

(A) 7R11 (B) 11

R18 (C) 11R7 (D) 18

R11

Q.32 Power generated across a uniform wire connected across a supply is H. If the wire is cut into n equalparts and all the parts are connected in parallel across the same supply, the total power generated in thewire is

(A) 2nH (B) n2H (C) nH (D)

n

H

Q.33 A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developedin it. The heat developed is doubled if(A) both the length and the radius of the wire are halved.(B) both the length and the radius of the wire are doubled(C) the radius of the wire is doubled(D) the length of the wire is doubled

P. No. 18

Q.34 When electric bulbs of same power, but different marked voltage are connected in series across thepower line, their brightness will be :(A) proportional to their marked voltage(B) inversely proportional to their marked voltage(C) proportional to the square of their marked voltage(D) inversely proportional to the square of their marked voltage(E) the same for all of them

Q.35 Two bulbs rated (25 W 220V) and (100W 220V) are connected in series to a 440 V line. Whichone is likely to fuse?(A) 25 W bulb (B) 100 W bulb (C) both bulbs (D) none

Q.36 Rate of dissipation of Joules heat in resistance per unit volume is (symbols have usual meaning)(A)E (B) J (C) J E (D) None

Q.37 If the length of the filament of a heater is reduced by 10%, the power of the heater will(A) increase by about 9% (B) increase by about 11%(C) increase by about 19% (D) decrease by about 10%

Q.38 A heater A gives out 300 W of heat when connected to a 200 V d.c. supply. A second heater B gives out600 W when connected to a 200 v d.c. supply. If a series combination of the two heaters is connectedto a 200 V d.c. supply the heat output will be(A) 100 W (B) 450 W (C) 300 W (D) 200 W

Q.39 Two bulbs one of 200 volts, 60 watts & the other of 200 volts, 100 watts are connected in series to a200 volt supply. The power consumed will be(A) 37.5 watt (B) 160 watt (C) 62.5 watt (D) 110 watt

Q.40 Three 60 W light bulbs are mistakenly wired in series and connected to a 120 V power supply. Assumethe light bulbs are rated for single connection to 120 V. With the mistaken connection, the power dissipatedby each bulb is:(A) 6.7 W (B) 13.3 W (C) 20 W (D) 40 W

Q.41 The ratio of powers dissipatted respectively in R and 3R, as shown is:

(A) 9 (B) 27/4 (C) 4/9 (D) 4/27

Q.42 In the figure shown the power generated in y is maximum when y = 5.Then R is(A) 2 (B) 6 (C) 5 (D) 3

Q.43 In the circuit shown, the resistances are given in ohms and thebattery is assumed ideal with emf equal to 3.0 volts. The resistorthat dissipates the most power is(A) R1(B) R2(C) R3(D) R4

P. No. 19

Q.44 What amount of heat will be generated in a coil of resistance R due to a charge q passing through it if thecurrent in the coil decreases to zero uniformly during a time intervalt(A)

tRq

34 2

(B) ln t2Rq2

(C) t3Rq2 2

(D) ln

Rqt2

2

Q.45 The variation of current (I) and voltage (V) is as shown in figure A. The variationof power P with current I is best shown by which of the following graph

(A) (B) (C) (D)

Q.46 When an ammeter of negligible internal resistance is inserted in series with circuit it reads 1A. When thevoltmeter of very large resistance is connected across X it reads 1V. When the point A and B are shortedby a conducting wire, the voltmeter measures 10 V across the battery. The internal resistance of thebattery is equal to(A) zero(B) 0.5 (C) 0.2 (D) 0.1

Q.47 In the box shown current i enters at H and leaves at C. If iAB = 6i

, iDC = 32i

,

iHA = 2i

, iGF = 6i

, iHE = 6i

, choose the branch in which current is zero

(A) BG (B) FC (C) ED (D) none

Q.48 In a galvanometer, the deflection becomes one half when the galvanometer isshunted by a 20 resistor. The galvanometer resistance is(A) 5 (B)10(C)40 (D)20

Q.49 A galvanometer has a resistance of 20 and reads full-scale when 0.2 V is applied across it. To convertit into a 10 A ammeter, the galvanometer coil should have a(A) 0.01 resistor connected across it (B) 0.02 resistor connected across it(C) 200 resistor connected in series with it (D) 2000 resistor connected in series with it

Q.50 A milliammeter of range 10 mA and resistance 9 is joined in a circuit asshown. The metre gives full-scale deflection for current I when A and B are usedas its terminals, i.e., current enters at A and leaves at B (C is left isolated). Thevalue of I is(A) 100 mA (B) 900 mA (C) 1 A (D) 1.1 A

Q.51 A galvanometer coil has a resistance 90 and full scale deflection current 10 mA. A 910 resistance isconnected in series with the galvanometer to make a voltmeter. If the least count of the voltmeter is 0.1V,the number of divisions on its scale is(A) 90 (B) 91 (C) 100 (D) none

P. No. 20

Q.52 In the circuit shown the resistance of voltmeter is 10,000 ohm and that of ammeteris 20 ohm. The ammeter reading is 0.10 Amp and voltmeter reading is 12 volt.Then R is equal to(A) 122 (B) 140 (C) 116 (D)100

Q.53 By error, a student places moving-coil voltmeter V (nearly ideal) in series withthe resistance in a circuit in order to read the current, as shown. The voltmeterreading will be(A) 0 (B) 4V (C) 6V (D) 12V

Q.54 ln a balanced wheat stone bridge, current in the galvanometer is zero. It remains zero when:[1] battery emf is increased[2] all resistances are increased by 10 ohms[3] all resistances are made five times[4] the battery and the galvanometer are interchanged(A) only [1] is correct (B) [1], [2] and [3] are correct(C) [1], [3] and [4] are correct (D) [1] and [3] are correct

Q.55 A Wheatstone's bridge is balanced with a resistance of 625 in the third arm,where P, Q and S are in the 1st, 2nd and 4th arm respectively. If P and Q areinterchanged, the resistance in the third arm has to be increased by 51 tosecure balance. The unknown resistance in the fourth arm is(A) 625 (B) 650 (C) 676 (D) 600

Q.56 In the figure shown for gives values of R1 and R2 the balance point forJockey is at 40 cm from A. When R2 is shunted by a resistance of 10,balance shifts to 50 cm. R1 and R2 are (AB = 1 m):

(A) 310 , 5 (B) 20 , 30

(C) 10 , 15 (D) 5 , 215

Q.57 A 6 V battery of negligible internal resistance is connected across auniform wire of length 1 m. The positive terminal of another battery ofemf 4V and internal resistance 1 is joined to the point A as shown infigure. The ammeter shows zero deflection when the jockey touches thewire at the point C. The AC is equal to(A) 2/3 m (B) 1/3 m(C) 3/5 m (D) 1/2 m

Q.58 The figure shows a metre-bridge circuit, with AB = 100 cm, X = 12and R = 18, and the jockey J in the position of balance.If R is now made 8, through what distance will J have to be moved toobtain balance?(A) 10 cm (B) 20 cm(C) 30 cm (D) 40 cm

P. No. 21

Q.59 A potentiometer wire has length 10 m and resistance 10. It is connected to a battery of EMF 11 voltand internal resistance 1, then the potential gradient in the wire is(A) 10 V/m (B) 1 V/m (C) 0.1 V/m (D) none

Q.60 The length of a potentiometer wire is l. A cell of emf E is balanced at a length l/3 from the positive end ofthe wire. If the length of the wire is increased by l/2. At what distance will the same cell give a balancepoint.

(A) 32l (B) 2

l (C) 6l (D) 3

4l

Q.61 In the figure, the potentiometer wire AB of length L and resistance 9r is joined tothe cell D of emf and internal resistance r. The cell Cs emf is /2 and itsinternal resistance is 2r. The galvanometer G will show no deflection when thelength AJ is

(A) 9L4 (B) 9

L5 (C) 18L7 (D) 18

L11

Q.62 An ammeter A of finite resistance, and a resistor R are joined in series to an idealcell C. A potentiometer P is joined in parallel to R. The ammeter reading is I0and the potentiometer reading is V0. P is now replaced by a voltmeter of finite resistance. The ammeter reading now is I and the voltmeter reading is V.(A) I > I0, V < V0 (B) I > I0, V = V0 (C) I = I0, V < V0 (D) I < I0, V =V0

Q.63 In the given potentiometer circuit length of the wire AB is 3 mand resistance is R = 4.5. The length AC for no deflection ingalvanometer is(A) 2 m (B) 1.8 m(C) dependent on r1 (D) none of these

Q.64 A battery of emf E0 = 12 V is connected across a 4m long uniform wire havingresistance 4/m. The cells of small emfs 1 = 2V and 2 = 4V having internalresistance 2 and 6 respectively, are connected as shown in the figure. Ifgalvanometer shows no deflection at the point N, the distance of point N fromthe point A is equal to

(A) 61

m (B) 31

m (C) 25 cm (D) 50 cm

Q.65 In the arrangement shown in figure when the switch S2 is open, thegalvanometer shows no deflection for l = L/2. When the switch S2 isclosed, the galvanometer shows no deflection for l = 12L5 . The internalresistance (r) of 6 V cell, and the emf E of the other battery arerespectively(A) 3, 8V (B) 2, 12V(C) 2, 24V (D) 3, 12V

P. No. 22

Q.66 The diagram besides shows a circuit used in an experiment to determine the emf and internal resistanceof the cell C. A graph was plotted of the potential difference V between the terminals of the cell againstthe current I, which was varied by adjusting the rheostat. The graph is shown on the right ; x and y are theintercepts of the graph with the axes as shown. What is the internal resistance of the cell ?

(A) x (B) y(C) x/y (D) y/x

Q.67 Which of the following wiring diagrams could be used to experimentally determine R using ohm's law?Assume an ideal voltmeter and an ideal ammeter.

(A) (B) (C) (D)

ONE OR MORE THAN ONE OPTION MAY BE CORRECTTake approx. 3 minutes for answering each question.

Q.1 A metallic conductor of irregular cross-section is as shown in the figure. A constant potential differenceis applied across the ends (1) and (2). Then :

(A) the current at the cross-section P equals the current at the cross-section Q(B) the electric field intensity at P is less than that at Q.(C) the rate of heat generated per unit time at Q is greater than that at P(D) the number of electrons crossing per unit area of cross-section at P is less than that at Q.

Q.2 Which of the following quantities do not change when a resistor connected to a battery is heated due tothe current?(A) drift speed (B) resistivity (C) resistance (D) number of free electrons

Q.3 A current passes through a wire of nonuniform cross section. Which of the following quantities areindependent of the cross-section?(A) the charge crossing in a given time interval.(B) drift speed(C) current density(D) free-electron density.

Q.4 In the circuit shown E, F, G and H are cells of e.m.f. 2V, 1V, 3Vand 1V respectively and their internal resistances are 2, 1,3 and 1 respectively.(A) VD VB = 2/13 V(B) VD VB = 2/13 V(C) VG = 21/13 V = potential difference across G.(D) VH = 19/13 V = potential difference across H.

P. No. 23

Q.5 A simple circuit contains an ideal battery and a resistance R. If a second resistor is placed in parallel withthe first,(A) the potential across R will decrease(B) the current through R will decreased(C) the current delivered by the battery will increase(D) the power dissipated by R will increased.

Q.6 Consider the circuit shown in the figure(A) the current in the 5 resistor is 2 A(B) the current in the 5 resistor is 1 A(C) the potential difference VA VB is 10 V(D) the potential difference VA VB is 5 V

Q.7 A battery is of emf E is being charged from a charger such that positive terminal of the battery is connectedto terminal A of charger and negative terminal of the battery is connected to terminal B of charger. Theinternal resistance of the battery is r.(A) Potential difference across points A and B must be more than E.(B) A must be at higher potential than B(C) In battery, current flows from positive terminal to the negative terminal(D) No current flows through battery

Q.8 The equivalent resistance of a group of resistances is R. If another resistance is connected in parallel tothe group , its new equivalent becomes R1 & if it is connected in series to the group , its new equivalentbecomes R2 we have :(A) R1 > R (B) R1 < R (C) R2 > R (D) R2 < R

Q.9 Two identical fuses are rated at 10A. If they are joined(A) in parallel, the combination acts as a fuse of rating 20A(B) in parallel, the combination acts as a fuse of rating 5A(C) in series, the combination acts as a fuse of rating 10A.(D) in series, the combination acts as a fuse of rating 20A.

Q.10 A battery of emf E and internal resistance r is connected across a resistance R.Resistance R can be adjusted to any value greater than or equal to zero. A graphis plotted between the current (i) passing through the resistance and potentialdifference (V) across it. Select the correct alternative(s).(A) internal resistance of battery is 5 (B) emf of the battery is 20V(C) maximum current which can be taken from the battery is 4A(D) V- i graph can never be a straight line as shown in figure.

Q.11 The value of the resistance R in figure is adjusted such that powerdissipated in the 2 resistor is maximum. Under this condition(A) R = 0(B) R = 8(C) power dissipated in the 2 resistor is 72 W.(D) power dissipated in the 2 resistor is 8 W.

P. No. 24

Q.12 A galvanometer may be converted into ammeter or voltmeter. In which of the following cases the resistanceof the device will be the largest ? (Asssume maximum range of galvanometer = 1 mA)(A) an ammeter of range 10A (B) a voltmeter of range 5 V(C) an ammeter of range 5 A (D) a voltmeter of range 10 V.

Q.13 Mark out the correct options.(A) An ammeter should have small resistance.(B) An ammeter should have large resistance.(C) A voltmeter should have small resistance.(D) A voltmeter should have large resistance.

Q.14 In the circuit shown the readings of ammeter and voltmeter are 4A and20V respectively. The meters are non ideal, then R is :(A) 5 (B) less than 5(C) greater than 5 (D) between 4 & 5

Q.15 A micrometer has a resistance of 100 and a full scale range of 50A. It can be used as a voltmeter ora higher range ammeter provided a resistance is added to it. Pick the correct range and resistancecombination(s).(A) 50 V range with 10 k resistance in series. (B) 10 V range with 200 k resistance in series.(C) 5 mA range with 1 resistance in parallel. (D) 10 mA range with 1 k resistance in parallel.

Q.16 In a potentiometer wire experiment the emf of a battery in the primary circuit is 20V and its internalresistance is 5. There is a resistance box in series with the battery and the potentiometer wire, whoseresistance can be varied from 120 to 170. Resistance of the potentiometer wire is 75. The followingpotential differences can be measured using this potentiometer.(A) 5V (B) 6V (C) 7V (D) 8V

Q.17 In the given potentiometer circuit, the resistance of thepotentiometer wire AB is R0. C is a cell of internal resistance r.The galvanometer G does not give zero deflection for anyposition of the jockey J. Which of the following cannot be areason for this?(A) r > R0 (B) R > > R0(C) emf of C > emf of D (D) The negative terminal of C is connected to A.

P. No. 25

ANSWER KEYEXERCISE # I

Q.1 1.56 102 m/s Q.2 5m, 5 108m2, 6.8 Q.3 (a) a > b > c, (b) a > b > c

Q.4 2IR5 Q.5 60/11 V Q.6 30 V Q.7 1

Q.8 I = 2.5 A, V = 3.5 Volts Q.9 2235 Q.10 12A, 20W Q.11 21RR

Q.12 5r3 Q.13 4 Q.14 1 Q.15 600 Q.16 1 V

Q.17 46.67 cm Q.18 4 ohm Q.19 310 , 5 Q.20 20 ohm

EXERCISE # II

Q.1 (a) J0A/3; (b) 2J0A/3 Q.2 53

RR

1

2 Q.3 (i) 10.52; (ii) 0.3125

Q.4 (i)k

)1k( 2; )1k(

k (ii)

3

02

RVk)1k(

Q.5 4/9 kg/sec., 450 secQ.6 (i) V

ab = 12 V, (ii) 3 amp from b to a

Q.7 R =

e

11A

L0 ; I =

1ee

LAV

0

0 ; V = 1

1L/x0

e1)ee(V

Q.8 7.2 m

Q.10 V922 Q.11

eff = 45 Q.12 (a) 6 m, (b) 1

Q.13 (a) 1.01 W, (b) 0-5A, 0-10V, (c) 0.05 A Q.14 7.5 m, 8.75 m, 6.25 m

EXERCISE # III

Q.1 D Q.2 A Q.3 A Q.4 D

Q.5 (a) No, (b) (c) 8 Q.6 A Q.7 A

P. No. 26

Q.8 Battery should be connected across A and B. Out put can be taken across the terminals A and C or Band C

Q.9 A Q.10 C

Q.11Ammeter

10-3

E

G2

G1106

Voltmeter

100

Q.12 B Q.13 D

Q.14 This is true for r1= r2; So R2 given most accurate value Q.15 A Q.16 AQ.17 C Q.18 D

OBJECTIVE QUESTION BANKONLY ONE OPTION IS CORRECT

Q.1 C Q.2 C Q.3 D Q.4 D Q.5 C Q.6 B Q.7 BQ.8 B Q.9 C Q.10 D Q.11 C Q.12 B Q.13 D Q.14 AQ.15 C Q.16 D Q.17 C Q.18 C Q.19 B Q.20 D Q.21 CQ.22 B Q.23 A Q.24 B Q.25 B Q.26 D Q.27 A Q.28 BQ.29 A Q.30 A Q.31 D Q.32 B Q.33 B Q.34 C Q.35 AQ.36 C Q.37 B Q.38 D Q.39 A Q.40 A Q.41 D Q.42 DQ.43 A Q.44 A Q.45 B Q.46 C Q.47 B Q.48 D Q.49 BQ.50 C Q.51 C Q.52 D Q.53 D Q.54 C Q.55 B Q.56 AQ.57 A Q.58 B Q.59 B Q.60 B Q.61 B Q.62 A Q.63 DQ.64 C Q.65 B Q.66 D Q.67 B

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 ABCD Q.2 D Q.3 AD Q.4 ACD Q.5 C Q.6 AQ.7 ABC Q.8 BC Q.9 AC Q.10 A Q.11 AC Q.12 DQ.13 AD Q.14 C Q.15 BC Q.16 ABC Q.17 A