XII_CH_3_ CURRENT ELECTRICITY.pdf

KVS ZIET BHUBANESWAR
CBTI XII PHY CH-3 CURRENT ELECTRICITY
Q. NO QUESTION
MCQ s 1 MARK EACH
1. The current in a conductor varies with time t as I =2t+3t2
, where I is in ampere and t
in seconds. Electric charge flowing through a section of the (a) conductor during t=2
sec to t=3 sec is
(a) 10 C (b) 24 C (c) 33 C (d) 44 C
2. What length of the wire (specific resistance 48x 10 -8
ohm m) is needed to make a
resistance of 4.2 ? (Diameter = 0.4 mm)
(a) 1.1 m (b) 3.1 m (c) 2.1 m (d) 4.1 m
3. A battery is connected to the conductor of
non-uniform cross-sectional area. The quantities or quantity which remain constant
is/are
(a) electric field only
(b) drift speed and electric field
(c) electric field and current
(d) current only
4. The relaxation time in conductors
(a) increases with the increases of temperature
(b) decreases with the increases of temperature
(c) it does not depends on temperature
(d) all of sudden changes at 400 K
5. By increasing the temperature, the specific resistance of a conductor and a semiconductor
(a) increases for both
(b) decreases for both
(c) increases for a conductor and decreases for a
semiconductor
(d) decreases for a conductor and increases for a
semiconductor
6. An electric current is passed through a circuit (a containing two wires of same
material, connected in parallel. If the lengths and radii of the wires are in the ratio of
3: 2 and 2: 3, then the ratio of the currents passing through the wires will be
(a) 2:3
(b) 3:2
(c) 8:27
(d) 27:8
7. A lead-acid battery of a car has an emf of 12 V. If in the the internal resistance of the
battery is 0.5 ohm, the rmaximum current that can be drawn from the battery will be
the
(a) 30 A

(b) 20 A
(c) 6 A
(d) 24 A
8. A constant voltage is applied between the two ends of a uniform metallic wire, heat
'H' is developed in it. If another wire of the same material, double the radius and
twice the length as compared to original wire is used, then the heat developed in it
will be
(a) H/2
(b) H
(c) 2 H
(d) 4 H
9. Resistances in the two gaps of a metre bridge are 10 ohm and 30 ohm respectively. If
the resistances are interchanged, the balance point shifts by
(a) 33.3 cm
(b) 66.67 cm
(c) 25 cm
(d) 50 cm
10. Kirchhoff's first law for the electric junction is based on
(a) Law of conservation of charge
(b) Law of conservation of energy (c) Law of conservation of angular momentum
(d) Law of conservation of mass
11. 1. Which of the following is wrong?
Resistivity of a conductor is
a) Independent of temperature.
b) Inversely proportional to temperature
c) Independent of dimension of conductor.
d) Less than resistivity of a semiconductor.

12. 2. For a cell, a graph is plotted between the potential difference V across the terminals of the cell and
the current I drawn from the cell (as shown in figure). The emf and internal resistance of the cell are-
a) 2V,0.5ohm
b) 2V,0.4ohm
c) >2V,0.5 ohm
d) >2V,0.4 ohm
13. For a fixed potential difference applied across a conductor, the drift speed of free electrons does not
depend upon
a) free electron density in the conductor.
b) mass of the electrons.
c) length of the conductor
d) temperature of the conductor
14. Two sources of equal emf are connected to an external resistance in series R. The internal resistances
of the two sources are R1 and R2(R2>R1). If the potential difference across the source of internal
resistance R2, is zero, then
a) R=(R2−R1)R2×(R1+R2)
b) R=R2−R1
c) R=(R2+R1)R1R2
d) R=(R2−R1)R1R2
15. If a potential difference V is applied across the conductor is increased to 2V, with its temperature
kept constant. The drift velocity of the free electrons in a conductor will be-
a) remain same
b) become half of its initial value
c) Become doubles of its initial value.
d) Become 0.
16. A battery is connected to the conductor of a non-uniform cross section area. The quantities or
quantity which will remain constant-
a) Electric field only
b) drift speed and electric field only
c) electric field and current
d) current only
17. 7. A current of 0.8A flows in a conductor of 40 ohm for 1 minute. The heat produced in the conductor
will be
a.1445 J b.1536 J c.1569 J d.1640 J
18. The resistivity of alloy manganin is
(a) Nearly independent of temperature
(b) Increases rapidly with increase in temperature

(c) Decreases with increase in temperature
(d) Increases rapidly with decrease in temperature
19. A strip of copper and another of germanium are cooled from room temperature to 80 K. The
resistance of
(a) each of these increases
(b) each of these decreases
(c) copper strip increases and that of germanium decreases
(d) copper strip decreases and that of germanium increases
20. The Kirchhoff’s second law (∑iR = ∑E), where the symbols have their usual meanings, is based on
(a) conservation of momentum
(b) conservation of charge
(c) conservation of potential
(d) conservation of energy
21. In a current carrying conductor the net charge is
(a) 1.6 x 10–19
coulomb
(b) 6.25 x 10–18
coulomb
(c) zero
(d) infinite
22. A current passes through a wire of nonuniform cross-section. Which of the following quantities are
independent of the cross-section?
(a) The charge crossing
(b) Drift velocity
(c) Current density
(d) Free-electron density
23. In the equation AB = C, A is the current density, C is the electric field, Then B is
(a) resistivity
(b) conductivity
(c) potential difference
(d) resistance
24. The relaxation time in conductors
(a) increases with the increases of temperature
(b) decreases with the increases of temperature
(c) it does not depends on temperature
(d) all of a sudden changes at 400 K
25. In conductor when electrons move between two collisions, their paths are … A… when external
fields are absent and … B…when external filed is present. Here, A and B refer to
(a) straight lines, straight lines
(b) straight lines, curved lines
(c) curved lines, straight lines
(d) curved lines, curved lines
26. The example of non-ohmic resistance is
(a) diode
(b) copper wire
(c) filament lamp
(d) carbon resistor
27. Constantan wire is used for making standard resistance, because it has
(a) high melting point
(b) low specific resistance
(c) high specific resistance
(d) negligible temperature coefficient of resistance
28. To minimise the power loss in the transmission cables connecting the power stations to homes and
factories, the transmission cables carry current

(a) at a very low voltage.
(b) at a very high voltage
(c) at 220 volt
(d) neither at a very high voltage nor at a very low voltage
29. A cell of internal resistance r is connected to an external resistance R. The current will be maximum
in R, if
(a) R = r
(b) R < r
(c) R > r
(d) R = r/2
30. A cell of internal resistance r is connected across an external resistance nr. Then the ratio of the
terminal voltage to the emf of the cell is
(a) 1/n
(b) 1/(n+1)
(c) n/(n+1)
(d) (n-1)/n
31. The voltage V versus Current I graphs for a conductor at two different temperatures are shown in the
figure. The relation between T1 and T2 is:
(a) T1 > T2 (b) T1 < T2 (c) T1 = T2 (d)T1 =2T2
32. Two batteries of emf 4V and 8V with internal resistances 1Ω and 2 Ω respectively are connected to
an external resistance R = 9Ω as shown in the figure. The current in circuit and the potential
difference P and Q respectively will be
(a)
1
9
A, 9V (b)
1
12
A, 12V (c)
1
3
A, 3V (d)
1
6
A, 4V
33. Figure shows a balanced Wheatstone bridge. Seema by mistake has changed the resistor P to 11 Ω.
Then she tried to bring the bridge back to balanced condition. Which of the following steps will not
bring the bridge to balance again?
(a) increasing R by 2Ω (b) increasing Q by 10Ω
(c) increasing S by 20Ω (d)making RQ = 2200 Ω2

34. 4 cells of identical emf E, internal resistance r, are connected in series to a variable resistor. The
graph shows the variation of terminal voltage of the combination with the current output. What is the
internal resistance of each cell?
(a) 0.7 Ω (b) 2.8 Ω (c) 1.4 Ω (d)0 Ω
35. The temperature T dependence of resistivity of material A and material B is represented by Fig (i)
and Fig (ii) respectively. Identify material A and material B.
(a) Material A is copper and material B is germanium.
(b) Material A is germanium. and material B is copper.
(c) Material A is nichrome and material B is germanium.
(d) Material A is copper and material B is nichrome.
36. A cell having an emf E and internal resistance r is connected across a variable external resistance R.
As the resistance R is increased, the plot of potential difference V across R is given by
37. If the potential difference V applied across a conductor is increased to 2V with its temperature kept
constant, the drift velocity of the free electrons in the conductor will
(a) remains the same.
(b) becomes half.
(c)be double of its initial value.
(d) becomes zero.

38. Which of the given materials should be used the make standard resistors?
Material Temperature coefficient of
resistivity at 0o
C
SILVER 0.0041
COPPER 0.0068
MANGANIN (ALLOY) 0.002 × 10–3
IRON 0.0065
(a) Silver
(b) Copper
(c)Manganin
(d) Iron.
39. The value of current I in the given circuit is
(a) 4.5 A (b) 3.7 A (c) 2.0 A (d) 2.5 A
40. An ammeter and a voltmeter are connected in series to a battery with an emf of 10V. When a
certain resistance is connected in parallel with the voltmeter, the reading of the voltmeter
decreases three times, whereas the reading of the ammeter increases two times.
Find the voltmeter reading after the connection of the resistance.
(a) 1 V
(b) 2 V
(c) 3 V
(d) 4 V
41. A voltmeter having a resistance of 1800 Ω is employed to measure the potential difference
across a 200 Ω resistor which is connected to the terminals of a DC power supply having an emf
of 50 V and an internal resistance of 20 Ω. What is the percentage decrease in the potential
difference across the 200 Ω resistor as a result of connecting the voltmeter across it?
(a)1% (b) 5% (c) 10% (d) 25%
42. A galvanometer of resistance 10 Ω gives full-scale deflection when 1 mA current passes through
it. The resistance required to convert it into a voltmeter reading up to 2.5 V is
(a) 24.9 Ω (b) 249 Ω (c) 2490 Ω (d) 24900 Ω
43. A coil is embedded in a block of ice placed in an insulated box. If a current of 1.0 A is passed
through the coil by applying a potential difference of 210 V across it, the amount of ice melted in one
hour is
(a) 2.00 kg (b) 2.25 kg (c) 2.50 kg (d) 2.75 kg

44. A battery of emf E and internal resistance r is connected across a variable external resistance R.
Which of the graphs shown in the figure depicts the variation of power P consumed with increase in
R?
45. The current I in the circuit shown in figure is
(a) 1A (b)2A (c)3A (d) 4A
46. The current density J through a plane area has a magnitude 6 Am-2
. If J makes a angle of 600
with the
area vector of magnitude 3 m2
, the magnitude of the current through the area is
(a) 9A (b) 9√3 A (c) 12 A (d) zero
47. A battery of emf 12 V and internal resistance 0.5 Ω is charged by a battery of charger which
supplies a 132 V dc supply using a series resistance of 11.5 Ω. What is the terminal voltage of
the battery during charging?
(a) 15V (b) 16V (c) 17V (d) 18 V
48. A voltmeter reads 3 V at full-scale deflection and is graded as 6000 Ω/V. What resistance should be
connected in series with it so that it reads 12 V at full-scale deflection?
(a) 1.8 x 104 Ω (b) 3.6 x 104 Ω (c) 5.4 x 104 Ω
(d) 7.2 x 104 Ω
49. In 1942, a German physicist Kirchhoff extended Ohm's law to complicated circuits and gave two
laws, which enable us to determine current in any part of such a circuit. According to Kirchhoff's

first rule, the algebraic sum of the currents meeting at a junction in a closed electric circuit is zero.
The current flowing in a conductor towards the junction is taken as positive and the current flowing
away from the junction is taken as negative. According to Kirchhoff's second rule, in a closed loop,
the algebraic sum of the emf's and algebraic sum of the products of current and resistance in the
various arms of the loop is zero. While traversing a loop, if negative pole of the cell is encountered
first, then its emf is negative, otherwise positive.
Kirchhoff's Ist
law follows
(a) law of conservation of energy
(b) law of conservation of charge
(c) law of conservation of momentum
(d) Newton's third law of motion
50. Whenever an electric current is passed through a conductor, it becomes hot after some time. The
phenomenon of the production of heat in a resistor by the flow of an electric current through it is
called heating effect of current or Joule heating. Thus, the electrical energy supplied by the source
of emf is converted into heat. In purely resistive circuit, the energy expended by the source entirely
appears as heat. But if the circuit has an active element like a motor, then a part of energy supplied
by the source goes to do useful work and the rest appears as heat. Joule’s law of heating forms the
basis of various electrical appliances such as electric bulb, electric furnace, electric press etc.
If the coil of a heater is cut to half, what would happen to heat produced?
(a) Doubled
(b) Halved
(c) Remains same
(d) Becomes four times.
51. A cell having an emf E and internal resistance r is connected across a variable external resistance
R. As the resistance R is increased, the plot of potential difference V across R is given by
52. If n cells each of emf e and internal resistance r are connected in parallel, then the total emf and
internal resistance will be

53. Which of the following I-V graph represents ohmic conductors?
54. The resistivity of alloy manganin is
(a) Nearly independent of temperature
(b) Increases rapidly with increase in temperature
(c) Decreases with increase in temperature
(d) Increases rapidly with decrease in temperature
55. An electric heater is connected to the voltage supply. After few seconds, current gets its steady
value then its initial current will be
(a) equal to its steady current
(b) slightly higher than its steady current
(c) slightly less than its steady current
(d) zero
56. Directions: The questions from 6 to 10 consists of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the following four
responses.
(a) If both Assertion and Reason are correct and the Reason is a correct explanation of the
Assertion.
(b) If both Assertion and Reason are correct but Reason is not a correct explanation of the
Assertion.
(c) If the Assertion is correct but Reason is incorrect.
(d) If both the Assertion and Reason are incorrect.
Assertion : In a simple battery circuit, the point of the lowest potential is positive terminal of the
battery.
Reason : The current flows towards the point of the higher potential, as it does in such a circuit
from the negative to the positive terminal.
57. Assertion : Voltmeter is connected in parallel with the circuit.
Reason : Resistance of a voltmeter is very large.
58. Assertion : An electric bulb becomes dim, when the electric heater in parallel circuit is switched on.
Reason : Dimness decreases after sometime.
59. Case study questions: Q no 9 and 10
Whenever an electric current is passed through a conductor, it becomes hot after some time. The
phenomenon of the production of heat in a resistor by the flow of an electric current through it is called
heating effect of current or Joule heating. Thus, the electrical energy supplied by the source of emf is
converted into heat. In purely resistive circuit, the energy expended by the source entirely appears as
heat. But if the circuit has an active element like a motor, then a part of energy supplied by the source

goes to do useful work and the rest appears as heat. Joule’s law of heating forms the basis of various
electrical appliances such as electric bulb, electric furnace, electric press etc.
(i) If the coil of a heater is cut to half, what would happen to heat produced?
(a) Doubled
(b) Halved
(c) Remains same
(d) Becomes four times.
60. (ii) A 25 W and 100 W are joined in series and connected to the mains. Which bulb will glow
brighter?
(a) 100 W
(b) 25 W
(c) Both bulbs will glow brighter
(d) None will glow brighter
61.
VSA 2 MARKS EACH
1. Define the term ‘Mobility’ of charge carriers in a conductor. Write its S.I. unit.
2. Show variation of resistivity of copper as a function of temperature in a graph.
3. A storage battery of emf 8.0 V and internal resistance 0.5 is being charged by a 120 V
dc supply using a series resistor of 15.5 ohm. What is the current during charging?
4. For household electrical wiring, one uses Copper or Aluminum. What considerations are kept in mind?
5. Two wires one of manganin and the other of copper have equal length & equal resistance. Which one
of these wires will be thicker? Justify your answer.
6. The emf of a cell is always greater than the terminal voltage of that cell. Why?
7. Two electric bulbs A and B are marked 220V, 40 W and 220V, 60 W respectively. Which one has
greater resistance?
8. Whenever current flows through any electrical network,voltage drops across each electrical elements.
Arun found the voltage drop across the resistor R1 in the circuit given below with E= 60V,
, and as 40 volts? Is he correct? Justify
9. A single cell provides a feeble current. In order to get a higher current in a circuit, we often use a
combination of cells A combination of cells is called a battery, Cells can be joined in series, parallel
or in a mixed way.
Two cells are said to be connected in series when negative terminal of one cell is connected to
positive terminal of the other cell and so on. Two cells are said to be connected in parallel if positive
terminal of each cell is connected to one point and negative terminal of each cell connected to the
other point. In mixed grouping of cells, a certains number of identical cells are joined in series, and all
such rows are then connected in parallel with each other.

To draw the maximum current from a combination of cells, how should the cells be grouped?
(a) Parallel (b) Series (c) Mixed grouping
(d) Depends upon the relative values of internal and external resistances
10. Metals have a large number of free electrons nearly 1028
per cubic metre. In the absence of electric
field, average terminal speed of the electrons in random motion at room temperature is of the order
of 105
m s-1
When a potential difference V is applied across the two ends of a given conductor, the free
electrons in the conductor experiences a force and are accelerated towards the positive end of the
conductor. On their way, they suffer frequent collisions with the ions/atoms of the conductor and lose
their gained kinetic energy. After each collision, the free electrons are again accelerated due to electric
field, towards the positive end of the conductor and lose their gained kinetic energy in the next
collision with the ions/atoms of the conductor. The average speed of the free electrons with which
they drift towards the positive end of the conductor under the effect of applied electric field is called
drift speed of the electrons.
The drift speed of the electrons depends on
(a) dimensions of the conductor
(b) number density of free electrons in the conductor
(c) both (a) and (b)
(d) neither (a) nor (b)
11. The resistance of a conductor at temperature to
C is given by Rt = Ro (1 + αt)
where Rt is the resistance at to
C, R0 is the resistance at 0o
C and α is the characteristics constants of the
material of the conductor.
Over a limited range of temperatures, that is not too large. The resistivity of a metallic conductor is
approximately given by ρt = ρ0 (1 + αT)
where α is the temperature coefficient of resistivity. Its unit is K-1
For metals, α is positive i.e., resistance increases with rise in temperature.
For insulators and semiconductors, α is negative i.e., resistance decreases with rise in temperature.
For a metallic wire, the ratio V/I (V = applied potential difference and I = current flowing) is
(a) independent of temperature
(b) increases as the temperature rises
(c) decreases as the temperature rises

(d) increases or decreases as temperature rises depending upon the metal
12. The plot of the variation of potential difference across a combination of three identical cells in series,
versus current is as shown in the figure. What is the emf of each cell? (Delhi 2008)
13. A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the
ends of a A diameter 2AB?
14. Two metallic wires of the same material have the same length but cross-sectional area is in the ratio
1 : 2. They are connected
(i) in series and
(ii) in parallel. Compare the drift velocities of electrons in the two wires in both the cases (i) and (ii).
SA 3 MARKS EACH
1. a. Define emf of a cell.
b. Under what condition emf is equal to terminal potential difference.
c. A 5 V battery of negligible internal resistance is connected across a 200 V
battery and a resistance of 39 Ω as shown in the figure. Find the value of the
current.
2. The network PQRS, shown in the circuit diagram, has the batteries of 4 V and 5 V and
negligible internal resistance. A milliammeter of 20 Ω resistance is connected between P and
R. Calculate the reading in the milliammeter.
3. 1. Define current sensitivity and voltage sensitivity of a galvanometer. Increasing the current
sensitivity may not necessarily increase the voltage sensitivity of a galvanometer. Justify.
4. i)Show on a plot, variation of resistivity of a) a conductor b) a typical semiconductor as a function of
a temperature.
ii) Using the expression for the resistivity in terms of number density and relaxation time between
the collisions explain how resistivity in case of a conductor increases while its decreases for
semiconductor, with rise of temperature.

5. When a 60W, 220v bulb and 100W, 220v bulb are connected in series then which of the bulb will be
brighter and why?
6. A variable resistor R is connected across a cell of emf E and internal resistance r.
a) Draw the circuit diagram.
b) Plot the graph showing variation of potential drop across R as a function of R.
c) At what value of R current in circuit will be maximum.
7. The following table gives the length of three copper wires, their diameter and the applied potential
difference across their ends. Arrange the wires in increasing order of the following:
(i)The magnitude of the electric field within them,
(ii)the drift speed of electrons through them, and
(iii)the current density within them.
Wire no. Length Diameter Potential difference
1 l 3d V
2 2l d V
3 3l 2d 2V
8. Analyze the following statements and give reasons to justify them.
(i)The electron drift speed is very small still current is established
almost instantly as circuit is closed?
(ii)The electron drift arises due to force experienced by electrons
in the electric field which causes acceleration, still electrons
acquire a steady average drift speed.
(iii)Even if electron drift speed and electronic charge is very
small, still we obtain large amounts of current in a conductor.
9. Potential Difference V is applied across the ends of the copper wire of length l and diameter D.What
is the effect on drift velocity of electrons if
a)V is doubled? b) l is doubled? c) Dis doubled?
10. The variation of resistance of a metallic conductor with temperature is given in figure.
(a) Calculate the temperature coefficient of resistance from the graph.
(b) State why the resistance of the conductor increases with the rise in temperature.

11. At room temperature 27.0ºC the resistance of a heating element is 100 Ω. What is the temperature of
the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the
material of the resistor is 1.70 x 10-4
℃ .
12. Calculate the current drawn from the battery in the given network.
13. A wire of 15 Ω resistance is gradually stretched to double its original length. It is then cut into two
equal parts. These parts are then connected in parallel across a 3.0 volt battery. Find the current
drawn from the battery.
14. A battery of emf 6 V and internal resistance 2Ω is connected to a resistor. If the current in the circuit
is 0.25 A, find
(i) the resistance of the resistors;
(ii) the terminal voltage of the battery.
CASE BASED QUESTIONS 4 MARKS
1. Any source of emf has some internal resistance itself, called internal or source
resistance. When we connect the terminals of a cell, a current flows in the wire from
positive terminal of the cell towards the negative terminal. But inside the electrolyte
of the cell, the positive ions flow from the lower to the higher potential (or negative
ions from the higher to the lower potential) against the background of other ions and
neutral atoms of the electrolyte. So the electrolyte offers some resistance to the flow
of current inside the cell.
The resistance offered by the electrolyte to the flow of current between its
electrodes is called the internal resistance of the cell. It depends on nature and
concentration of electrolyte, separation and common area of the electrodes dipped
in the electrolyte, and temperature of the electrolyte. Internal resistance causes
energy loss which occurs inside a battery when a current is driven round an external
circuit. The greater the current, the greater the energy loss and the small is the
terminal p.d. of the battery. The internal resistance of a battery increases with age
and so reduces the current it can drive. The knowledge of internal resistance
becomes important when we consider how a source of emf can deliver maximum
power to an appliance connected to it. According to maximum power theorem this
occurs when the internal resistance of the source equals the resistance of the
appliance.
(i) Define internal resistance
(ii) Define emf of a cell
(iii) A variable resistor R is connected across a cell of emf and internal resistance
r as shown in the figure.
Draw a plot showing the variation of (i) terminal voltage V and (ii) the
current I, as a function of R.

2. Wheatstone bridge. It is an arrangement of four resistances used to determine one
of these resistances quickly and accurately in terms of the remaining three
resistances. This method was first suggested by a British physicist Sir Charles F.
Wheatstone in 1843.
A Wheatstone bridge consists of four resistances P, Q,R and S; connected to form the
arms of a quadrilateral ABCD. A battery of emf & is connected between point A and C
called cell arm and a sensitive galvanometer between Band D called galvanometer
arm,
Let S be the resistance to be measured. The resistance R is so adjusted that there is
no deflection in the galvanometer. The bridge is said to balanced when the potential
difference across the galvanometer is zero so that there is no current through the
galvanometer. In the balanced condition of the bridge,
(i) What will happen to null point if cell arm and galvanometer arm are
interchanged?
(ii) Name a device based on the principle of Wheatstone bridge
(iii) The Wheatstone's bridge of fig is showing no deflection in the galvanometer
joined between the points B and D. Compute the value of R.
3. If n cells each of emf E & internal resistance r are connected in series and an external resistance R is
connected to combination. If the polarity of m cells is reversed, Find the current in external resistance.
4. At room temperature, the resistance of the heating element is 100 ohm. At what temperature does
the resistance of the element change to 117 ohm?
( The temperature coefficient of the given material is 1.7*10-4/⁰C )
5. When the electric cell (source of EMF) is in a closed circuit, the current flows through the circuit.
There is a fall of potential across the internal resistance of the cell. The terminal potential difference
between the two electrodes of the cell becomes less than the EMF of the cell by an amount equal to
potential drop across the internal resistance of the cell. Thus, in a closed circuit the terminal potential
difference of a cell is always less than the EMF of the cell.

(i) EMF of a cell is independent of:
(a) size of the electrodes
(b) quantity of electrolyte presents in the cell
(c) distance between the electrodes
(d) all of these
(ii)Three cells of EMF, 2.0 V,2.5 V and 3.0 V are connected in series. Their internal resistances are
0.20 Ω, 0.20Ω and 0.15Ω respectively. The battery is connected to an external resistor of
6.5 Ω wire through a very low resistance ammeter, what would be the reading of ammeter?
(a) 1.06 Ω (b) 1Ω (c) 1.2 Ω (d) 2.1 Ω
(iii) A cell of emf E and internal resistance r is connected in series with an external resistance nr. Then
ratio of terminal potential difference to emf is:
(a)1/n (b) 1/(n+1) (c) n/(n+1) (d) (n+1)/n
(iv) For a cell, the terminal potential difference is 3.6 V, when the circuit is open. If the potential
difference reduces to 3V, when the cell is connected to 5 Ω resistance, the internal resistance of the
cell is:
(a)1 Ω (b) 2 Ω (c) 4 Ω (d) 8 Ω
6. Consider a resistor connected to a source of emf. The energy gets dissipated entirely in the form of
heat. This phenomenon of production of heat in a resistor by the flow of current through it is called
heating effect of current.
When potential difference is applied across the ends of conductor, its free electrons get accelerated in
the opposite direction of the applied field. The kinetic energy gained by the free electrons is
transferred to the metal ions at the time of collisions. According to Joule’s law of heating, the amount
of heat produced is H = I2Rt
(i)If two identical heaters each rated as (1000W,220V) are connected in parallel to 220V, then power
consumed is
(a) 200 W (b) 2500 W (c) 250 W (d) 2000 W

(ii)Two wires having resistances R and 2R are connected in parallel then ratio of heat generated is R
and 2R is
(a) 3:2 (b) 2:1 (c) 1:4 (d) 4:1
(iii)When 4 equal resistors are connected in series with a battery, they dissipate a power of 10W.What
will be the power dissipated through any of them if it is individually connected across the same battery?
(a) 40 W (b) 10/3 W (c) 90 W (d) 10 W
(iv)Bulb B1(100W-250V) and Bulb B2(100W-200V) are connected across 250V.What is the potential
drop across B2 ?
(a) 200 V (b) 250 V (c) 98 V (d) 48 V
7. CASE BASED QUESTION :
A single cell provides a feeble current. In order to get a higher current in a circuit, we often use a
combination of cells A combination of cells is called a battery, Cells can be joined in series, parallel
or in a mixed way.
Two cells are said to be connected in series when negative terminal of one cell is connected to
positive terminal of the other cell and so on. Two cells are said to be connected in parallel if positive
terminal of each cell is connected to one point and negative terminal of each cell connected to the
other point. In mixed grouping of cells, a certains number of identical cells are joined in series, and
all such rows are then connected in parallel with each other.
i)To draw the maximum power from a cell of emf E and internal resisrance r connected to an
external resistance R what should be the value of R?
(a) R = r (b) R = r/2 (c) R = 0 (d) R = 2r
(ii) The total emf of the cells when n identical cells each of emf E are connected in parallel is
(a) nε
(b) n2ε
(c) E
d) εn
(iii) 4 cells each of emf 2 V and internal resistance of 1Ω
are connected in parallel to a load resistor of 2Ω
. Then the current through the load resistor is
(a) 2 A (b) 1.5 A (c) 1 A (d) 0.888 A
(iv) If two cells out of n number of cells each of internal resistance 'r' are wrongly connected in
series, then total resistance of the cell is
(a) 2nr (b) nr - 4r (c) nr (d) r
8. The following questions consist of two statements – Assertion(A)and Reason (R).
Answer these questions by selecting the appropriate option given below:
(a) Both A and R are true and R is the correct explanation of A.
(b)Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false and R is also false.
1) Assertion (A): The resistance of a conductor increases with an increase in its length.
Reason (R): The resistance of a conductor is directly proportional to its length.

2) Assertion (A): The drift velocity of charge carriers in a conductor is directly proportional to the
electric field applied to the conductor.
Reason (R): Drift velocity is the average velocity of charge carriers and depends on the strength of
the electric field.
3) Assertion (A): Electric potential is a vector quantity.
Reason (R): Electric potential is a scalar quantity representing the electric potential energy per unit
charge at a point.
4) Assertion (A): An ideal ammeter has zero resistance and is connected in parallel in a circuit.
Reason (R): An ideal ammeter should not change the current in the circuit when connected.
9. The network PQRS, shown in the circuit diagram, has the batteries of 4 V and 5 V and negligible
internal resistance. A milliammeter of 20 Ω resistance is connected between P and R. Calculate the
reading in the milliammeter.
10. An ammeter of resitance 1 Ω can measure current upto 1.0 A
(i) What must be the value of the shunt resistance to enable the ammeter to measure upto 5.0 (A)?
(ii) What is the combined resistance of the ammeter and the shunt?
LA ( 5MARKS)
1 Why do the 'free electrons', in a metal wire, 'flowing by themselves', not cause any
current flow in the wire ?
(b) Define 'drift velocity' and obtain an expression for the current flowing in a wire, in
terms of the 'drift velocity' of the free electrons.
(c) Use the above expression to show that the 'resistivity', of the material of a wire, is
inversely proportional to the 'relaxation time' for the 'free electrons' in the metal.
2 19.a) Find the current through 1 ohm
b) By using Kirchhoff’s laws obtain balance condition of a Wheatstone bridge.
3 Use Kirchhoff’s rules to obtain conditions for the balance condition in a Wheatstone bridge.
Calculate the current drawn from the battery by the network of resistors shown in the figure.

4 (i)Two cells of emfs E1 and E2 and internal resistances r1 and r2
are connected in parallel. Derive the expression for the net
emf and net resistance for this combination.
(ii)A cell of emf E and internal resistance r is connected across a
variable resistance R. Plot graphs showing variation of
(a)E and R and
(b)Terminal potential difference V and R.
Examine the second graph to predict under which V
becomes equal to E.
5 i)The figure shows a plot of terminal voltage ‘V’ versus the current ‘i’ of a given cell. Calculate from
the graph
(a) emf of the cell and
(b) internal resistance of the cell.
ii)A cell of emf 4 V and internal resistance 1 Ω is connected to a d.c. source of 10 V through a
resistor of 5 Ω. Calculate the terminal voltage across the cell during charging
ANSWERS FOR MCQs
1. (b) 24 C
2. (a) 1.1 m
3. (d) current only
4. B
5. (c) increases for a conductor and decreases for a
semiconductor
6. (c) 8:27
7. (d) 24 A
8. (c) 2 H
9. (d) 50 cm
10. (a) Law of conservation of charge
11. A
12. D

13. A
14. B
15. C
16. D
17. B
18. A
19. D
20. D
21. (c)
Explanation:
In a current carrying conductor, the net charge is zero.
22. (d)
23. a)
Explanation:
J =σE ⇒ Jρ=E
J is current density, E is electric field
so B = ρ = resistivity.
24. (b)
Explanation:
Because as temperature increases, the resistivity increases and hence the relaxation time decreases
for conductors
25. b)
Explanation:
In conductor when electrons move between two collisions, their paths are straight lines when external
fields are absent and paths are curved in general when external field is present.
26. a)
27. d)
28. (b) The power dissipated in the transmission cables is inversely proportional to the square of voltage
at which current is transmitted through the cables. Therefore to minimize the power loss the
transmission cables carry current at a very high voltage.
29. a)
30. c) n/(n+1)
31. (a) T1 > T2
32. (c)
1
3
A, 3V
33. (c) increasing S by 20Ω
34. (a) 0.7 Ω
35. (b) Material A is germanium. and material B is copper.
36. (b)
37. (c) be double of its initial value.
38. (c)Manganin
39. c) 2.0 A
40. b) 2 V
41. a) 1%
42. c) 2490 Ω
43. b) 2.25 kg
44. d)
45. c) 3A
46. a) 9A
47. c) 17V
48. c) 5.4 x 104 Ω

49. b) law of conservation of charge
50. b) Halved
51. b
52. a
53. a
54. a
55. b
56. d
57. b
58. b
59. a
ANSWERS FOR VSA ( 2 MARKS)
1 Mobility of charge carriers is defined as the magnitude of the drift velocity per unit electric field E.
Mobility=Vd/E =eτ/m
2 Graph showing resistivity increasing with temperature
3 net emf in the circuit will be
= 120-8.0=112 V
I= E' / R+r =112/ {15.5+0.5}. = 7A
4 i) Cost of metal.
ii)Good conductivity of metal.
5 Copper wire R=ρc/Ac,
manganin wire R=ρml/Am
ρc/Ac=ρm/Am
Ac/Am=ρc/ρm
we know ρm>ρc (as manganin is an alloy)
Ac<Am
6 The emf of a cell is greater than its terminal voltage because there is some potential drop
across the cell due to its small internal resistance.
V=E-Ir
7
We know
For Bulb A,
For Bulb B
Bulb A has higher resistance because its power is less.
8
are in series
= = 15
Now are parallel
= = 6

Now are series
Rnet =
Rnet = 6+18 = 24
I= =
Now voltage drop across
Arun is not correct .
9 a) Parallel
10 b) number density of free electrons in the conductor
11 b) increases as the temperature rises
12 Total emf of three cells in series = P.D corresponding to zero current = 6V
∴ The emf of each cell = 63 = 2V
13 The effective resistance between A and BO
14 i)2:1 ii) 1:1
15
ANSWERS FOR SA ( 3 MARKS)
1. b. Value of current 200-5/39 = 5 A
2. . Applying loop rule to loop PQRP
-4 = 60(I – I1) – 20 I1 = 0
or – 4 = 60I – 60I1 – 20I1
or 20I1 -15 I = 1 …[+ by 4 …(i)]
Applying loop Yule to loop PRSP, we get
-5 + 200 I + 20 I1 = 0
4I1 + 40 I = 1 …[+ by 5 …(ii)]
3. Current sensitivity is defined as the deflection produced in the galvanometer when unit current is passed
through its coil. Current Sensitivity = θ/I = nBA/K,n – number of turns in galvanometer,K- restoring
cofficient
Voltage sensitivity is defined as the deflection produced in the galvanometer when unit voltage is applied
across the coil of the galvanometer.
Voltage Sentivity = θ /V= nBA/KR ,R- Resistance of galvanometer coil

4. From the equation if we increase the temperature
then relaxation time will decrease. So for conductor
the resistivity will increase.
For semi-conductor the relaxation time will decrease
as like conductors, but along with that the no. of
conducting ions (electrons and holes) will also
increase rapidly. So, the resistivity will decrease for
semiconductors.
5. P=V2/R, Here in series connection V is constant
So, P is inversely proportional to R2
For P then R will be less and vice versa. For small value of R, more current will flow through that
bulb. So, 100W bulb will glow brightly.
6. a)
b)
c) We have, V = IR or, I = V/R When R = 0, Current will be maximum. Hence, Maximum current drawn will be
at R =0
7. (i)E1 =V/l, E2 =V/2l, E3 =2V/3l ∴ E2 < E3< E1
(ii)As vd ∝ E,∴ vd2 < vd3< vd1
(iii) j = ne vd, ∴ j2 < j3< j1
8. (i) As soon as the circuit is closed, electric field is set up throughout the circuit instantly. Electrons in
every part begins to drift and current starts to flow instantly.
(ii) As the electron accelerates it collides with positive ion of the metal. It loses its drift speed after
collision but starts to accelerates and increase its speed again only to suffer a collision again and
so
on. On average, therefore an electron acquires a steady average drift speed.
(iii) As I = neAvd, even if e and vd are very small, we obtain a large current because the electron
density (n) is very large (of the order of 1029
m-3
).
9. Since
=
V is doubled, drift velocity gets doubled.
(2) If l is doubled, drift velocity gets halved.
(3) Since V of is independent of D, drift velocity remains unchanged.
10. (a) Temperature coefficient of Resistance
Where R is the resistance of the conductor and θ is the temperature corresponding to pt.A
(b) Since R =

When temperature increases, no of collisions increases average relaxation time decreases, hence
resistance Increases.
11. Room temperature, T=27
Resistance of the heating element at
Temperature co-efficient of the material of the filament,
is given by the relation,
Therefore, at 1027 the resistance of the element is 117 .
12. 2 A
13. R = 15 Ω
On stretching to double its original length, the resistance becomes R1 = 60 Ω, as on
stretching volume is constant and Rα l2
.
The two cut parts will have a resistance of 30 Ω each as they are connected in parallel, then,
I= 0.2 A
14. i)R =22 Ohm ii)V= 5.5 V
ANSWERS FOR CBQ ( 4 MARKS)
1. (i) Definition 1mark
(ii) Definition 1mark
(iii) Graph 2 mark
2. (i) No change 1 mark
(ii) Metre bridge 1 mark
(iii) 25 ohm 2 mark
3. For n no of cells total emf nE
If polarity of m cells reversed then emf will be (nE-mE)
Total resistance (nr+R)
So the current will be I= (nE-mE)/(nr+R)
4. Temperature coefficient = (Rt-R27)/R27(t-27)
From calculation, t=1027οC
5. (i) (d) all of these
(ii) (a) 1.06 Ω
(iii) (c) n/(n+1)
(iv) (a)1 Ω
6. (i) (d) 2000 W
(ii) (d) 4:1
(iii) (a) 40 W
(iv) (c) 98 V
7. (i) a (ii) c (iii) d (iv) c
8. (a)Both A and R are true and R is the correct explanation of A.
(a) Both A and R are true and R is the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

9. . Applying loop rule to loop PQRP
-4 = 60(I – I1) – 20 I1 = 0
or – 4 = 60I – 60I1 – 20I1
or 20I1 -15 I = 1 …[+ by 4 …(i)]
Applying loop Yule to loop PRSP, we get
-5 + 200 I + 20 I1 = 0
4I1 + 40 I = 1 …[+ by 5 …(ii)]
∴ Reading of milliammeter = 0.064 A
10.
KEY 5 MARKS
1 While flowing themselves, the free electrons have random motion in a metal. There in no net flow of charge
across any section of the wire. So no current flows in the wire.
(b) Drift velocity. Force exerted on a free electron by the external field E is
F=-eE or ma =-eE a= -eE/m Average thermal velocity of free electrons in a conductor is zero, u = 0
The average time elapsed between two successive collisions of a drifting electron is relaxation time (t). The
average velocity gained by a free electron during this time is the drift velocity given by

2 )By applying KVL in both of the loops
We will get the current 0.13A through 1 ohm resistance.
b) By applying KVL in the loop of Wheatstone bridge, in balanced condition when the current through
galvanometer will be 0 then P/Q=R/S
3 Conditions for the balance condition in a Wheatstone bridge :
Applying Kirchoffs loop rule to the loop ABDA we have
This is the required balance condition in a Wheatstone bridge arrangement.
Circuit diagram can be rearranged as shown below :
It forms a wheatstone’s bridge
It is the condition of null point when no current flows through BD arm, i.e. 5 Ω.
Resistances P = (1 Ω) and R = (2 Ω) are in series;
Similarly, Resistances Q = (2 Ω) and S in series,

4 (i)Correct derivation -------------------- (3)
Enet = E1r2 + E2r1/r1 + r2
rnet = r1r2/ r1 + r2
(ii)
---------------------------- (
1
2
+
1
2
)
From the graph,
V = IR = (E/R+r) R = E / 1+
𝑟
𝑅
When R --› 0, V = 0
When R --›∞, V = E ------------------------------------------- (1)
5 i)
ii)

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