Summer Vacation Holiday

Electric Field & Charges and Electrostatic Potential & Capacitance

(Week – 1)

1. Derive an expression for torque acting on a dipole placed in an

external electric field.
2. Derive an expression for electric field due to a line charge.
3. Derive an expression for electric field due a uniformly charged thin
sheet.
4. Find an expression for electric potential due to a point charge.
5. Find an expression for electric potential energy of a dipole placed in a
uniform external electric field.
6. Deduce an expression for electric potential at an axial point due to a
dipole.
7. Find an expression for electric potential at an equatorial point due to
a dipole.
8. Derive an expression for potential energy of a two point charge
system.
 Summer Vacation Assignment
Current Electricity (Week 2)
Class XII Physics
Objectives (Week 2)
Q1: Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2 is v. If the
electron density of copper is 9 × 1028/m3 the value of v in mm/s is close to (Take charge of electron to be =
1.6 × 10–19 C)
(a) 3 (b) 0.2 (c) 2 (d) 0.02
Q2: Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these
resistances are now connected in parallel combination to the same battery, the electric power consumed will
be
(a) 240 W (b)120 W (c) 60 W (d) 30 W
Q3: A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W.
Dissipated power when an ideal power supply of 11 V is connected across it is
(a) 11 × 10–4 W (b) 11 × 10–5 W (c) 11 × 105 W (d) 11 × 10–3 W
Q4: An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer
of length 1 m and resistance 5 . The value of R, to give a potential difference of 5 mV across 10 cm of
potentiometer wire is
(a) 490 (b) 495 (c) 395 (d) 480
Q5: A cell of internal resistance r drives current through an external resistance R. The power delivered by the
cell to the external resistance will be maximum when
(a) R = 0.001 r (b) R = r (c) R = 2r (d) R = 1000 r
Q6: A metal wire of resistance 3 is elongated to make a uniform wire of double its previous length. This new
wire is now bent and the ends joined to make a circle. If two points on this circle make an angle 60° at the
centre, the equivalent resistance between these two points will be
(a) (7/2) Ω (b) (5/2) Ω (c) (12/5) Ω (d) (5/3) Ω
Q7: On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The
resistance of the combination is 1 kΩ. How much was the resistance on the left slot before the interchange?
(a) 990 (b) 505 (c) 550 (d) 910
Q8: A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius
of the wire is doubled, the rate of heat developed in the wire will be
(a) Increased 8 times (b) Unchanged (c) Doubled (d) Halved
Q9: A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of
220 V, a steady current of 2 A passes in it and the temperature is 500°C more than room temperature. What
is the temperature coefficient of resistance of the heating element?
(a) 1×10– 4 °C–1 (b) 2 × 10– 4 °C–1 (c) 0.5 × 10– 4 °C–1 (d) 5 × 10– 4 °C–1
Q10: A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r/2.The
resistance of new wire will be
(a) 400 Ω (b)100 Ω (c) 200 Ω (d)1600 Ω
Q11: A 2 W carbon resistor is colour coded with green, black, red and brown, respectively. The maximum
current which can be passed through this resistor is
(a) 20 mA (b) 0.4 mA (c) 100 mA (d) 63 mA
Q12: In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW.
The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be
(a) 14 A(b) 8 A(c) 10 A(d) 12 A
Q13: If a wire is stretched to make it 0.1% longer, its resistance will
(a) increase by 0.05% (b) increase by 0.2% (c) decrease by 0.2% (d) decrease by 0.05%
Q14: A thermocouple is made from two metals, antimony and bismuth. If one junction of the couple is kept
hot and the other is kept cold then, an electric current will
(a) flow from antimony to bismuth at the cold junction
(b) flow from antimony to bismuth at the hot junction
(c) flow from bismuth to antimony at the cold junction
(d) not flow through the thermocouple.
Q15: The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be
(a) 3 ohm (b) 2 ohm (c) 1 ohm (d) 4 ohm
16.If 25% part of length of wire is stretched by 25%, then percentage change in resistance of wire will be
about
a) 7%b) 14%c) 25%d) 62.5%
17.A boy has two spare light bulbs in his drawer. One is marked 240 V and 100 W and the other is marked
240 V and 60 W. He tries to decide which of the following assertions are correct?

(A) The 60 W light bulb has more resistance and therefore burns less brightly.
(B) The 60 W light bulb has less resistance and therefore burns less brightly.
(C) The 100 W bulb has more resistance and thereforeburns more brightly.
(D) The 100 W bulb has less resistance and therefore burns less brightly.
18.In a circuit a cell with internal resistance r is connected to an external resistance R. The condition for the
maximum current that drawn from the cell is

(A) R= r (B) R < r (C) R > r (D) R =0

19.In parallel combination of n cells, we obtain

(A)more voltage (B) more current (C) less voltage (D) less current

20.1 ampere current is equivalent to

18 –1 18 –1
(A) 6.25 × 10 electrons s (B) 2.25 × 10 electronss
14 –1 14 –1
(C) 6.25 × 10 electrons s (D) 2.25 × 10 electrons s

21.The voltage V and current I graphs for a conductor at two different temperatures T1 and T2 are shown in the figure.
The relation between T1 and T2 is

(A) T1 T2 (B) T1 T2

 (C) T1 =T2 (d)T1=1/T2

22.Figure (a) and figure (b) both are showing the variation of resistivity () with temperature (T) for some
materials. Identify the type of these materials.

(a)Conductor and semiconductor

(B)Conductor and Insulator

©Insulator and semiconductor

(d)Both are conductors

23.Figure shows current in a part of an electric circuit, then current I is

(A)1.7 A (B) 3.7 A

(C) 1.3 A (D) 1A
24.In the given circuit the potential at point B is zero, the potential at points A and D will be

(A) VA = 4V; VD = 9V (C) VA = 9V; VD = 3V

(B) VA = 3V; VD =4V

(D) VA = 4V
 −6 2
25.An electric current of 16 A exists in a metal wire of cross section 10 m and length 1 m. Assuming one free
3 3
electron per atom. The drift speed of the free electrons in the wire will be (Density of metal = 5  10 kg/m , atomic
weight = 60)

−3 −3
(A) 5  10 m/s (B) 2  10 m/s
−3 −3
(C) 4  10 m/s (D) 7.5  10 m/s

26. KVL is based upon law of conservation of

(a) charge (b) energy (c) mass (d) momentum

27.To get maximum current in a resistance of 3 , one can use n parallel rows of m cells each (connected
in series). If the total no. of cells is 24 and the internal resistance is 0.5 ohm then

(A) m = 12, n = 2 (B) m = 8, n = 3

(C) m = 2, n = 12 (D) m = 6, n = 4

28.In the given circuit, the resistance R hasa value that depends on the
current. Specifically, R is 20 ohms when I is zero and the increase in R
resistance (in ohms) is numerically equal to one-half of the current in
amperes. What is the value of current I in the circuit?
250 V

(a)12.5 A (B) 10 amp (c)18.5 (d)8.33 A

Derivations (Week 3)

1. Define drift velocity and derive an expression for it.

2. Derive the expression I=nAevd
3. Deduce Ohm's law from elementary ideas and hence write an expression for
resistance and resistivity.
4. Derive an expression for conductivity in terms of mobility
5. Derive an expression for the current in a circuit with external resistance R when (a) n
identical cells of emf E and internal resistance r are connected in series (b) m identical
cells are connected in parallel
6. State and explain Kirchhoff’s laws.
7. State and explain the principle of Wheat Stone's principle. Deduce it using
Kirchhoff’s laws.
8. Explain the variation of resistance and resistivity with temperature and hence define
temperature coefficient of resistance and resistivity.
9. State the limitations of ohm’s law.
10. Prove that emf of a cell is greater than its potential difference.
11. Obtain the expression of internal resistance of a cell.
Suggested Investigatory Projects (Week 4)

1. To study various factors on which the internal resistance/EMF of a cell depends. (Roll No.
01,06,11,16,21,26)

2. To study the variations in current flowing in a circuit containing an LDR because of a

variation in (a) the power of the incandescent lamp, used to 'illuminate' the LDR (keeping all
the lamps at a fixed distance). (b) the distance of a incandescent lamp (of fixed power) used
to 'illuminate' the LDR. (Roll No 02,07,12,17,22,27)

3. To find the refractive indices of (a) water (b) oil (transparent) using a plane mirror, an equi
convex lens (made from a glass of known refractive index) and an adjustable object
needle.(Roll No 03,08,13,18,23)

4. To investigate the relation between the ratio of (i) output and input voltage and (ii) number
of turns in the secondary coil and primary coil of a self-designed transformer. (Roll No
04,09,14,19,24,30)

5. To investigate the dependence of the angle of deviation on the angle of incidence using a
hollow prism filled one by one, with different transparent fluids. (Roll No 05,10,15,20,25,35)

6. To estimate the charge induced on each one of the two identical Styrofoam (or pith) balls
suspended in a vertical plane by making use of Coulomb's law. (Roll No 28, 31,34,36,41)

7. To study the factor on which the self-inductance of a coil depends by observing the effect of
this coil, when put in series with a resistor/(bulb) in a circuit fed up by an A.C. source of
adjustable frequency. (Roll No29, 32,37,39,42)

8. To study the earth's magnetic field using a compass needle -bar magnet by plotting magnetic
field lines and tangent galvanometer. (Roll No 33,38 ,40)