## Assertion and Reason Type Question

Following question consider two statements one labelled as statement-1 and another as statement-2. Study both statements and mark your answer using the codes given blow.
1. Both Statement-1 and Statement-2 are true and Statement-2 is correct explanation of Statement-1.
2. Both Statement-1 and Statement-2 are true and Statement-2 is not a correct explanation of Statement-1.
3. Statement-1 is true but statement-2 is false.
4. Statement-1 is false and statement-2 is true.
Question-1
Statement-1 Free electrons in conductor are always in state of continuous random motion.
Statement-2 The random motion of free electrons is due to thermal energy of the conductor.

Question-2
Statement-1 Drift velocity of electrons in a conductor increase on increasing the temperature of the conductor.
Statement-2 On increasing the temperature of a conductor, resistivity of the conductor increases.

Question-3
Statement-1 For metals relaxation time for electrons decreases with increase in temperature.
Statement-2 With the increase in temperature, number of collision per unit time that electrons made with lattice ion also increases.

## Multiple Choice Type Questions

Question-4
Resistivity of the material of a conductor having uniform area of cross-section varies along its length according to the relation
ρ= ρ0 (a+bx)
if L is the length of the conductor and be the area of cross-section then resistivity of the conductor given by relation

Question-5
Given a current carrying wire of non-uniform cross-section. Which of the following is constant through out the wire.
(a)Current only
(b)Current and drift speed
(c)Drift speed only
(d)Current, drift speed and electric field

Question-6
When potential difference across a given copper wire is increase, drift velocity of charge carriers
(a)Decreases
(b)Increases
(c)Remain same
(d)Get reduced to zero

Question-7
A material B has twice the specific resistance of the material A. A circular wire made of B has twice the diameter of the wire made of A. Then , for the two wires to have to have the same resistance, the ratio
La/Lb of their respective lengths must be
(a) ½
(b) 2
(c) ¼
(d)1

Question-8
What will be the equivalent resistance between A and D

(a)40 Ω
(b)20Ω
(c)30Ω
(d)10Ω

Question-9
In the given circuit below the equivalent resistance between points A and C

(a)32
(b)30.7
(c)33.07
(d)3.07

Question-10
A circular ring having negligible resistance is used to connect four resistors as shown below in the figure.
The equivalent resistance between point A and B is

(a)10R
(b)2R
(c)3R
(d)R

## Paragraph Type Questions

Two concentric metal spherical shells of radius a and b respectively are separated by weakly conducting material of conductivity σ
A potential difference V is applied across the two shells
Question 11
Find the resistance between the shells

Question 12
Find the electric field at a distance r from the center

## Multiple Choice Type Questions

Question 13
A potential difference of V is applied at the ends of a copper wire of length l and diameter d. On doubling only d, drift velocity
(a) Becomes two times
(b) Becomes half
(c) Does not change
(d) Becomes one fourth

Question 14
The effective resistance between points P and Q of the electrical circuit shown in the figure is

(a) $\frac {2Rr}{R+r}$
(b) $8R(R+r)(3R+r)$
(c) $2r+4R$
(d) $\frac {5R}{2} + 2r$

Question 15
Which of the following characteristics of electrons determines the current in a conductor?
(a) Drift velocity alone.
(b) Thermal velocity alone.
(c) Both drift velocity and thermal velocity.
(d) Neither drift nor thermal velocity.
Question 16
Water of volume 2 litre in a container is heated with a coil of 1 kW at 27 °C. The lid of the container is open and energy dissipates at rate of 160 J/s. In how much time temperature will rise from 27°C. to 77°C. [Given specific heat of water is 4.2 kJ/kg]
(a) 8 min 20 s
(b) 6 min 2 s
(c) 7 min
(d) 14 min

Question 17
If a wire is stretched to make it 0.1% longer, its resistance will
(a) increase by 0.2%
(b) increase by 0.05%
(c) decrease by 0.2%
(d) decrease by 0.05%

Question 18
Six identical resistors are connected as shown in the figure. The equivalent resistance will be

(a)Maximum between P and R
(b)Maximum between Q and R
(c)Maximum between P and Q
(d) All are equal

Question 19
An ideal gas is filled in a closed rigid and thermally insulated container . A coil of 100 ω resistor carrying a current of 1 A for 5 minutes supplies heat to the gas . The change in the internal energy of the gas is
(a) 10 kJ
(b)30 kJ
(c) 20 kJ
(d) 0 kJ

Question 20
Temperature dependence of resistivity $\rho(T)$ of semiconductors, insulators and metals is significantly based on the following factors:
(a) number of charge carriers can change with temperature T.
(b) time interval between two successive collisions can depend on T.
(c) length of material can be a function of T.
(d) mass of carriers is a function of T.

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