SECTION – A

This section consists of 25 multiple choice questions with over tilt choice to attempt any 20 questions. In case more than desirable number of questions are attempted, only first 20 questions will be considered for evaluation. 

Question 1.
An electric dipole placed in a non-uniform electric field will experience: 

1. Only a force 
2. Only a torque 
3. both force and torque 
4. Neither force nor torque

Question 2.
Let NI be the number of electric field lines going out of an imaginary cube of side that encloses an isolated point charge 2q and N₂ be the corresponding number for an imaginary sphere of radius that encloses an isolated point charge 3q. Then (N₁/N₂) is:

Question 3.
In the circuit given below P ≠ R and the reading of the galvanometer is same with Switch S open or closed. Then: 

1. I_Q = I_R
2. I_R =I_G
3. I_P = I_G
4. I_Q = I_G

A current I is flowing through the loop as shown in the figure (MA = R, MB = 2R). The magnetic field at the centre of the loop is   times: 

1.  
2.   
3.  
4. 

The vertical component of earth's magnetic field at a place is , times the horizontal J3 component. The angle of dip at that place is: 

1. 0° 
2. 30° 
3. 45°
4. 60° 

Electric flux of an electric field    g through an area d   is given by:

Question 20.
An electron is projected with velocity   along the axis of a current carrying long solenoid. Which one of the following statements is true? 

Question 21.
If the speed v of a charged particle moving in a magnetic field   (  is perpendicular to  ) is halved, then the radius of its path will:

Question 23.

In an ac circuit the applied voltage and resultant current are E = E₀ sin ⍵t and    respectively. The average power consumed in the circuit is:

 

Three identical charges are placed on x-axis from left to right with adjacent charges separated by a distance d. The magnitude of the force on a charge from its nearest neighbour charge is F. Le   be the unit vector along + x axis, then the net force on each charge from left to right is :  

Question 31.

In a certain region field    and magnetic field    are perpendicular to each other. An electron enters the region perpendicular to the direction of both   and    moves undeflected. The speed of the electron is :  

1.   
2. 
3. 
4. 

 

Question 32.

A test charge of 1.6 × 10^-19 C is moving with a velocity   in a magnetic field   . The force on this test charge is : 

1.   
2.   
3.   
4. 0

Question 33.

In a series LCR circuit, at resonance the current is equal to :

1.  
2. 
3. 
4. 

 

Question 34.

The frequency of an ac source for which a 10 μF capacitor has  a reactance of 1000Ω is : 

1. 
2. 50 Hz
3. 
4. 

Question 35.

In the given network all capacitors used are identical and each one is of capacitance C. Which of the following is the equivalent capacitance between the points A and B? 

 

1. 6C 
2. 
3.   
4.  

Question 36.

The given figure shows I – V graph of a copper wire whose length and area of cross-section are L and A respectively. The slope of this curve becomes :

 

1. less if the length of the wire is increased
2. more if the length of the wire is increased  
3. more if a wire of steel of same dimension is used 
4. more if the temperature of wire is increased 

 

Question 37.

When a potential difference V is applied across a conductor at temperature T, the drift velocity of the electrons is proportional to :

1. T
2. 
3. V
4. 

 

Question 38.

Two identical thick wires and two identical thin wires, all of the same material and the same length form a square in three different ways P, Q and R as shown. Due to the current in these loops the magnetic field at the centre of the loop will be zero in case of :

 

1. P and R only
2. Q and R only
3. P and Q only
4. P, Q and R 

 

Question 39.

A circular current carrying coil produces a magnetic field B₀ at its centre. The coil is rewound so as to have three turns and the same current is passed through it. The new magnetic field at the centre is:

1. 3 B₀ 
2.  
3. 
4. 9 B₀ 

 

Question 40.

Which one of the following statements is true?

1. An inductor has infinite resistance in a dc circuit.
2. A inductor and a capacitor both cannot conduct in a dc circuit. 
3. A capacitor can conduct in a dc circuit but not an inductor.
4. An iductor can conduct in a dc circuit but not a capacitor.

 

Question 41.

The magnetic flux linked with a coil is given by ϕ = 5t² + 3t + 16, where is ϕ in webers and t in seconds. The induced emf in the coil at t = 5 s will be:

1. 53 V 
2. 43 V 
3. 10V 
4. 6V

 

Question 42.

If a charge is moved against a coulomb force of an electric field, then the:

1. intensity of the electric field increases
2. intensity of the electric field decreases
3. work is done by the electric field
4. work is done by the external source

Question 43.

A charge Q is located at the centre of a circle of radius r. The work done in moving a test charge q0 from point A to point B (at opposite ends of diameter AB) so as to complete a semicircle is  :

1. 
   
2. 
3. kq₀Qr
4. Zero

 

Question 44.

A long solenoid carrying current produces a magnetic field B along its axis. If the number of turns in the solenoid is halved and current in it is doubled, the new magnetic field will be:

1. 
2. B
3. 2B
4. 4B

 

Question Nos. 45 to 49 are Assertion (A) and statements Reason (R) type questions. Given below are two statements labelled as Assertion (A) and Reason (R). Select the most appropriate answer from the options given below.

 

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true, but Reason (R) is false.
4. Assertion (A) is false, but Reason (R) is true.

 

Question 45.

Assertion (A): A bar magnet experiences a torque when placed in a magnetic field.

Reason (R): A bar magnet exerts a torque on itself due to its own magnetic field.

 

Question 46.

Assertion (A): In a series LCR circuit connected to an ac source, resonance can take place.

Reason (R): At resonance X_L = X_C.

 

Question 47

Assertion (A): When a charged particle moves with velocity   in a magnetic field  , the force on the particle does no work.

Reason (R): The magnetic force is perpendicular to the velocity of the particle.

 

Question 48.

Assertion (A): Induced emf in two coils made of wire of the same length and the same thickness, one of copper and another of aluminium is same. The current in copper coil is more than the aluminium coil.

Reason (R): Resistance of aluminium coil is more than that of copper coil.

 

Question 49.

Assertion (A): A transformer is used to increase or decrease ac voltage only.

Reaon (R): A transformer works on the basis of mutual induction.

 

SECTION C

This section consists of 6 multiple choice questions with an overall choice to attempt any 5 questions. In case more than the desirable number of questions are attempted, only the first 5 questions will be considered for evaluation.

 

Question 50.

Two charged spheres A and B having their radii in the ratio 1: 2 are connected together with a conducting wire. The ratio of their surface charge densities  will be.

1. 
2. 2
3. 
4. 4

 

Question 51.

A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is  , the net force on the remaining three arms of the loop will be.

1. 3  
2. -3   
3.   
4. -   

Case – Study

 

A battery is a combination of two or more cells. In the following figure, a single batter is represented in which two cells of emf Ɛ₁ and Ɛ₂, and internal resistance r₁ and r₂ respectively are connected.

 

Answer the following questions:

 

 

Question 52.

The equivalent emf of this combination is :

1. 
2. 
3. 
4. 

 

Question 53.

For terminal B to be negative :

1.  
2.  
3.  
4.  

Question 54.

The current in the internal circuit is:

1.  
2.  
3.  
4.  

 

Question 55.

The equivalent internal resistance of the combination is:

 

1.  
2.  
3.  
4.  

     Section A

Ans 1. Correct option – c: Both force and torque
An electric dipole placed in a non-uniform electric field will experience both force and torque.

Ans 2. Correct option – b: 2/3
Ф = q/Ԑ
= (2q/ Ԑ0)/ (3_q/ Ԑ₀)
Thus, N₁/N₂ = 2/3 

Ans 3. Correct option – b: I_R =I_G
From given diagram, we can observe that when switch is closed or open the reading on galvanometer is same and resistance P and R are not same.
Using the balanced condition, we can say that
Current in resistance R and G will be same.
Thus, I_R =I_G 

Ans 4. Correct option – d:
Given that,
Length of wire 1, L₁ = L
Diameter of 1st wire, D1 = 2D

Similarly,
Length of wire 2, L₂ = 2L
Diameter of 2^nd wire, D₂ = 3D

Hence, the ratio of the potential difference of two wires are

Ans 5. Correct option – a: 
Given that,
N₁ = 30
A₁ = 3.6 × 10^-3 m²
B₁ =0.25 T
N₂ = 42
A₂ = 1.8 × 10^-3 m²
B₂ =0.5 T
Now,

Ans 6. Correct option – d:  , into the plane of the paper.
Now for the given figure, the magnetic field at centre M due to current flowing through DA will be
 
Similarly, the magnetic field due to the current flowing through BC is 
 
Whereas, magnetic field due to AB and CD will be zero since point M lies on the straight line.
Hence net magnetic field for the given case will be
And by using the right-hand thumb rule we can conclude that direction of the magnetic field will be in the plane of the paper.

Ans 7. Correct option – d:
a dielectric is introduced into the gap between the plates of the capacitor.
From the given condition, the effective resistance for two circuits is
 
Based on the preceding equations, we may conclude that increasing the gap between the plates of the capacitor reduces capacitance, which causes R1 to increase, resulting in a decrease in current.
As a result, the brightness of the bulb will diminish because its brightness is directly proportional to the current running through it.
Hence, the bulb will glow brighter when a dielectric is introduced into the gap between the plates of the capacitor.

Ans 8.  Correct option – d: 250 V
Given that,
f = 50 Hz
L = 318 mH = 0.318
R = 75 Ω
V_R = 150 V
Current through R, 
Now,
X_L=2πfL=2π×50×0.318≈100 Ω
V_L=IX_L=2×100=200 V
Hence the total voltage,

Ans 9.  Correct option – d: 
Now,
Electric potential for a dipole is given as

 

Ans 10.   Correct option – b: k
The force between two small spheres is given as

  Whereas the force between them in the dielectric medium is 

Ans 11.  
Correct option – d: a gap only
Taking out the infinity plug introduces the air gap in the circuit. Since air is a bad conductor of electricity, no current flows, implying that the infinity resistance in the circuit is introduced.

Ans 12.   Correct option – b: 270 J
Given that,
Voltage, V = 15 V
Time, t =60 s
Internal resistance, r = 50 Ω
Now,
Heat energy dissipated in time t is given gas
E =VIt 

Ans 13.   =Correct option – a: Energy
Lenz’s law is based on the principle of conservation of energy.

Ans 14. Correct option – b: 30°
Given that,

 

Ans 15.  Correct option – a: 1.2 μT, Vertically upward
Given that,
Current, I = 15 A
Distance, d = 2.5 m
Now,

The magnitude of the magnetic field, 
∴B=1.2 μT
And according to the right-hand thumb rule, the direction magnetic field will be upward.

Ans 16.   Correct option – c:  102 V
Given that,
Inductance, L = 10 H
ΔI = 11 – 2 = 9 A
Time, t = 0.9 sec
Now,

 

Ans 17.   Correct option – d: 
A charge Q is placed at the centre of the line joining two charges q and q as shown below.

Now, for the system to be in equilibrium force between charges must be zero (ie., F =0).

Ans 18.  Correct option – c:  
For the given case we know that electric flux is the dot product of the electric field and area of the cross section.

Ans 19.  Correct option – d: 2 Ω
Given that,
Balancing length, l1 = 120 cm
Shunted resistance, R = 1 Ω
New balancing length after shunting, l2= 40 cm
Now,
Internal resistance, 

Ans 20. Correct option – d:
The electron will continue to move with the same velocity v along the axis of the solenoid.
As we know when an electron is projected with velocity v along the axis of a current-carrying long solenoid, it will continue to move with the same velocity v along the axis of the solenoid.

• Passing DC or AC through plates
• Keeping it time-varying magnetic field which produces induced current.

Ans 23. Correct option –  d:  Zero
Now,
Power = V_I or E_I

Ans 24.  Correct option –  a: 6×10⁶ m/s
Given that,
Potential difference, V =100 V
Charge of electron, e = 1.6× 10^-19 C
Now,

Ans 25.  Correct option – c: A stationary charge
As we know charges at rest or rest remain unaffected by magnetic fields since force depends on velocity, and velocity is zero in the case of stationary charges.

Given that,

Two-point charge +16q and -4q and located at x =0 and x = L

Now, we know that

 

Given that,

Dipole moment, p = 4× 10^-5 C-m.

Electric field, E = 10^-3 N/C

Torque, τ =2× 10^-8 Nm

Now,

The torque due to dipole is given as

 

 

Ans 28.  Correct option – c: 

Charge, q = q₁ = q₂ = q₃

Distance between two charges = d

Now,

Force on the first charge due to charge q₃ will be

Force on the first charge due to charge q₃ will be

  

Thus net force acting on charge q1 is 

   

Here, the negative sign shows that force will be along the negative x-axis.

From this, we can conclude that force acting on three charges are    

Given that,

According to the conclusion of A:

Charge flowing in 1 min, Q = 300 C

Time, t = 1 min = 60 sec

According to the conclusion of B:

Number of electron flows in 1 sec, n = 3.125× 10¹⁹ electron

Now,

Total current trough circuit according to 

Similarly 

The total current through circuit according to 

 

Correct option – a: 10.6×10^-8 Ω-m

Given that,

R₁ = 2 Ω

R₂ = 8 Ω

L₁ = L₂ =L

A₁ =A₂ = A

Now,

Correct option – c: 

According to the equation of Lorentz force, the net force acting on electrons due to the electric and magnetic field is given as

 

Correct option – d: 0

Given that,

Charge, q = 1.6× 10^-19 C 

Velocity,  ̂

Magnetic field, 
Now the force acting on test charge is

F_B=q(v×B)=0 N 

Ans 33.  Correct option – a: 

At resonance, the value of current can be expressed as

 

 

Now,

As we know reactance of capacitor can be expressed as

 

The frequency of an ac source for which a 10μF capacitor have a reactance of 1000 Ω is  

 

Correct option – a: will be less if the length of wire is increased.

From Ohm’s law, we know that,

Hence for the given case, we can modify the above equation as

 

Now from this, we can conclude that the slope will be less if the length of the wire is increased.

 

Correct option – c: V

When a potential difference V is applied across a conductor at temperature T, the drift velocity of the electrons is proportional to V as we can see below.

Now,

For the given case 2πr =3× 2πr’ ⇒ r’=r/3

Initial magnetic field

 

 

The magnetic flux linked with a coil is given by ϕ 

As we know according to Faraday’s law of electromagnetic induction, the emf induced by the current-carrying coil is given as

 

 

 

Ans 42.  Correct option – d: Work is done by the external source

As we know the work is said to be done by an external source when a charge is moving against a coulomb’s force of an electric field.

 

Ans 43.  Correct option – d: Zero

A charge Q is at the centre of a circle with radius r. the work done in moving a test charge q₀ from point A to point B. 

i.e.,W = Fs cos ⁡θ=0  

 

Ans 44.  Correct option – b: B

The magnetic field produced by a solenoid of N turns will be given as

B=μ₀ NI 

And for our case, if the number of turns is reduced to half and the current flowing through it doubled its initial value then the magnetic field produced by them will be

 

 

 

Ans 45. Correct option – c: Assertion (A) is true, but Reason (R) is false.

For the given case, we know that a bar magnet experiences torque when it placed in a magnetic field Also, we must note that the bar magnet doesn’t exert a net torque on itself due to its own magnetic field although some of its components do.

 

 

  

Ans 46.  Correct option – b: Both Assertion (A) and Reason (R) are true, but Reason (R) is not the

correct explanation of Assertion (A).

For an LCR circuit that is connected to an AC power source the resonating frequency is given as

Here, X_c and X_L are Capacitive reactance & Inductive reactance respectively.

Hence we can conclude that both Assertion and Reason are correct but Reason is not the correct explanation for assertion.

 

 

Ans 47.  Correct option – a: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

According to the equation of Lorentz force, the direction of the magnetic field is always perpendicular to the velocity of the particle and the force acting on it is expressed as.

 And from the above equation, we can see that force is also perpendicular to velocity or displacement.

Hence the force on the particle does not work because force is perpendicular to the displacement.

i.e., W=F.dr=Fdr cos ⁡θ=0

 

 

Ans 48.  Correct option – a: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

For the given case, we know that resistance of the material is directly proportional to resistivity which is the intrinsic property of material, as a result of this resistance offered to the current flowing through the aluminium coil will be greater than the copper coil.

Hence we can conclude that the current in the copper coil is more than the aluminium coil although the induced emf is the same for both.

  

 

Ans 49.  Correct option – a: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

As we know, a transformer works on the principle of mutual inductance and it is used to increase or decrease AC voltage only.

 

 Section C

Ans 50. Correct option – b: 2

For a uniform charged distribution the surface charged density for the sphere can be expressed as

 

Now since both the spheres are connected, the electric potential across both surfaces will be

 

 

Ans 51. Correct option – d: -F 

 

Thus the force on the arm opposite to the one on which force acting is F will be –F.Hence option d is correct among all.As we know force on two parallel arms of the current-carrying square loop will be zero, since 

 

 

 Case – study

 

 

Ans 52.Correct option –  c: 

The equivalent emf of the given combination is given as shown below.

 

 

Ans 53.Correct option – b: r₂ϵ₁+r₁ϵ₂ 

As we know for the given combination the equivalent emf is given as shown below. 

Hence from this, we can conclude that for the given combination of cells, the thermal B can be negative only if r₂ ϵ₁<r₁ ϵ₂. 

  

 

 

Ans 54. Correct option – a: 

According to Ohm’s law, we know that electric current in a circuit is directly proportional to potential difference or emf across any given circuit.

 

 

Ans 55. Correct option –  c:

In the given combination the cells are connected in parallel hence the equivalent internal resistance for the given circuit will be