Class – XII
Subject –Physics

Time: 2 Hours                                                               Max. Marks: 45

Q 1        An electron and a proton moving with same speed enter the same magnetic field region at right angles to the   

            direction of the field. For which of the two particles will the radius of the circular path be smaller?             1

Q 2.     If a wire is stretched to double its original length without loss of mass, how will the resistivity of the

             wire be influenced?                                                                                                                       1

Q 3.     Why do magnetic lines of force prefer to pass through iron than through air?                             1

Q 4.     Name the device used for measuring the internal resistance of a secondary cell?             (1 mark)

Q5.      A set of n identical resistors, each of resistance R ohm, when connected in series have an effective resistance X ohm and when the resistors are connected in parallel, their effective resistance is Y ohm. Find the relation between R, X and Y.                                                                                 (2 marks)

 Q6.       State Kirchhoff's rules for electrical networks.                                                                  (2 marks)

Q7       The electron drift speed in metals is small (~mms^-1) and the charge of the electron is also very small (~10^-19C),  

              but   we can still obtain a large amount of current in a metal. Why?                                                  (2 marks)       

Q:8        An electron travelling west to east enters a chamber having a uniform electrostatic field in north to    

            south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the  

             electron from deflecting from its straight line path.                                                             (2 marks)

Q:9       The given figure shows the experimental set up of a metre bridge. The null point is found to be 60 cm away from the end A  

                with  X and Y in position as shown.

When a resistance of 15Ω is connected in series with ‘Y’, the null point is found to shift by 10 cm towards the end A of the wire. Find the position of null point if a resistance of 30Ω were connected in parallel with ‘Y’.                             (2 marks)

Q:10     A galvanometer coil has a resistance of 15 Ω and the metre shows full scale deflection for a current of 4 mA.    

             How will you convert the metre into an ammeter of range 0 to 6 A?                                                          (2 marks)

Q:11    The voltage –current graph for two resisters of same material and same radii with lengths L₁ and L₂ are shown. If  

             L₁ > L₂, state with reason , which reason which of the graphs represents voltage –current change for L₁

                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

                                                        (2 marks)

Q:12    You are given 8 W resistor. What length of constantan wire of resistance 120 W m^{‑ 1} should be joined in parallel  

             with it to get a value of 6W?                                                                                                              (2 marks)

Q:13    Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of 10 A and 5A   

             respectively in opposite direction. Calculate the magnitude and the direction of force on a 20 cm length of the

             wireY. (3 marks)

                                                            OR

A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B. What is the magnitude of the magnetic field?

Q:14         Determine the currents I₁ , I₂ , I₃ in the following network using Kirchhoff’s laws. (3 marks)

Q:15   Derive the expression for the torque on a rectangular coil of area A carrying current I placed in a magnetic field B.  

            The angle b/w direction of B and the area vector of the coil is θ.                                                             (3 marks)

Q:16. Derive an expression for the equivalent emf and internal resistance of a parallel combination of 2

          primary cells. Under what condition is the potential difference across a cell equal to its emf? (3 marks)

Q:17. Explain with the help of a circuit diagram how the value of an unknown resistance can be determined  

           using a Wheatstone bridge. Give the formula used.                                                                (3 marks)

Q18 . A straight wire carries a current of 3A.Calulate the magnitude of the magnetic field at a point 10cm

          away from the wire. Draw diagram to show the direction of the magnetic field.                    (3 marks)

Q:19  Why is a potentiometer preferred over a voltmeter for determining the emf of a cell? (3 marks)

                                                                     OR

           Two cells of emf E₁ and E₂ are   connected together in two ways shown below

     

     

          The balance points in a given potentiometer experiment for these two combinations of cells are found to be at 351   

          cm and 70.2 cm respectively. Calculate the ratio of the emfs of the two cells.

 Q:20 Derive an expression for the magnetic field at a point
           on the axis of a current carrying circular loop.

Two coaxial circular loops L₁ and L₂ of radii 3 cm and 4 cm are placed as shown. What should be the magnitude and direction of the current in the loop L₂ so that the net magnetic field at the point O is zero?                                           

(4 marks)

ROTATIONAL MECHANICS

The rotational analogue of force is moment of force (also referred to as torque) If a force acts on a single particle at a point P whose position with respect to the origin O is given by the position vector r  the moment of the force acting on the particle with respect to the origin O is defined as the vector product   τ = r × F

The moment of force (or torque) is a vector  quantity. The symbol τ  stands for the Greek letter tau. The magnitude of τ  is

                                                                τ  = rF sin θ

the quantity angular momentum is the rotational analogue of linear momentum. It could also be referred to as moment of (linear) momentum

Consider a particle of mass m and linear momentum p at a position r relative to the origin O. The angular momentum l of the particle with

respect to the origin O is defined to be

                                                                    l = r × p

The magnitude of the angular momentum vector is l = r p sin   where p is the magnitude of p and θ is the angle between r and p.

A rigid body is said to be in mechanical equilibrium, if both its linear momentum and angular momentum are not changing with time,

or equivalently, the body has neither linear acceleration nor angular acceleration. This means

(1) the total force, i.e. the vector sum of the forces, on the rigid body is zero;

If the total force on the body is zero, then the total linear momentum of the body does not change with time. Eq. (7.30a) gives the

condition for the translational equilibrium of the body.

(2) The total torque, i.e. the vector sum of the torques on the rigid body is zero, If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time. Eq. (7.30 b) gives the condition for the rotational equilibrium of the body.

A body may be in partial equilibrium, i.e., it may be in translational equilibrium and not in rotational equilibrium, or it may be in rotational

equilibrium and not in translational equilibrium.

Theradius of gyration of a body about an axis

may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia

is equal to the moment of inertia of the body about the axis.

the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.

Iz  =I x  +I y

The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing

through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.

I_z′ = I_z + Ma²