A rectangular conductor LMNO is placed in a uniform magnetic field of 0.5 T. The field is directed perpendicular to the plane of the conductor. When the arm MN of length of 20 cm is moved towards left with a velocity of 10 ms–1, calculate the emf induced in the arm. Given the resistance of the arm to be 5 (assuming that other arms are of negligible resistance) find the value of the current in the arm.
Emf induced in a moving rod is given by,
E = -Blv
Emf induced in a moving rod is given by,
E = + Blv
= 0.5 x 0.2 x 10
= 1 v
Therefore, current in the rod is given by,
A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth’s magnetic field. The Earth’s magnetic field at the plane is 0.4 G and the angle of dip is 60°. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased?
Emf induced in a rod of length ‘l’ with angular speed in a uniform magnetic field is given by,
For earth’s magnetic field,
Horizontal component is given by,
Vertical component is given by,
Therefore, emf induced is given by,
Emf induced is not dependent on the number of spokes.
A parallel beam of light of 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.
Distance of nth minima from the centre of screen is given by, a is the width of the slit.
For first minimum, n=1
So, width of the slit is given by,
Draw typical output characteristics of an n-p-n transistor in CE configuration. Show how these characteristics can be used to determine output resistance.
The output characteristics of an n-p-n transistor in CE configuration are shown below:
Output resistance is defined as the ratio of change in collector-emitter voltage to change in collector current at a constant base current. The reciprocal of the slope of the linear part of the output characteristics represents the output resistance.
The graph shown in the figure represents a plot of current versus voltage for a given semiconductor.
Identify the region, if any, over which the semiconductor has a negative resistance.
The part of the curve BC has a negative slope because with increase in current, voltage decreases.
Define the current sensitivity of a galvanometer. Write its S.I. unit. Figure shows two circuits each having a galvanometer and a battery of 3 V. When the galvanometers in each arrangement do not show any deflection, obtain the ratio R1 / R2.
Current sensitivity is defined as the ratio of deflection produced in the galvanometer to the current flowing through it.
Mathematically it is given as,
SI unit is radian per ampere.
No current flows through the galvanometer for balanced Wheatstone bridge.
A wire AB is carrying a steady current of 12 A and is lying on the table. Another wire CD carrying 5A is held directly above AB at a height of 1 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB.
[Take the value of g = 10 ms–2]
Current carried by wire AB= 12 A
Current carried by CD = 5 A
i) The current carrying conductors will repel each other if the direction of current along both the conductor is same.
ii) When current along the conductors is flowing in the same direction, then the wires will attract each other.
When CD remains suspended above AB,
where r is the distance between the wires.
The direction of current in CD should be opposite to the direction of current in AB.
Define the activity of a given radioactive substance. Write its S.I. unit.
The rate of decay of a radioactive substance is called activity of that substance. Activity is the negative of the rate of decay of the radioactive substance.
SI unit is Becquerel (Bq.)
Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’ and mass ‘m’, when it is accelerated by a potential V.
De-broglie wavelength for a charged particle is given by,
A convex lens of focal length f1 is kept in contact with a concave lens of focal length f2. Find the focal length of the combination.
Focal length of convex lens = +f1
Now, using lens formula, we have
For concave lens of formula, focal length is (-f2)
Now, adding equations (1) and (2), we have
Now, for the combined lens using the lens formula, we have,
Therefore, from equations (3) and (4), we have
This is the required focal length of the combination of lenses.