Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

A long, straight wire carries a current i. Let B₁ be the magnetic field at a point P at a distance d from the wire. Consider a section of length l of this wire such that the point P lies on a perpendicular bisector of the section B₂ be the magnetic field at this point due to this second only. Find the value of d/l so that B₂ differs from B₁ by 1%.    

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?

A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry a current i as shown in figure. Find the magnetic field B at the centre of the loop. 

Calculate n(T)/n(1000 K) for tungsten emitter at T = 300 K, 2000 K and 3000 K, where n(T) represents the number of thermions emitted per second by the surface at temperature T. Work function of tungsten is 4.52 eV.

A tungsten cathode and a thoriated-tungsten cathode have the same geometric dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other cathode. The constant A in the Richardson−Dushman equation is 60 × 10⁴ Am ⁻² K⁻² for pure tungsten and 3.0 × 10⁴ Am ⁻² k⁻² for thoriated tungsten. The work function of pure tungsten is 4.5 eV and that of thoriated tungsten is 2.6 eV. Find the operating temperature.

If the temperature of a tungsten filament is raised from 2000 K to 2010 K, by what factor does the emission current change? Work function of tungsten is 4.5 eV.

Derive the relation a sin θ = λ  for the first minimum of the diffraction pattern produced due to a single slit of width ‘a’ using light of wavelength λ.

Using the monochromatic light of same wavelength in the experimental set-up of the diffraction pattern  as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found  to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the  screen is kept at the same distance from the slit in the two cases.

An electric dipole of dipole moment `vecP` is placed in a uniform electric field `vecE` with its axis inclined to the field. Write an expression for the torque `vecT` experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that the torque acting on it is:

1. maximum
2. Zero

Answer the following question.
What is the end error in a meter bridge? How is it overcome? The resistances in the two arms of the metre bridge are R = Ω and S respectively.  When the resistance S is shunted with equal resistance, the new balance length found to be 1.5 l₁, where l₂ is the initial balancing length. calculate the value of s.

Answer the following question.
Two infinitely long straight wire A₁ and A₂ carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A₃ carrying current 1.5 I be placed between A₁ and A₂ so that it experiences no net force due to A₁ and A₂? Does the net force acting on A₃ depend on the current flowing through it?

Complete the following nuclear reactions for α and β deca :

(i) `"_92^238U ->?  + _2^4He + Q`

(ii) `"_11^22Na ->?  + _10^22Ne + v`

The potential difference across the resistor is 160 V and that across the inductor is 120 V. Find the effective value of the applied voltage. If the effective current in the circuit is 1⋅0 A, calculate the total impedance of the circuit.

Derive the relation a sin θ = λ for the first minimum of the diffraction pattern produced due to a single slit of width 'a' using light of wavelength λ.

Deduce the expression for the torque `vec"τ"` acting on a planar loop of area `vec"A"` acting on a planar loop of area `vec"B"`. If the loop is free to rotate, what would be its orientation in stable equilibrium?

Draw a labelled ray diagram showing the formation of image by a compound microscope in normal adjustment. Derive the expression for its magnifying power.

How does the resolving power of a microscope change when
(i) the diameter of the objective lens is decreased?
(ii) the wavelength of the incident light is increased ?
Justify your answer in each case.

A series combination of an inductor (L), capacitor (C) and a resistor (R) is connected across an ac source of emf of peak value E₀, and angular frequency (ω). Plot a graph to show variation of impedance of the circuit with angular frequency (ω).