Question
Explain the concept of energy bands with a figure.
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A parallel-plate capacitor having plate area 20cm2 and separation between the plates 1.00mm is connected to a battery of 12.0V. The plates are pulled apart to increase the separation to 2.0mm.
- Calculate the charge flown through the circuit during the process.
- How much energy is absorbed by the battery during the process?
- Calculate the stored energy in the electric field before and after the process.
- Using the expression for the force between the plates, find the work done by the person pulling the plates apart.
- Show and justify that no heat is produced during this transfer of charge as the separation is increased.
White coherent light (400nm - 700nm) is sent through the slits of a Young's double slit experiment (figure.) The separation between the slits is 0.5mm and the screen is 50cm away from the slits. There is a hole in the screen at a point 1.0mm away (along the width of the fringes) from the central line.
- Which wavelength (s) will be absent in the light coming from the hole?
- which wavelength (s) will have a strong intensity?
A charge of $1\mu\text{C}$ is given to one plate of a parallel-plate capacitor of capacitance $0.1\mu\text{F}$ and a charge of $2\mu\text{C}$ is given to the other plate. Find the potential difference developed between the plates.
→- a cross - section of a ‘light pipe’ made of a glass fibre of refractive. The outer covering of the pipe is made of a material of refractive. What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure.
- What is the answer if there is no outer covering of the pipe?
A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.
Natural water contains a small amount of tritium $\big(\text{ }^3_1\text{H}\big).$ This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the $\text{}^3_1\text{H}$ radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.
→A body is in translational equilibrium under the action of coplanar forces. If the torque of these forces is zero about a point, is it necessary that it will also be zero about any other point?
A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle $\theta$ it slides.
→Given below are two electrical circuits A and B. Calculate the ratio of power factor of circuit B to the power factor of circuit A.
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes 2cm, 1m/s and 10m/s2 at a certain instant. Find the amplitude and the time period of the motion.