The entropy of a system, S, is related to the accessible phase space volume G by S = k_{B}lnG(E, N, V) where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that G
Let dw be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about dw is correct?
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A vector perpendicular to any vector that lies on the plane defined by x + y + z = 5, is
Two events, separated by a (spatial) distance 9 x 10^{9} m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 10^{8} m/s) is
Consider three polarizers P_{1} ,P_{2} and P_{3} placed along an axis as shown in the figure
The pass axis of P_{1} and P_{3} are at right angles to each other while the pass axis of P_{2} makes an angle θ with that of P_{1} . A beam of unpolarized light of intensity l_{0} is incident on P_{1} as shown . The intensity of light emerging from P_{3} is
A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT Neglecting radiation loss, the amplitude of oscillation after the field is switched off is
A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V_{∞}= 20v. Assuming V_{be} = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v
The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effectivebasewidth caused by___
A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is
A particle of mass m is in a potential given by
where a and r_{0 }are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is
A planet of mass m moves in a circular orbit of radius r_{0} in the gravitational potential V(r) = where k is a positive constant. The orbital angular momentum of the planet is
The solution of the differential equation
subject to the boundary conditions y(0) = 1 and y(∞) = 0, is
In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I_{0} and I_{0}, respectively. The intensities of the individual waves are
Identify the CORRECT statement for the following vectors
Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E_{D }and E_{F} are conduction band, valence band, impurity level and Fermi level, respectively.
A pendulum suspended from the ceiling of the train is at rest. What will be the time period of pendulum if the train accelerates at 10 m/s^{2} (Take g = 10 m/s^{2})
A rod of proper length l_{0} oriented parallel to the xaxis moves with speed 2c/3 along the xaxis in the. Sframe, where c is the speed of the light in free space. The observer is also moving along the xaxis with speed c/2 with respect to the Sframe. The length of the rod as measured by the observer is
Given is a constant vector and r is the position vector. The value of where C is a circle of unit radius centered at origin is _____ .
A system has two energy levels with energies ε and 2ε. The lower is 4fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is
A spherical conductor of radius a is placed in a uniform electric field the potential at a point for r > a, is given by
where r is the distance of P from the centre O of the sphere and q is the angle OP makes with the zaxis.
The charge density on the sphere at q = 30° is
The solution of the differential equation for subject to the initial conditions is
A particle of mass m is confined in the potential
Let the wave function of the particle be given by
where y_{0} and y_{1} are the eigen functions of the ground state and the first excited state respectively. The expectation value of the energy is
Two magnetic dipoles of magnitude m each placed in a plane as shown. The energy of interaction is given by
A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r_{0} and angular speed w_{0} by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass
For the BJT circuit shown, assume that the β of the transistor is very large and V_{BE} = 0.7V. The mode of operation of the BJT is ___
If for a silicon npn transistor, the basetoemitter voltage (V_{BE}) is 0.7V and the collectortobase voltage (V_{CB}) is 0.2V. then the transistor is operating in the___
Assuming V_{CEsat} = 0.2V and β= 50. the minimum base current (l_{B}) required to drive the transistor in the given figure to saturation is___
In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is
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