A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 460 A/cm2. What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.53 A?

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

Agas is contained in a vertical, frictionless piston–cylinder device. the piston has a mass of 3.2 kg and a cross-sectional area of 35 cm2. a compressed spring above the piston exerts a force of 190 n on the piston. if the atmospheric pressure is 95 kpa, determine the pressure inside the cylinder.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele