When moving coil galvanometer (MCG) is converted into a voltmeter, the series resistance is '$$n$$' times the resistance of galvanometer. How many times that of MCG the voltmeter is now capable of measuring voltage?

The self induction (L) produced by solenoid of length '$$l$$' having '$$\mathrm{N}$$' number of turns and cross sectional area '$$A$$' is given by the formula ($$\phi=$$ magnetic flux, $$\mu_0=$$ permeability of vacuum)

A wire $$P Q$$ has length $$4.8 \mathrm{~m}$$ and mass $$0.06 \mathrm{~kg}$$. Another wire QR has length $$2.56 \mathrm{~m}$$ and mass $$0.2 \mathrm{~kg}$$. Both wires have same radii and are joined as a single wire. This wire is under tension of $$80 \mathrm{~N}$$. A wave pulse of amplitude $$3.5 \mathrm{~cm}$$ is sent along the wire $$\mathrm{PQ}$$ from end $$\mathrm{P}$$. the time taken by the wave pulse to travel along the wire from point P to R is ?

When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in glass is parallel to the base of the prism. If '$$i$$' and '$$e$$' denote the angles of incidence and emergence respectively, then