First a set of n equal resistors of R each is connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is ‘n’?

Derive an expression (in vector form) for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?

What is relaxation time? Derive an expression for resistivity of a wire in terms of member density of free electrons and relaxation time.

An equi-convex lens (of refractive index 1.50) is placed in contact with a liquid layer on top of a plane mirror as shown. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Obtain an expression for focal length of a combination of thin lenses in contact.