In a moving coil galvanometer, there is a coil of copper having number of insulated turns N, each of area A. The coil is suspended in a radial magnetic field B. The moment of inertia of the coil about its rotational axis is I. The scale divisions in the galvanometer are n and resistance of the coil is R.
If a current `i_0` in the coil produces a deflection of `pi//3` radian to the pointer of galvanometer, the value of torsional constant of the spring is

Options

A. `(NBAi_0)/(3pi)`
B. `(3NBAi_0)/(2pi)`
C. `(NBAi_0pi)/(3)`
D. `(3NBAi_0)/(pi)`

Answer

D

Explanation

As `i=(k)/(NBA)theta`,
so `k=(NBAi)/(theta)=(NBAi_0)/(pi//3)=(3NBAi_0)/(pi)`