In a moving coil galvanometer, torque on the coil can be expressed as $$\tau=k i$$, where $$i$$ is current through the wire and $$k$$ is constant. The rectangular coil of the galvanometer having numbers of turns $$\mathrm{N}$$, area $$\mathrm{A}$$ and moment of inertia I is placed in magnetic field B. Find

(A) $$k$$ in terms of given parameters $$\mathrm{N}, \mathrm{I}, \mathrm{A}$$ and B;

(B) The torsional constant of the spring, if a current $$i_{0}$$ produces a deflection of $$\frac{\pi}{2}$$ in the coil;

(C) The maximum angle through which coil is deflected, if charge $$\mathrm{Q}$$ is passed through the coil almost instantaneously. (Ignore the damping in mechanical oscillations.)