A moving coil galvanometer consists of a coil  in a uniform magnetic field B_o, suspended fro a fibre of torque constant C, current I produces a deflection O=nAB_oi/c where n is the number of turns  and A is the area of the coil. The period of oscillation T=2?(I/C)^1/2 where I is the moment of inertia. The resistance of the coil and the circuit in which it is placed is adjusted to give a critical dumping R_c=n² A²B_o²/2(ic)^1/2 . if the minimum detectable current produces deflection equal to thermal -root mean square value O, show that minimum current is given by

i_min  =( ?KT/ TR_c)^1/2