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_{o}i/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}=n^{2} A^{2}B_{o}^{2}/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}