A moving coil galvanometer consists of a coil in a uniform magnetic field Bo, suspended fro a fibre of torque constant C, current I produces a deflection O=nABoi/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 Rc=n2 A2Bo2/2(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
imin =( ?KT/ TRc)1/2