Question: While detecting a very feeble current with the help of a moving-coil galvanometer, one must ensure that an observed deflection is not just a stray

While detecting a very feeble current with the help of a moving-coil galvanometer, one must ensure that an observed deflection is not just a stray kick arising from the Brownian motion of the suspended system. If we agree that a deflection \(\theta\), whose magnitude exceeds \(4 \theta_{\text {r.m.s. }}\left[=4(k T / c)^{1 / 2}\right.\) ], is highly unlikely to be due to the Brownian motion, we obtain a lower limit to the magnitude of the current that can be reliably recorded with the help of the given galvanometer. Express this limiting current in terms of the time period \(\tau\) and the critical damping resistance \(R_{c}\) of the galvanometer.

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