Q.Describe Kelvin's method to determine the resistance of a galvanometer by using a meter bridge.

[!TLDR] Put the galvanometer in one gap of the metre bridge and a known resistance R in the other; adjust and tap-test until the deflection stops changing with/without jockey contact -- that D is the balance point, giving $G = R\,l_g/(100-l_g)$. [!ANSWER] $G = R\,l_g/(100-l_g)$.

Kelvin's method (Section 9.3.1) finds a galvanometer's own resistance G using the ordinary metre-bridge circuit, with the galvanometer itself connected in one gap and a known resistance box R in the other. Procedure: a suitable value is set on the resistance box, the key is closed, and the galvanometer's steady deflection is noted WITHOUT touching the jockey to the wire at all; the rheostat is then adjusted to give a convenient deflection, around two-thirds of full scale. The jockey is next tapped at different points along the wire until a point D is found where the deflection shows NO CHANGE whether the jockey touches the wire there or not -- an unchanging deflection means no current flows between the central strip and D through the jockey, so B (the central strip's node) and D must be at the same potential, exactly the balance condition of an ordinary metre-bridge measurement. The length $l_g$ of wire between A and D (opposite the galvanometer arm) and the remaining length $l_r=100-l_g$ (opposite the resistance-box arm) are then measured. Since the bridge is balanced, $G/R = R_{AD}/R_{DC} = l_g/l_r$, giving

This method's real advantage is that it never needs to pass a potentially damaging, large measuring current directly through the sensitive galvanometer coil to find its resistance. [!ANSWER] $G = R\,l_g/(100-l_g)$.

Describe the special balance test (deflection unchanged with/without jockey contact) that identifies the null point, then apply the ordinary metre-bridge balance ratio to the two resulting lengths.

Confusing the balance CRITERION here (deflection stays the SAME with or without jockey contact) with the ordinary metre-bridge criterion (deflection becomes ZERO) -- Kelvin's method's own arrangement gives a non-zero but UNCHANGING deflection at balance.