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

Replace one arm of a Wheatstone/metre bridge network with the galvanometer whose resistance is to be measured, and use a separate, more sensitive galvanometer-cum-cell arrangement to detect the balance point.

Kelvin's method for finding galvanometer resistance using a metre bridge:

The metre bridge is set up in the usual Wheatstone's bridge configuration: a metre-long resistance wire $AC$ is stretched over a scale, with a jockey that can touch it at any point $D$. A resistance box $R$ is connected in the left gap, and the galvanometer $G$ (whose own resistance $G$ is to be determined) is connected in the right gap, in place of the usual "unknown resistance."

However, since the galvanometer whose resistance is being measured is itself now part of the bridge (and so cannot simultaneously act as the balance-detecting instrument), a key modification is needed: a battery (with a key and a suitable protective resistance) is connected between the ends $A$ and $C$ of the wire (across the whole bridge, as usual), and a second, more sensitive galvanometer $G_2$ (or the jockey circuit) is used, connected between the junction of $R$ and $G$ (point $B$) and the jockey (point $D$) on the wire, to detect the balance condition — i.e. the jockey is moved along $AC$ until $G_2$ shows no deflection.

At this balance point $D$, dividing the wire into lengths $l$ (from $A$ to $D$) and $(100-l)$ (from $D$ to $C$), the Wheatstone bridge balance condition gives

$\frac{R}{G}=\frac{l}{100-l}$

so

$G=R\times\frac{100-l}{l}$

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