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(D) The resistance of an ammeter is given by $R_A = \frac{G \cdot S}{G + S}$,where $G$ is the galvanometer resistance and $S$ is the shunt resistance.

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Statement-$I$ is false,Statement-$II$ is true.

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(D) The resistance of an ammeter is given by $R_A = \frac{G \cdot S}{G + S}$,where $G$ is the galvanometer resistance and $S$ is the shunt resistance.To increase the range $(I)$ of an ammeter,the shunt resistance $S$ must be decreased,as $S = \frac{I_g G}{I - I_g}$.As the range $I$ increases,the required shunt resistance $S$ decreases,which in turn decreases the total resistance of the ammeter $R_A$. Therefore,Statement-$I$ is false.Statement-$II$ is true because connecting an additional shunt in parallel effectively reduces the total resistance and allows a larger current to bypass the galvanometer,thereby increasing the range.

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