Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A galvanometer of resistance G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

\frac{S^2}{S+G}

\frac{SG}{S+G}

\frac{G^2}{S+G}

\frac{G}{S+G}

Step-by-Step Solution

Initial Condition: The resistance of the circuit component is simply the resistance of the galvanometer, $G$ .
Shunted Condition: When a shunt resistance $S$ is connected in parallel with the galvanometer, the equivalent resistance of this parallel combination ( $R_p$ ) is: $R_p = \frac{GS}{G+S}$ .
Problem Statement: To keep the main current in the circuit unchanged, the total resistance of the modified circuit (galvanometer + shunt + series resistance) must equal the original resistance ( $G$ ).
Calculation: Let $R$ be the resistance added in series. The total resistance becomes $R_{total} = R_p + R$ . Equating to the original resistance: $G = \frac{GS}{G+S} + R$ $R = G - \frac{GS}{G+S}$ $R = \frac{G(G+S) - GS}{G+S}$ $R = \frac{G^2 + GS - GS}{G+S}$ $R = \frac{G^2}{S+G}$

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