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A galvanometer having resistance G is connected in parallel with a shunt of resistance S ohm. If the total current in the circuit is to remain the same, the resistance that must be connected in series with the galvanometer is

1. S² / (S + G)
2. SG / (S + G)
3. G² / (S + G)
4. G / (S + G)

Correct answer: G² / (S + G)

Solution

To keep the total current unchanged, the series resistance P plus the parallel combination must equal the original G: P + GS/(G+S) = G, giving P = G - GS/(G+S) = G^2/(S+G).

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