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A galvanometer has a current sensitivity of 1 mA per division. A variable shunt is connected across the galvanometer and the combination is put in series with a resistance of 500 $Ω$ and cell of internal resistance 1 $Ω$ . It gives a deflection of 5 division for shunt of 5 $Ω$ and 20 division for shunt of 25 $Ω$ . The emf of cell is

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$47.1 V$

$57.1 V$

$67.1 V$

$77.1 V$

answer is A.

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Detailed Solution

$I = \frac{E}{R + r + \frac{G S}{G + S}} & I_{G} = \frac{I . S}{G + S}, ∴ I_{G} = \frac{E S}{(R + r) (G + S) + G S}$

For $S = 5 Ω, I_{G} = 5 \times 10^{- 3} A, 5 \times 10^{- 3} = \frac{E \times 5}{501 (G + 5) + 5 G}$

For $S = 25 Ω, I_{G} = 20 \times 10^{- 3} A, 20 \times 10^{- 3} = \frac{E \times 25}{501 (G + 25) + 25 G}$

On simplifying, $G = 88.2 Ω$

$∴ E = 10^{- 3} [501 (88.2 + 5) + 5 \times 88.2], ∴ E = 47.1 v o l t$

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