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A galvanometer with 50 divisions and a variable shunt is used as an ammeter, connected in series with a 90 ohm resistor and a battery of internal resistance 10 ohm. With shunt resistances of 10 ohm and 50 ohm, the deflections are 9 and 30 divisions respectively. Find (i) the galvanometer resistance, and (ii) the emf of the cell, given that full-scale deflection (50 divisions) corresponds to a galvanometer current of 300 mA.

1. (i) G = 233.3 ohm, EMF = 30 V
2. (i) G = 100 ohm, EMF = 30 V
3. (i) G = 233.3 ohm, EMF = 60 V
4. (i) G = 50 ohm, EMF = 15 V

Correct answer: (i) G = 233.3 ohm, EMF = 30 V

Solution

Using current division for both shunt settings and proportionality of deflection to galvanometer current gives two equations whose solution yields G ~ 233 ohm; then total-current and circuit relations give EMF = 30 V.

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