Two moving coil galvanometers 1 and 2 are with identical field magnets and suspension torque constants, but with coil of different number of turns $N_{1}$ and $N_{2}$ , area per turn $A_{1}$ and $A_{2}$ , and resistance $R_{1}$ and $R_{2}$ . When they are connected in series in the same circuit, they show defections $θ_{1}$ and $θ_{2}$ . Then $θ_{1} / θ_{2}$ is

A_{1} N_{1} / A_{2} N_{2}

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A_{1} N_{2} / A_{2} N_{1}

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A_{1} R_{2} N_{2} / A_{2} R_{2} N_{2}

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A_{1} R_{1} N_{1} / A_{2} R_{2} N_{2}

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Solution

The correct option is A $A_{1} N_{1} / A_{2} N_{2}$
We know that current in the moving coil galvanometer is $I = \frac{k θ}{N B A}$

As they are connected in series so same current flow though each galvanometer.

i.e, $I_{1} = I_{2}$

or $\frac{k θ_{1}}{N_{1} B A_{1}} = \frac{k θ_{2}}{N_{2} B A_{2}}$

or $\frac{θ_{1}}{θ_{2}} = \frac{N_{1} A_{1}}{N_{2} A_{2}}$

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