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Two tangent galvanometer coils of same radius connected in series. The current flowing produces deflection of $60^o$ and $45^o$. The ratio of number of turns in coil is
$\frac {4}{3}$
$\frac {\sqrt 3+1}{1}$
$\frac {\sqrt 3+1}{\sqrt 3-1}$
$\frac {\sqrt 3}{1}$
Solution
Tangent galvanometers are connected in series so current will be same in both.
${\mathrm{k}_{1} \tan \theta_{1}=\mathrm{K}_{2} \tan \theta_{2}}$
${\frac{\mathrm{k}_{1}}{\mathrm{k}_{2}}=\frac{\tan \theta_{2}}{\tan \theta_{1}}=\frac{1}{\sqrt{3}}}$
$\mathrm{k} \propto \frac{\mathrm{R}}{\mathrm{N}}$ (radius is same for both)
$\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\frac{\mathrm{N}_{2}}{\mathrm{N}_{1}}$
$\Rightarrow \frac{\mathrm{N}_{1}}{\mathrm{N}_{2}}=\frac{\mathrm{K}_{2}}{\mathrm{K}_{1}}=\frac{\sqrt{3}}{1}$
