A) \[1:1\]
B) \[3:1\]
C) \[1:2\]
D) \[1:6\]
E) None of the Above
Correct Answer: E
Solution :
: For a tangent galvanometer \[I=\frac{2r{{B}_{H}}\tan \theta }{n{{\mu }_{0}}}\] where r is the radius of the coil and n is the number of turns. For tangent galvanometer 1 \[{{I}_{1}}=\frac{2r{{B}_{H}}}{n{{\mu }_{0}}}\tan {{30}^{o}}\] For tangent galvanometer 2 \[{{I}_{2}}=\frac{2r{{B}_{H}}}{{{n}_{2}}{{\mu }_{0}}}\tan {{60}^{o}}\] As they are connected in parallel, \[\therefore \] \[{{V}_{1}}={{V}_{2}}\] \[{{I}_{1}}{{R}_{1}}={{I}_{2}}{{R}_{2}}\] \[\frac{2r{{B}_{H}}\,\tan {{30}^{o}}}{{{n}_{1}}{{\mu }_{0}}}{{R}_{1}}=\frac{2r{{B}_{H}}\,\tan {{60}^{o}}}{{{n}_{2}}{{\mu }_{0}}}{{R}_{2}}\] \[\therefore \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\frac{\tan {{30}^{o}}}{\tan {{30}^{o}}}=\frac{1}{3}\frac{\tan {{30}^{o}}}{3\tan {{60}^{o}}}=\frac{1}{9}\] \[\left( \because \,\,\,\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{3}(Given) \right)\] * None of the given options is correct.
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