A) \[\sqrt{3}/1\]
B) \[(\sqrt{3}+1)(\sqrt{2}-1)\]
C) \[(\sqrt{3}+1)/1\]
D) 4/3
Correct Answer: A
Solution :
In the first galvanometer \[{{i}_{1}}={{K}_{1}}\tan \,o{{|}_{1}}={{K}_{1}}\tan {{60}^{o}}={{K}_{1}}\sqrt{3}\] In the second galvanometer \[{{i}_{2}}={{K}_{2}}\tan \,o{{|}_{2}}={{K}_{2}}\tan {{45}^{o}}={{K}_{2}}\] But, \[i\propto n\] \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{{{n}_{1}}}{{{n}_{2}}}\Rightarrow \frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{i}_{1}}}{{{i}_{2}}}\] \[\Rightarrow \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{K\sqrt{3}}{K}=\frac{\sqrt{3}}{1}\] \[(\because \,{{K}_{1}}={{K}_{2}}=K)\] Hence, \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{3}:1\]
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