A) 4/3
B) \[(\sqrt{3}+1)/1\]
C) \[(\sqrt{3}+1)/(\sqrt{3}-1)\]
D) \[\sqrt{3}/1\]
Correct Answer: D
Solution :
In the first galvanometer \[{{i}_{1}}={{K}_{1}}\tan {{\theta }_{1}}={{K}_{1}}\tan {{60}^{o}}={{K}_{1}}\sqrt{3}\] In the second galvanometer \[{{i}_{2}}={{K}_{2}}\tan {{\theta }_{2}}={{K}_{2}}\tan {{45}^{o}}={{K}_{2}}\] In series i1 = i2 Þ \[{{K}_{1}}\sqrt{3}={{K}_{2}}\Rightarrow \frac{{{K}_{1}}}{{{K}_{2}}}=\frac{1}{\sqrt{3}}\] But \[K\propto \frac{1}{n}\Rightarrow \] \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{{{n}_{2}}}{{{n}_{1}}}\] \ \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{\sqrt{3}}{1}\].
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