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5.Magnetism and Matter
hard
Two tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of $60° $ and $45°$ respectively. The ratio of the number of turns in the coils is
A
$4/3$
B
$(\sqrt 3 + 1)/1$
C
$(\sqrt 3 + 1)/(\sqrt 3 - 1)$
D
$\sqrt 3 /1$
Solution
(d)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 $i_1 = i_2 $ $==>$ ${K_1}\sqrt 3 = {K_2} \Rightarrow \frac{{{K_1}}}{{{K_2}}} = \frac{1}{{\sqrt 3 }}$
But $K \propto \frac{1}{n} \Rightarrow $ $\frac{{{K_1}}}{{{K_2}}} = \frac{{{n_2}}}{{{n_1}}}$ $\frac{{{n_1}}}{{{n_2}}} = \frac{{\sqrt 3 }}{1}$.
Standard 12
Physics
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