b
(b)In tangent galvanometer, \(I \propto \tan \theta \) \(\therefore \;\frac{{{I_1}}}{{{I_2}}} = \frac{{\tan {\theta _1}}}{{\tan {\theta _2}}} \Rightarrow \frac{{{I_1}}}{{{I_1}/\sqrt 3 }} = \frac{{\tan {{45}^0}}}{{\tan {\theta _2}}}\) \( \Rightarrow \sqrt 3 \tan {\theta _2} = 1 \Rightarrow \tan {\theta _2} = \frac{1}{{\sqrt 3 }} \Rightarrow {\theta _2} = {30^o}\) So deflection will decrease by \(45^o- 30^o = 15^o.\)