Question

Two tangent galvanometers A and B are identical except in their number of turns. They are connected in series. On passing a current through them, deflections of ${60}^{\circ }$ and ${30}^{\circ }$ are produced. The ratio of the number of turns in A and B is

• A. $1:3$
  
• B. $3:1$
  
• C. $1:2$
  
• D. $2:1$
  

Answer 1

The correct option is B $3:1$

We know that deflection in Galvanometer $\left(\theta \right)$ and Current $\left(I\right)$

are related as $\tan \theta =kNI$

where k = constant

N= No of turns

I= Current

Here, ${\theta }_1={60}^0$

And, ${\theta }_2={30}^0$

$\Rightarrow \frac{\tan {60}^0}{\tan {30}^0}=\frac{k{N}_{1}I}{k{N}_{2}I}$

$\Rightarrow \frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=\frac{N_1}{N_2}$

$\Rightarrow \frac{N_1}{N_2}=\frac{3}{1}$

Therefore, B is correct option.