Question

Two tangent galvanometers, which are identical except in their number of turns, are connected in parallel. The ratio of their resistances of the coils is $1:3$. If the reflection in the two tangents galvanometers are ${30}^o$ and ${60}^o$ respectively, then the ratio of their number of turns is:

• A. $2:3$
• B. $3:1$
• C. $1:2$
• D. $1:6$

Answer 1

The correct option is A $2:3$

$V_1=V_2$ as galvanometers are in parallel.

$I_1{R}_1=I_2{R}_2$

$⟹\frac{I_1}{I_2}=3$ as it is given $\frac{R_2}{R_1}=3$

For a galvanometer, deflection is given by:

$\theta =\frac{NBAI}{k}$

$\therefore \frac{{\theta }_1}{{\theta }_2}=\frac{N_1{I}_1}{N_2{I}_2}$

$\frac{{60}^o}{{30}^o}=\frac{3N_1}{N_2}$

$\frac{N_1}{N_2}=\frac{2}{3}$