Question

The coils made of the same material in two moving coil galvanometers have their areas in the ratio of $2:3$ and the number of turns in the ratio of $4:5$. These two coils carry the same current and are situated in the same field. The deflections produced by these two coils will be in the ratio of:

• A. $8:15$
• B. $15:8$
• C. $8:1$
• D. $1:4$

Answer 1

Answer: (A)

$8:15$

Deflection in a galvanometer is given by:

$\theta =\frac{I}{G}$

where

$G=\frac{k}{BNA}:$ galvanometer constant

$I:$ Current

$\therefore \theta \propto NA$ where $N$ is the number of turns and $A$ is the area of the coil.
Given $\frac{N_1}{N_2}=\frac{4}{5}$ and $\frac{A_1}{A_2}=\frac{2}{3}$
$\therefore \frac{{\theta }_1}{{\theta }_2}=\frac{N_1{A}_1}{N_2{A}_2}=\frac{2}{3}\times \frac{4}{5}=\frac{8}{15}$