Question

A moving coil galvanometer $\text{A}$ has $100$ turns and resistance $50\Omega$. Another moving coil galvanometer $\text{B}$ has number of turns $500$ and resistance $200\Omega$. The other quantities are same in both cases. They are connected by a battery of internal resistance of $50\Omega$ respectively. The ratio of deflection of $\text{B}$ to $\text{A}$ is (Give integer value)

Answer 1

For a moving coil galvanometer, $BiAN=C\theta$

$\theta \propto iN$ (Since, other quantities are same.)

For $\text{A}:-$

${\theta }_A\propto i_A{N}_A$

${\theta }_A\propto \frac{E}{(G_A+r))}{N}_A\dots \left(1\right)$

For$\text{B}:-$

${\theta }_B\propto \frac{E}{(G_B+r))}{N}_B\dots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get,

$\frac{{\theta }_B}{{\theta }_A}=\frac{N_B}{N_A}\times \frac{(G_A+r)}{(G_B+r)}$

Substituting the data given in the question,

$\frac{{\theta }_B}{{\theta }_A}=\frac{500}{100}\times \frac{(50+50)}{(200+50)}$

$=5\times \frac{100}{250}$

$=2$

Accepted answer : $2$