In a moving coil galvanometer the deflection of the coil, $ heta$ is related to the electrical curr

Question

In a moving coil galvanometer the deflection of the coil, $	heta$ is related to the electrical current $i$ by the relation\

Professor PC Thomas Classes · Answer

In a moving coil galvanometer $\mathrm{I}=\mathrm{k} 	heta$
where $\mathrm{I}=$ current, $\mathrm{k}=$ galvanometer constant $	heta=$ deflection.
$\mathrm{I} \propto 	heta$. The scale is linear. The scale is linear because the magnetic field is radial
In a radial magnetic field the torque on the coil is $B A N I$. It is equal to the internal torque $c 	heta$\ $ B A N I =c 	heta$
$\mathrm{I}=\left(\frac{\mathrm{c}}{\mathrm{BAN}}ight) 	heta=\mathrm{k} 	heta$
where $\mathrm{k}=\frac{\mathrm{c}}{\mathrm{BAN}}=$ galvanometer constant
c is the torque per unit twist of the torsion fibre. A galvanometer is sensitive if k is small ie.
$\frac{\mathrm{C}}{\mathrm{BAN}}$ is small. For this,
   $c$ is small
   $B$ is large
   A is lar*ge
   N is large
$\mathrm{c}=\frac{\pi \mathrm{Gr}^{4}}{2 \ell}$ where
G = shear modulus of the suspension wire
$\mathrm{r}=$ its radius
$l=$ its length
For C to be small
1) G small
2) r small
3) $l$ large. i.e. a thin and long wire