The deflection in a moving coil galvanometer is reduced to half when it is shunted with a $X \ \Omega$ coil. The relation between $X$ and the resistance of the galvanometer $G$ is:

Derive the expression for the shunt resistance required to increase the current-measuring capacity of a galvanometer by a factor of $n$.

$A$ galvanometer of resistance $100\,\Omega$ has $50$ divisions on its scale and a sensitivity of $20\,\mu A/\text{division}$. It is to be converted into a voltmeter with three ranges: $0-2\,V$,$0-10\,V$,and $0-20\,V$. The appropriate circuit to do so is:

$A$ galvanometer with $50$ divisions on the scale has a resistance of $25 \Omega$. $A$ current of $2 \times 10^{-4} \text{ A}$ gives a deflection of one scale division. The additional series resistance required to convert it into a voltmeter reading up to $25 \text{ V}$ is $.... \Omega$.

Which one of the following modifications may increase the sensitivity of a moving coil galvanometer?
$1^{st}$ Way: By using a spring of smaller torsion constant.
$2^{nd}$ Way: By using a smaller coil.
$3^{rd}$ Way: By using a stronger magnet.
$4^{th}$ Way: By using a coil having fewer number of turns.

$A$ galvanometer has a resistance of $80 \Omega$ and it is shunted with a resistance of $20 \Omega$. If $20 \%$ of the main current flows through the galvanometer, what is the value of the main current (in $\text{ A}$)?