$A$ galvanometer of resistance $50 \ \Omega$ giving full scale deflection for a current of $10 \ mA$ is to be changed into a voltmeter of range $100 \ V$. $A$ resistance of . . . . . . $\Omega$ has to be connected in series with the galvanometer.

The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic fields in the region of the coils. The coil of the first one is in the shape of a square of side $a$ and that of the second one is circular of radius $\frac{a}{\sqrt{\pi}}.$ When the same current is passed through the coils, the ratio of the torque experienced by the first coil to that experienced by the second one is

$A$ voltmeter has a range $0-V$ with a series resistance $R$. With a series resistance $2R$,the range is $0-V'$. The correct relation between $V$ and $V'$ is

$A$ moving coil galvanometer has $100$ equal divisions. Its current sensitivity is $10$ divisions per milliampere and voltage sensitivity is $2$ divisions per millivolt. In order that each division reads $1 \ V$,the resistance in Ohm's needed to be connected in series with the coil will be

The sensitivity of a galvanometer of resistance $406\, \Omega$ is decreased by $30$ times. The shunt used is .................. $\Omega$.

In the diagram shown,the reading of the voltmeter is $20\, V$ and that of the ammeter is $4\, A$. The value of $R$ should be (Consider the given ammeter and voltmeter are not ideal).