Two galvanometers $A$ and $B$ require $3\,mA$ and $5\,mA$ respectively to produce the same deflection of $10$ divisions. Then:

$A$ galvanometer is used in the laboratory for the null point in electrical experiments. If,on passing a current of $6 \, mA$,it produces a deflection of $2^{\circ}$,its figure of merit is close to:

An ammeter with internal resistance $90\,\Omega$ reads $1.85\,A$ when connected in a circuit containing a battery and two resistors $700\,\Omega$ and $410\,\Omega$ in series. The actual current in the circuit (without the ammeter) will be:

Given below are two statements:
Statement $I$: If the number of turns in the coil of a moving coil galvanometer is doubled,then the current sensitivity becomes double.
Statement $II$: Increasing the current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio.
In the light of the above statements,choose the correct answer from the options given below:

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

$A$ 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