$A$ moving coil galvanometer has $100$ turns and each turn has an area of $2.0 \,cm^2$. The magnetic field produced by the magnet is $0.01 \,T$ and the deflection in the coil is $0.05$ radian when a current of $10 \,mA$ is passed through it. The torsional constant of the suspension wire is $x \times 10^{-5} \,N-m / rad$. The value of $x$ is . . . . . . .

The ratio of heats generated through shunt and galvanometer is $7: 5$ when they are connected to make an ammeter. If the resistance of the galvanometer is $112 \Omega$,then the resistance of the shunt is: (in $\Omega$)

Moving coil galvanometers $M_{1}$ and $M_{2}$ have resistance, number of turns, area of coil, and magnetic field as follows:
$R_{1}=10 \ \Omega, R_{2}=14 \ \Omega, N_{1}=30, N_{2}=42$
$A_{1}=3.6 \times 10^{-3} \ m^{2}, A_{2}=1.8 \times 10^{-2} \ m^{2}, B_{1}=0.25 \ T, B_{2}=0.50 \ T$
(Spring constants are same for both galvanometers).
The ratio of $(i)$ current sensitivity and (ii) voltage sensitivity for galvanometer ($M_{2}$ to $M_{1}$) is respectively:

If a galvanometer is shunted by $(\frac{1}{n-1})^{th}$ of the value of its resistance, then the fraction of the total current passing through the galvanometer is

An ammeter reads up to $1\, A$. Its internal resistance is $0.81\, \Omega$. To increase the range to $10\, A$,the value of the required shunt is ............ $\Omega$.

When a shunt of $4\,\Omega$ is connected to a galvanometer,the deflection reduces to $1/5$ of its initial value. If an additional shunt of $2\,\Omega$ is connected in parallel,what will be the new deflection?