$A$ student uses the resistance of a known resistor $(1 \,\Omega)$ to calibrate a voltmeter and an ammeter using the circuits shown below. The student measures the ratio of the voltage to current to be $1 \times 10^3 \,\Omega$ in circuit $(a)$ and $0.999 \,\Omega$ in circuit $(b)$. From these measurements,the resistance (in $\Omega$) of the voltmeter and ammeter are found to be close to

Two identical moving coil galvanometers have $10 \Omega$ resistance and full scale deflection at $2 \mu A$ current. One of them is converted into a voltmeter of $100 \text{ mV}$ full scale reading and the other into an ammeter of $1 \text{ mA}$ full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with $R = 1000 \Omega$ resistor by using an ideal cell. Which of the following statement$(s)$ is/are correct?
$(1)$ The measured value of $R$ will be $980.2 \Omega$.
$(2)$ The resistance of the voltmeter will be $50 \text{ k} \Omega$.
$(3)$ The resistance of the ammeter will be $0.02 \Omega$ (rounded off to the $2^{\text{nd}}$ decimal place).
$(4)$ If the ideal cell is replaced by a cell having internal resistance of $5 \Omega$,then the measured value of $R$ will be more than $1000 \Omega$.

The deflection in a moving coil galvanometer is reduced to half when it is shunted with a $40 \Omega$ coil. The resistance of the galvanometer is (in $Omega$)

$A$ 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:

$A$ 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 . . . . . . .

$A$ moving coil galvanometer has a coil with $175$ turns and an area of $1 \, cm^2$. It uses a torsion band with a torsion constant of $10^{-6} \, N \cdot m/rad$. The coil is placed in a magnetic field $B$ parallel to its plane. The coil deflects by $10^{\circ}$ for a current of $1 \, mA$. The value of $B$ (in Tesla) is approximately: