$A$ galvanometer of resistance $50 \Omega$ gives a full-scale deflection for a current of $5 \times 10^{-4} \text{ A}$. The resistance that should be connected in series with the galvanometer to read $3 \text{ V}$ is: (in $\Omega$)

To verify Ohm's law,a student is provided with a test resistor $R_T$,a high resistance $R_1$,a small resistance $R_2$,two identical galvanometers $G_1$ and $G_2$,and a variable voltage source $V$. The correct circuit to carry out the experiment is

$A$ galvanometer having a resistance $G$ and current $I_g$ flowing in it,produces full-scale deflection. If $S_1$ is the value of the shunt which converts it into an ammeter of range $0-I$ and $S_2$ is the value of the shunt for range $0-8I$,then the ratio $\frac{S_1}{S_2}$ will be:

The deflection in a moving coil galvanometer of resistance $45 \Omega$ falls from $30$ divisions to $3$ divisions. The length of the shunt wire required to convert the galvanometer into an ammeter is [specific resistance of the material of the shunt wire $= 5 \times 10^{-7} \Omega m$ and area of cross-section of the wire $= 4 \times 10^{-7} m^2$]. (in $m$)

$A$ moving coil galvanometer has a rectangular wire coil of enclosed area $0.001 \ m^2$ and $500$ turns. The coil operates in a radial magnetic field of $0.2 \ T$ and carries a current of $6 \pi \times 10^{-8} \ A$. If the torsional spring constant is $6 \times 10^{-7} \ N-m/rad$, then the angular deflection of the coil in radians is

$A$ galvanometer is used in a laboratory for detecting 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 (each division is $1^{\circ}$):