In a moving coil galvanometer,the deflection of the coil $\theta$ is related to the electrical current $i$ by the relation

The sensitivity of a galvanometer is $60 \text{ division/A}$. When a shunt is used,its sensitivity becomes $10 \text{ division/A}$. If the galvanometer is of resistance $20 \ \Omega$,the value of shunt used is (in $\Omega$)

An ideal ammeter and an ideal voltmeter have resistances of . . . . . . $\Omega$ and . . . . . . $\Omega$ respectively.

$A$ $100\, \Omega$ galvanometer gives full-scale deflection at $10\, mA$. How much shunt is required to read $100\, mA$?

When a resistance of $100 \Omega$ is connected in series with a galvanometer of resistance $R$,its range is $V$. To double its range,a resistance of $1000 \Omega$ is connected in series. Find $R$. (in $\Omega$)

Two moving coil meters,$M_{1}$ and $M_{2}$ have the following particulars:
$R_{1}=10 \,\Omega, \quad N_{1}=30$
$A_{1}=3.6 \times 10^{-3} \,m^{2}, \quad B_{1}=0.25 \,T$
$R_{2}=14 \,\Omega, \quad N_{2}=42$
$A_{2}=1.8 \times 10^{-3} \,m^{2}, \quad B_{2}=0.50 \,T$
(The spring constants are identical for the two meters). Determine the ratio of
$(a)$ current sensitivity and
$(b)$ voltage sensitivity of $M_{2}$ and $M_{1}$.