$4$A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it. The name is derived from the surname of Italian scientist L. Galvani, who in 1791 discovered that electric current makes a dead frog's leg jerk. A spring attached with the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring and we have: $\displaystyle \mathrm{NBAI}=\mathrm{k} \phi$ where N is the total number of turns in the coil A is the area of cross-section of each turn B is the radial magnetic field k is the torsional constant of the spring $\displaystyle \phi$ is the angular deflection of the coil As the current ( $\displaystyle \mathrm{I}_{\mathrm{g}}$ ) which produces full scale deflection in the galvanometer is very small, the galvanometer cannot as such be used to measure current in electric circuits. A small resistance, called shunt, of a suitable value is connected with the galvanometer to convert it into an ammeter of desired range. By using a higher resistance, a galvanometer can also be converted into a voltmeter. (i) The value of the current sensitivity of a galvanometer is given by : (A) $\displaystyle \frac{\mathrm{k}}{\text { NBA }}$ (B) $\displaystyle \frac{\text { NBA }}{\mathrm{k}}$ (C) $\displaystyle \frac{\mathrm{kBA}}{\mathrm{N}}$ (D) $\displaystyle \frac{\mathrm{kNB}}{\mathrm{A}}$ (ii) A galvanometer of resistance $\displaystyle 6 \Omega$ shows full scale deflection for a current of 0.2 A . The value of shunt to be used with this galvanometer to convert it into an ammeter of range ( $\displaystyle 0-5 \mathrm{~A}$ ) is : (A) $\displaystyle 0 \cdot 25 \Omega$ (B) $\displaystyle 0 \cdot 30 \Omega$ (C) $\displaystyle 0.50 \Omega$ (D) $\displaystyle 6 \cdot 0 \Omega$ (iii) The value of resistance of the ammeter in case (ii) will be : (A) $\displaystyle 0 \cdot 20 \Omega$ (B) $\displaystyle 0 \cdot 24 \Omega$ (C) $\displaystyle 6 \cdot 0 \Omega$ (D) $\displaystyle 6 \cdot 25 \Omega$ (iv) (a) A galvanometer is converted into a voltmeter of range ( $\displaystyle 0-\mathrm{V}$ ) by connecting with it, a resistance $\displaystyle \mathrm{R}_{1}$. If $\displaystyle \mathrm{R}_{1}$ is replaced by $\displaystyle \mathrm{R}_{2}$, the range becomes $\displaystyle (0-2 \mathrm{~V})$. The resistance of the galvanometer is : (A) $\displaystyle \left(\mathrm{R}_{2}-2 \mathrm{R}_{1}\right)$ (B) $\displaystyle \left(\mathrm{R}_{2}-\mathrm{R}_{1}\right)$ (C) $\displaystyle \left(\mathrm{R}_{1}+\mathrm{R}_{2}\right)$ (D) $\displaystyle \left(\mathrm{R}_{1}-2 \mathrm{R}_{2}\right)$

OR

(b) A current of 5 mA flows through a galvanometer. Its coil has 100 turns, each of area of cross-section $\displaystyle 18 \mathrm{~cm}^{2}$ and is suspended in a magnetic field $\displaystyle 0 \cdot 20 \mathrm{~T}$. The deflecting torque acting on the coil will be : (A) $\displaystyle 3.6 \times 10^{-3} \mathrm{Nm}$ (B) $\displaystyle 1.8 \times 10^{-4} \mathrm{Nm}$ (C) $\displaystyle 2.4 \times 10^{-3} \mathrm{Nm}$ (D) $\displaystyle 1.2 \times 10^{-4} \mathrm{Nm}$

Physics · Moving Charges and Magnetism · The Moving Coil Galvanometer