Question

Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity. Give reasons.

Answer 1

Galvanometer

1. A galvanometer is an electrical instrument used for the detection and measurement of currents and charges.
2. Ammeters and voltmeters are the modified forms of galvanometers.
3. Most commonly used galvanometers are of moving coil suspended type.
4. Here a moving coil is suspended in a magnetic field of a permanent magnet.
5. When current passes through the coil it experiences a torque and rotates until deflecting torque is balanced by the restoring torque of the suspension fibre.
6. The angle of deflection gives a measure of current.

Current Sensitivity

1. A galvanometer is said to be sensitive if it is able to measure a small current, voltage, or charge.
2. The current sensitivity $\left(S_i\right)$ of a galvanometer is defined as the deflection of the light spot in $mm$ on a scale placed at a distance of $1m$ from the galvanometer mirror when a current of $1\mu A$ is passed through the galvanometer.
3. Steady deflection $\theta$ produced by a current $i$ is given by $i=\frac{C}{NAB}\theta$, where $N$ is the number of turns, $A$ is the area of the galvanometer coil, $B$ is a uniform radial magnetic field, $C$ is the couple per unit angle of twist and $\theta$ is the angle of deflection.
4. Therefore, $S_i=\frac{d\theta }{di}=\frac{NAB}{C}$.
5. So for given values of $A$, $B$ and $C$, $S_i\propto N$.
6. If the number of turns $N$ is increased by keeping area $A$ constant then the length of the wire in the winding will increase $N$ times and the cross-sectional area of the wire must be necessarily reduced by a factor of $\frac{1}{N}$.
7. So the resistance $R_g$ of the wire in the winding will increase by $N^2\left(\because R_g=\rho .\frac{l_g}{A_g}\right)$.
8. Thus, $R_g\propto N^2,S_i\propto N$ and hence $S_i\propto \sqrt{R_g}$.
9. Hence, if $\left(S_i\right)$ is increased, $R_g$ will also increase.

Voltage Sensitivity

1. The voltage sensitivity $\left(S_V\right)$ of a galvanometer is defined as the deflection of the light spot in $mm$ on a scale placed at a distance $1m$ from the galvanometer mirror when a potential difference of $1\mu V$ is applied across the galvanometer.
2. The potential difference across the galvanometer for a steady-current $i$ is $V=i{R}_g$.
3. Therefore, $S_V=\frac{d\theta }{dV}=\frac{1}{R_g}\frac{d\theta }{di}=\frac{S_i}{R_g}$
4. As $S_i\propto \sqrt{R_g}$, therefore, $S_V\propto \frac{1}{\sqrt{R_g}}$.

Therefore, if $\left(S_i\right)$ is increased, $R_g$ will also increase, which will in turn balance the value of $\left(S_V\right)$.

Hence, increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.