What do you know about sensitivity of a galvanometer? Define current sensitivity and voltage sensitivity of a galvanometer.
Sensitivity of a galvanometer :
A galvanometer is said to be sensitive if a small current flowing through the coil of galvanometer produces a large deflection in the galvanometer.
(i) Current Sensitivity :
The current sensitivity of a galvanometer is defined as the deflection produced in the coil of the galvanometer per unit current flowing through it.
That is, current sensitivity
$= \dfrac{\phi}{I} = \dfrac{\phi}{k \phi / (NAB)} = \dfrac{NAB}{k}$
Current sensitivity of galvanometer can be increased either by
(a) increasing the magnetic field B by using a strong permanent horseshoe shaped magnet.
(b) increasing the number of turns N of the coil. But, number of turns of the coil cannot be increased beyond a certain limit. This is because the resistance of the galvanometer will increase subsequently and hence the galvanometer becomes less sensitive.
(c) increasing the area of the coil A. But this will make the galvanometer bulky and ultimately less sensitive.
(d) decreasing the value of restoring force constant $k$ by using a flat strip spring of phosphor-bronze instead of a circular spring of phosphor-bronze because the value of $k$ is small in case of a flat strip than a round wire.
(ii) Voltage Sensitivity :
Voltage sensitivity of a galvanometer is defined as the deflection produced in the coil of the galvanometer per unit voltage applied to it.
That is, voltage sensitivity $= \dfrac{\phi}{V} = \dfrac{\phi}{IR} = \dfrac{NBA}{kR}$
Voltage sensitivity can be increased by
(a) increasing N
(b) increasing B
(c) increasing A
(d) decreasing $k$
(e) decreasing R.
Explain , Increasing current sensitivity of a galvanometer may not necessarily increase the voltage sensitivity of the galvanometer ?
Current sensitivity of a galvanometer is given by
$(C.S.) = \frac{NAB}{k} \hspace{1cm} ...(1)$
If number of turns of the coil are doubled to increase the current sensitivity of the galvanometer, then new current sensitivity is given by
$(C.S.)' = 2 \left( \frac{NAB}{k} \right) = 2(C.S.) \hspace{1cm} ...(2)$
Thus, current sensitivity is doubled by doubling the number of turns of the coil.
The voltage sensitivity of the galvanometer before doubling the number of turn of the coil is given by
$(V.S.) = \frac{NBA}{kR} \hspace{1cm} ...(3)$
Since resistance of wire is directly proportional to the length of the wire, so the resistance $R$ of the coil of galvanometer is doubled $(2R)$ by doubling the number of turns.
The voltage sensitivity of the galvanometer after doubling the number of turns of the coil is given by
$(V.S.)' = \frac{2NBA}{k(2R)} = \frac{NBA}{kR} = (V.S.) \hspace{1cm} ...(4)$
Thus, voltage sensitivity of the galvanometer remains unchanged even if its current sensitivity is doubled by doubling the number of turns of the galvanometer.