Question

Define the current sensitivity of a galvanometer. Write S.I unit
Figure shows two circuits each having a galvanometer and a battery of 3V
When the galvanometer in each arrangement do not show any deflection obtain the ratio $R_1/R_2$

Answer 1

The deflecting torque in a radial magnetic field , on a coil of galvanometer is given by ,

$\tau =nBIA$ ,

where $n=$ number of turns ,

$I=$ current in coil ,

$A=$ are of coil ,

$B=$ magnetic field in which coil is placed ,

in equilibrium ,

$k\theta =nBIA$ ,

where $k=$ restoring torque/unit twist ,

$\theta =$ deflection in coil ,

therefore , $\theta /I=nBIA/k$ ,

this $\theta /I$ is called current sensitivity i.e. deflection in galvanometer for per unit current . Its S.I. unit is radian/A .

As there is no deflection in galvanometer in both arrangements therefore both are in balanced state ,

for first arrangement ,

$4/R_1=6/9$ ,

or $R_1=36/6=6\Omega$ ,

for second arrangement ,

$R_2/8=6/12$ ,

or $R_2=48/12==4\Omega$ ,

therefore $R_1/R_2=6/4=3/2$