The coil of a moving coil galvanometer has an effective area of $4 \times 10^{-2} \mathrm{~m}^2$. It is…
The coil of a moving coil galvanometer has an effective area of $4 \times 10^{-2} \mathrm{~m}^2$. It is suspended in a magnetic field of $5 \times 10^{-2} \mathrm{~Wb} \mathrm{~m}^{-2}$. If the deflection in the galvanometer coil is $0.2 \mathrm{rad}$, when a current of $5 \mathrm{~mA}$ is passed through it, then
torsional constant is $8 \times 10^{-5} \mathrm{~N} \mathrm{~m} \mathrm{rad}^{-1}$
current sensitivity is $40 \mathrm{rad} \mathrm{A}^{-1}$
torsional constant is $3 \times 10^{-3} \mathrm{~N} \mathrm{~m} \mathrm{rad}^{-1}$
current sensitivity is $40 \operatorname{deg} A^{-1}$
Solution
Given that, for a moving coil galvanometer,
Effective area, $A=4 \times 10^{-2} \mathrm{~m}^2$
Magnetic field, $B=5 \times 10^{-2} \mathrm{Wbm}^{-2}$
Angle of deflection, $\phi=0.2 \mathrm{rad}$
Electric current, $I=5 \mathrm{~mA}=5 \times 10^{-3} \mathrm{~A}$
By using the relation,
$N A B I=C \phi \quad$ [where, $C=$ torsional constant $]$
$\Rightarrow \quad C=\frac{N A B I}{\phi}$
By substituting the values, we get
$C=\frac{4 \times 10^{-2} \times 5 \times 10^{-2} \times 5 \times 10^{-3}}{0.2}$
$=5 \times 10^{-5} \mathrm{Nm} \mathrm{rad}^{-1}$
Current sensitivity,
$S_I=\frac{\phi}{I}=\frac{0.2}{5 \times 10^{-3}} \mathrm{rad} / \mathrm{A}=40 \mathrm{rad} \mathrm{A}^{-1}$