Question

A moving coil galvanometer has $50$ turns and each turn has an area $2 \times 10^{-4} m^{2}.$. The magnetic field produced by the magnet inside the galvanometer is $0.02\, T$. The torsional constant of the suspension wire is $ 10^{-4} \,N\,m\,rad^{-1}.$ When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by $0.2\, rad$. The resistance of the coil of the galvanometer is $50 \,\Omega$. This galvanometer is to be converted into an ammeter capable of measuring current in the range $0 - 1.0\, A$. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is ______ .

Answer 1

$n=50 $ turns
$ A=2 \times 10^{-4} m ^{2}$
$ B=0.02\, T $
$K =10^{-4} \,m ^{2}$
$Q_{m}=0.2 \,rad $
$ R_{g}=50\, \Omega $
$ I_{A}=0-1.0 \,A $
$\tau=M B=C \theta, M=n I A$
$ B I N A=C \theta ; $
$ 0.02 \times 1 \times 50 \times 2 \times 10^{-4}=10^{-4} \times 0.210$
$I_g = 0.1\,A$
For galvanometer, resistance is to be connected to ammeter in shunt.

$I_{g} \times R_{g}=\left(I-I_{g}\right) S$
$ 0.1 \times 50=(1-0.1) S $
$ S=\frac{50}{9}=5.55$