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 $0.02T$. The torsional constant of the suspension wire is $10^{-4}Nmra{d}^{-1}.$ When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by $0.2rad$. 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 $0-1.0A$. 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

Answer: 5.55

$n=50$ turns
$A=2\times 10^{-4}{m}^2$
$B=0.02T$
$K=10^{-4}{m}^2$
$Q_m=0.2rad$
$R_g=50\Omega$
$I_A=0-1.0A$
$\tau =MB=C\theta ,M=nIA$
$BINA=C\theta ;$
$0.02\times 1\times 50\times 2\times 10^{-4}=10^{-4}\times 0.210$
$I_g=0.1A$
For galvanometer, resistance is to be connected to ammeter in shunt.

$I_g\times R_g=\left(I-I_g\right)S$
$0.1\times 50=(1-0.1)S$
$S=\frac{50}{9}=5.55$