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. . . . . .
IIT 2018, Medium
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Number of turns $=50$
Area $=2 \times 10^{-4} m ^2$
$B=0.02 T$
Torsional constant $C =10^{-4}$
At full scale deflection $\theta=0.2 rad$
Resistance $R =50 \Omega$
Torque $\tau= C \theta=$ niAB
Full scale current $i =\frac{ C \theta}{ nAB }=\frac{0.2 \times 10^{-4}}{50 \times 2 \times 10^{-4} \times 0.02}$
$i =0.1 amp$
$0.9 \times S =0.1 \times R$
$S =\frac{ R }{9}=\frac{50}{9} \Omega$
$S =5.56 \Omega$
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