Question 368 of 380

A galvanometer having a coil resistance of $100\Omega$ gives a full scale deflection, when a current of $1mA$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10A$, is:

A$0.1\Omega$B$3\Omega$C$0.01\Omega$D$2\Omega$

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Answer: (C) $0.01\Omega$

As shown in figure a shunt resistance $\left(S\right)$ is connected parallel to the galvanometer to convert it into an ammeter. Let $G$ is the resistance of the galvanometer.
Where $G=100\Omega$ and full-scale deflection current is ${I}_{g}=10mA=10\times {10}^{-3}A$
For galvanometer ${V}_{g}={I}_{g}G=10\times {10}^{-3}\times 10=0.1volt$
From the figure, the shunt is parallel to galvanometer
$∴$${V}_{S}={V}_{g}\Rightarrow {I}_{S}S={V}_{g}...\left(1\right)$
For ammeter full-scale deflection current is
${I}_{S}\left(=I-{I}_{g}\right)\approx 10A$
$∴$ from equation $\left(1\right)$
$10S=0\cdot 1\Rightarrow S=0\cdot 01\Omega$