question_answer

A galvanometer coil has a resistance of \[15\Omega \] and gives full scale deflection for a current of\[4\,\,mA\]. To convert it to an am metal of range \[0\] to\[6\,\,A\]

A)  \[10\,\,m\Omega \] resistance is to be connected in parallel to the galvanometer

B)  \[10\,\,m\Omega \] resistance is to be connected in series with the galvanometer

C)  \[0.1\,\,\Omega \] resistance is to be connected in parallel to the galvanometer

D)  \[0.1\,\,\Omega \] resistance is to be connected in series with the galvanometer

Correct Answer: A

Solution :

To convert a galvanometer into an ammeter, shunt resistance in parallel is connected galvanometer. Since, galvanometer \[G\] and shunt \[S\] are in parallel, hence\[{{i}_{g}}G=(i-{{i}_{g}})\] \[\Rightarrow \]               \[S=\frac{{{i}_{g}}G}{i-{{i}_{g}}}\]                 \[=\frac{4\times {{10}^{-3}}\times 15}{6-4\times {{10}^{-3}}}\]                 \[=\frac{60\times {{10}^{-3}}}{5.996}\]                 \[=10\times {{10}^{-3}}\Omega \]                 \[=10\,\,m\Omega \]