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