question_answer

A galvanometer has a resistance \[50\,\,\Omega \]. A resistance of \[5\,\,\Omega \] is connected parallel to it. Fraction of the total current flowing through galvanometer is

A)  \[\frac{1}{10}\]

B)  \[\frac{1}{11}\]

C)  \[\frac{1}{50}\]

D)  \[\frac{2}{15}\]

Correct Answer: B

Solution :

The galvanometer G and shunt S is connected in parallel, hence potential difference is the same. \[\therefore \] \[{{i}_{g}}\times G=(i-{{i}_{g}})\times S\] \[\Rightarrow \] \[\frac{{{i}_{g}}}{i-{{i}_{g}}}=\frac{S}{G}=\frac{5}{50}=\frac{1}{10}\] \[\Rightarrow \] \[10{{i}_{g}}=i-{{i}_{g}}\] \[\Rightarrow \] \[11\,{{i}_{g}}=i\] \[\Rightarrow \] \[\frac{{{i}_{g}}}{i}=\frac{1}{11}\]