question_answer

A \[36\Omega \] galvanometer is shunted by resistance of\[4\Omega \]. The percentage of the total current, which passes through the galvanometer is

A) \[8%\]                                  

B) \[9%\]

C) \[10%\]                               

D)  \[91%\]

Correct Answer: C

Solution :

Let \[G\] be resistance of galvanometer and \[{{i}_{g}}\] the current which on passing through the galvanometer produces full scale deflection. If \[i\] is the maximum current, and since, \[G\]and \[S\] are in parallel.                 \[{{i}_{g}}\times G=(i-{{i}_{g}})\times S\] \[\Rightarrow \]               \[\frac{{{i}_{g}}}{i}=\frac{S}{S+G}\] Given,   \[G=36\Omega ,\,\,S=4\Omega \] \[\therefore \]  \[\frac{{{i}_{g}}}{i}=\frac{4}{36+4}=\frac{4}{40}\] \[\Rightarrow \]               \[{{i}_{g}}=\frac{i}{10}\] \[\therefore \]  \[100\times \frac{{{i}_{g}}}{i}=\frac{1}{10}\times 100\] \[\Rightarrow \]               \[\frac{{{i}_{g}}}{i}%=10%\]