question_answer

A \[50\Omega \] galvanometer is shunted by a resistance of\[5\Omega \]. The percentage of the total current, which passes through the galvanometer is

A) \[8.1%\]                              

B) \[10.1%\]

C) \[11.1%\]                            

D)   \[9.1%\]

Correct Answer: D

Solution :

Suppose, \[G\] is the resistance of galvanometer and \[{{I}_{g}}\] is the current for full scale deflection. If \[I\] is the maximum current, then                 \[{{I}_{g}}\times G=(I-{{I}_{g}})S\] Given,   \[G=50\Omega \]and\[S=5\Omega \] \[\therefore \]  \[\frac{{{I}_{g}}}{I}=\frac{S}{G+S}=\frac{5}{50+5}=\frac{5}{55}=\frac{1}{11}\] \[\Rightarrow \]               \[{{I}_{g}}=\frac{I}{11}\]or\[\frac{{{I}_{g}}}{I}=\frac{1}{11}\] or            \[\frac{{{I}_{g}}}{I}%=\frac{1}{11}\times 100%\approx 9.1%\]