question_answer

If shunt of \[4\,\,\Omega \] is attached to a galvanometer, the deflection is reduced to \[\frac{1}{5}th\]. If an additional shunt of \[2\,\,\Omega \] is attached. The deflection will be reduce to

A)  \[\frac{1}{10}\,th of initial\]       

B)  \[\frac{1}{13}\,th of initial\]

C)  remain same                

D)  None of these

Correct Answer: B

Solution :

Initial condition When shunt of \[4\,\Omega \] is used, \[\frac{I}{5}\times G=\frac{4}{5}\,I\times 4\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,G=16\,\,\Omega \] When additional shunt of \[2\,\Omega \] is attached, \[I'\times 16=(I-I')\frac{4}{3}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,12\,I'\,\times \,\,I\,\,-\,\,I'\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,I'=\frac{I}{13}\] It will reduce to \[\frac{1}{13}\] of the initial value.