question_answer

A galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is                                                           [AIPMT (M) 2011]

A)  \[\frac{{{S}^{2}}}{(S+G)}\]  

B)       \[\frac{SG}{(S+G)}\]

C)  \[\frac{{{G}^{2}}}{(S+G)}\]  

D)       \[\frac{G}{(S+G)}\]

Correct Answer: C

Solution :

[c] Current will be unchanged if resistance remains same so

\[G=\frac{GS}{G+S}+R\]

\[R=G-\frac{GS}{G+S}\]

\[R=\frac{{{G}^{2}}}{G+S}\]