question_answer

A galvanometer has resistance of \[400\Omega \]. and deflects full scale, for current of \[0.2\text{ }mA\]through it, the shunt resistance required to convert it into 3A ammeter is:

A)  \[0.027\Omega \]           

B)  \[0.054\Omega \]

C)  \[0.0135\Omega \]         

D)  none of these

Correct Answer: A

Solution :

Fact: Potential difference across shunt and galvanometer resistance is same. Suppose G be resistance of galvanometer and current ig. If i is the maximum current, then a part \[{{i}_{g}}\] should pass through G and rest \[i-{{i}_{g}}\] through s. Potential across G and S is same hence. \[{{i}_{g}}\times G=(i-{{i}_{g}})\times S\] \[\Rightarrow \] \[S=\frac{{{i}_{g}}\,G}{i-{{i}_{g}}}\] Here,   \[G=400\Omega ,\,\,{{i}_{g}}=0.2mA.\] \[=0.2\times {{10}^{-3}}A,\,\,i=3A.\] \[S=\frac{0.0002\times 400}{3-0.0002}=0.027\Omega \] Note: Shunt resistance is small compared to galvanometer resistance.