Question

A galvanometer has a resistance of 900 ohms. In order to send only 10 % of the main current through this galvanometer, the resistance of the required shunt is

• A. 100 ohms
• B. 405 ohms
• C. 0.9 ohms
• D. 90 ohms

Answer 1

The correct option is A

100 ohms

Step1: Given data

A galvanometer has a resistance of 900 ohms.

10 % of the main current flow through the galvanometer.

Step2: Formula used

$S=\frac{I_{g}G}{I-I_g}[whereS=resis\tan ceoftheshunt,I=totalcurrent,I_g=currentingalvanometer,G=resis\tan ceofgalvanometer]$

Step3: calculating the resistance of the required shunt

Let the main current be $I$
Now, current through galvanometer will be 10% of the main current,
$\Rightarrow I_g=0.1I$

So, current through shunt will be 90% of the main current,
$\Rightarrow I_s=0.9I$

Now, applying the formula for the resistance of the shunt, that we discussed above
$S=\frac{I_{g}G}{I-I_g}$

Using the given parameters in the formula for the resistance of the shunt
$$\begin{gathered} S=\frac{0.1I\times 900}{I-0.1I}[AsgivenG=900] \\ S=100\Omega \end{gathered}$$

So, in order to send only 10% of the main current through the galvanometer, the resistance of the required shunt will be option A, i.e.,100 ohms.

Hence, option A is the correct answer.