Question

If 10% of the main current is to be passed through the moving coil galvanometer of resistance \[99\Omega \], then the required shunt resistance will be:
A. \[9.9\Omega \]
B. \[10\Omega \]
C. \[11\Omega \]
D. \[9\Omega \]

Answer 1

Hint: In this question first we draw an ammeter by connecting a resistance ${R_{sh}}$ in a shunt across the galvanometer whose resistance is given as $99\Omega $. Then equating the potential as they are connected in parallel that is ${V_{Rsh}} = {V_G}$ and using this we can write ${I_{sh}} \times {R_{sh}} = {I_G} \times 99$. Then after solving this we get the shunt resistance as \[11\Omega \].

Complete Step-by-Step solution:
The first step is to know how an ammeter is constructed using a galvanometer. When we connect a parallel resistance across the galvanometer with very low resistance. And as mentioned in the question that only 10% of the main current is passing through the galvanometer. So we have drawn the ammeter with all the current components as shown in figure 1.

Figure1

Here, let us assume the main current be \[I\]
So current through galvanometer is ${I_G} = 10\% I = \dfrac{{10}}{{100}}I$
Now the current through the shunt resistance ${R_{sh}}$ is
 ${I_{sh}} = I - {I_G} = I - \dfrac{{10}}{{100}}I$
$ \Rightarrow {I_{sh}} = \dfrac{{90}}{{100}}I$
Now we are given that the resistance of galvanometer is $99\Omega $, so to find the overall shunt resistance ${R_{sh}}$ which can be further be used to calculate the overall ammeter resistance as
${R_A} = {R_{sh}}\parallel 99$
From the figure, we can see that the potential across ${R_{sh}}$ is the same as potential across$G$ that is
${V_{Rsh}} = {V_G}$
$ \Rightarrow {I_{sh}} \times {R_{sh}} = {I_G} \times 99$
Now solving this equation we will get
$ \Rightarrow \dfrac{{90}}{{100}}{I} \times {R_{sh}} = \dfrac{{10}}{{100}}{I} \times 99$
$ \Rightarrow {R_{sh}} = \dfrac{{1{0}}}{{9{0}}} \times 99 = 11$
Therefore the overall shunt resistance is $11\Omega $. So option C is correct.

Note: For these kinds of questions we first need to know how to construct an ammeter, voltmeter, and wattmeter using a galvanometer. Then we can find the overall resistances either by parallel connection or by the series connection of all the resistance that is present. We also need to have a good knowledge of KVL and KCL.