A moving coil galvanometer of resistance 100 $\Omega$ shows full scale deflection when a current of 100…

A moving coil galvanometer of resistance 100 $\Omega$ shows full scale deflection when a current of 100 micro-amperes passes through it. If it is intended to show full scale deflection when a current of 1 milliampere passes through it, the value of shunt resistance in ohms to be connected to the galvanometer is.
  1. $\frac{9}{4}$
  2. $\frac{10}{3}$
  3. $\frac{100}{9}$
  4. $\frac{900}{7}$

Solution

Resistance of galvanometer $ \begin{gathered} G=100 \Omega \\ I_g=100 \mu \mathrm{A}=100 \times 10^{-6} \mathrm{~A}=0.1 \times 10^{-3} \mathrm{~A} \\ I=1 \mathrm{~mA}=1 \times 10^{-3} \mathrm{~A} \end{gathered} $ Shunt resistance $ \begin{aligned} S & =\frac{I_g G}{I-I_g}=\frac{0.1 \times 10^{-3} \times 100}{1 \times 10^{-3}-0.1 \times 10^{-3}} \\ & =\frac{1 \times 10^{-2}}{0.9 \times 10^{-3}}=\frac{10^2}{9}=\frac{100}{9} \Omega \end{aligned} $

Asked in: AP EAMCET 2002

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