A galvanometer with a coil of resistance \( 30\,\Omega \) shows full scale deflection for a current of \( 2.0 \) mA. The value of shunt resistance required to convert it into an ammeter of range from \( 0 \) to \( 1 \) A is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.06\,\Omega \)
A galvanometer is converted into an ammeter by connecting a low resistance (shunt) in parallel with it, so that only the full-scale current \( I_g \) passes through the coil and the rest, \( I - I_g \), passes through the shunt.
Both are in parallel, so the voltage across them is the same:
\( G = 30\,\Omega \)
\( I_g = 2.0\,\mathrm{mA} = 2.0\times10^{-3}\,\mathrm{A} \)
\( I = 1\,\mathrm{A} \)
\( I_g G = (I - I_g)S \)
\( \displaystyle S = \frac{I_g G}{I - I_g} = \frac{(2\times10^{-3})(30)}{1 - 0.002}\,\Omega \)
\( \displaystyle S = \frac{0.06}{0.998}\,\Omega \approx 0.06\,\Omega \)