A galvanometer gives full scale deflection of 1 volt when acting like a voltmeter when connected in series with $2 k Ω$ resistance. The same galvanomeler gives 500 mA, fuIl scale deflection when acting like an ammeter when connected with shunt resistance of value $0.2 Ω$ in parallel.
Find out the resistance of galvanometer.

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$222 Ω$

$1.5 k Ω$

$250 Ω$

$108 Ω$

answer is B.

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Detailed Solution

$\begin{array}{l} V = I_{g} (R + G) \\ 1 = I_{g} (2000 + G) \Rightarrow I_{g} = \frac{1}{2000 + G} . .. (1) \end{array}$

$\begin{array}{l} I_{g} G = (0 .5 - I_{g}) \times 0 .2 \\ I_{g} G = 0 .1 - 0 .2 I_{g} \\ I_{g} (G + 0 .2) = 0 .1 . ... (2) \end{array}$

From (1) and (2),

$\begin{array}{l} (\frac{1}{2000 + G}) (G + 0 .2) = 0 .1 \\ G + 0 .2 = 200 + 0 .1 G \\ 0 .9 G = 199 .8 \\ G = 199 .8 / 0 .9 Ω = 222 Ω \end{array}$

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