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Q.

A multirange voltmeter can be constructed by using a galvanometer circuit as shown in figure. We want to construct a voltmeter that can measure 2V,20V and 200V using a galvanometer of resistance 10Ω and that produces maximum deflection for current of 1mA. The values of R₁,R₂ and R₃ are (in ohm)

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a

1990, 18000, 180000

b

18, 18000, 199

c

1800, 190, 18000

d

1990, 18, 1800

answer is A.

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Detailed Solution

$\begin{array}{l} V = i_{g} (G + R) \Rightarrow R = \frac{V}{i_{g}} - G \\ \Rightarrow R_{1} = \frac{2}{10^{- 3}} - 10 = 1990 Ω \\ \Rightarrow R_{1} + R_{2} = \frac{20}{10^{- 3}} - 10 = 19, 990 \\ R_{2} = 18000 Ω \\ \Rightarrow R_{1} + R_{2} + R_{3} = \frac{200}{10^{- 3}} - 10 = 199990 \\ R_{3} = 180000 Ω \end{array}$

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