Ncert Exercises & Solutions

A multirange voltmeter can be constructed by using a galvanometer circuit as shown in the 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 a current of 1 mA. Find $R_{1}, R_{2}, and R_{3}$ that have to be used.

Hint: The total potential drop in the galvanometer and the resistance will be equal to the range of the voltmeter.

Step 1: Applying expression in different situations:

For \begin{array}{ll} i_{G} (G + R_{1}) = 2 & for 2 V range \end{array}

For \begin{array}{ll} i_{G} (G + R_{1} + R_{2}) = 20 & for 20 V range \end{array}

and For \begin{array}{ll} i_{G} (G + R_{1} + R_{2} + R_{3}) = 200 & for 200 V range \end{array}

On solving, we get R_{1} = 1990 Ω, R_{2} = 18 Ω and R_{3} = 180 kΩ

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