A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R₁ in series with it. The additional resistance that should be connected in series with R₁ to increase the range of the voltmeter to 0 – 2 V will be :

Solution

Physics sir · 4 steps

Same full-scale current, double the voltage: the total resistance in the path has to double.

1. Fixed current. The galvanometer shows full deflection at one fixed current I_g, whatever range it is set to read. So the range V depends only on the total resistance in series: V = I_g × (total resistance).
2. First range. For the 0 to 1 V range the total resistance is G + R₁, so 1 = I_g(G + R₁).
3. New range. Add an extra resistance R in series for the 0 to 2 V range. Now 2 = I_g(G + R₁ + R). Divide this by the first equation and I_g cancels.

   (G + R₁ + R)/(G + R₁) = 2 ⇒ R = R₁ + G

4. So. The extra resistance must be R₁ + G, which is option (c).

The idea to keep. A voltmeter's range is I_g times the total series resistance, galvanometer included. To scale the range by n, make the whole resistance n times bigger.

Answer from the NTA final answer key. Solution by PrepWiser.