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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism5 Marks
Question
A multirange voltmeter can be constructed by using a galvanometer circuit as shown in Fig. 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. Find $R_1, R_2$ and $R_3$ that have to be used.
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Answer

Key concept: The galvanometer can also be used as a voltmeter to measure the voltage across a given section of the circuit. For this a very high resistance wire is to be connected in series with galvanometer. The relationship is given by $I_g(G + R)$ where $I_g$ is the range of galvanometer, G is the resistance of galvanometer and R is the resistance of wire connected in series with galvanometer.

Applying expression in different situations
For $I_g(G + R_1) = 2$ for 2V range
For $I_g(G + R_1 + R_2) = 20$ for 20V range
And For $I_g(G + R_1 + R_2 + R_3) = 200$  for 200V range
By solving, we get
$R_1 = 1990Ω, R_2 = 18kΩ$ and $R_3 = 180kΩ.$

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