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 the value of R₁, R₂ and R₃ that have to be used.

Given :

Resistance of the galvanometer (G) = 10 ohms

Current measured in the galvanometer (I_g) = 1 mA

We know that potential difference V = IR

R = V/I

For a Voltmeter measuring 2V

G + R₁ = V/I_g (As G and R₁ are in series)

R₁ = V/I_g - G

= (2/10^-3)-10

= 1990 Ω

For a Voltmeter measuring 20V

G + R₂ + R₁ = V/I_g ( As G, R₁ and R₂ are in series)

R₂ = V/I_g - G -R₁

= (20/10^-3)-10-1990

= 18 KΩ

For a Voltmeter measuring 200V

G + R₃ + R₂ + R₁ = V/I_g

R₃ = V/I_g - G - R₁-R₂

= (200/10^-3)-10- 1990- 18000

= 180 KΩ