A multirange voltmeter can be constructed by using . . .

Question : 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 detection for a current of 1 mA. Find the value of R₁, R₂ and R₃ that have to be used. 

Doubt by Rohan 

NCERT Exemplar + CBSE SQP 2017-2018

Solution : 

Here 
G = 10Ω
I_g= 1mA = 10^-3 A

V₁=2 V
V₂= 20 V

V₃ = 200 V

Case I 
R₁=V1/Ig-G
R₁=[2/10-3] - 10
R₁=[2000]-10
R₁=1990 Ω

Case II
R₁+R₂=V2/Ig-G
1990+R₂=[20/10-3] - 10
1990+R₂=[20000]-10
1990+R₂=20000-10
1990+R₂=19990
R₂=19990-1990
R₂=18000

R₂=18KΩ

Case III
R₁+R₂+R₃=V₃/Ig-G
1990+18000+R₃=[200/10-3] - 10
19990+R₃=[200000]-10
19990+R₃=200000-10
19990+R₃=199990
R₃=199990-19990
R₃=180000

R₃=180KΩ