JEE MAIN - Physics (2020 - 5th September Morning Slot - No. 18)
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 :
G
R1
R1 + G
R1 - G
Explanation
1 = ig(G + R1) ....(1)
2 = ig(R1 + R2 + G) ....(2)
Doing (1) $$ \div $$ (2), we get
$${1 \over 2} = {{{i_g}\left( {G + {R_1}} \right)} \over {{i_g}\left( {G + {R_1} + {R_2}} \right)}}$$
$$ \Rightarrow $$ R1 + R2 + G = 2R1 + 2G
$$ \Rightarrow $$ R2 = R1 + G
2 = ig(R1 + R2 + G) ....(2)
Doing (1) $$ \div $$ (2), we get
$${1 \over 2} = {{{i_g}\left( {G + {R_1}} \right)} \over {{i_g}\left( {G + {R_1} + {R_2}} \right)}}$$
$$ \Rightarrow $$ R1 + R2 + G = 2R1 + 2G
$$ \Rightarrow $$ R2 = R1 + G
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