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Question
A galvanometer shows full-scale deflection for current Ig. A resistance R1 is required to convert it into a voltmeter of range (0 - V) and a resistance R2 to convert it into a voltmeter of range (0 - 2V). Find the resistance of the galvanometer.
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Solution
In the first case the potential difference between A and B,
`V = I_gR_1 + I_gG`
`I_g = V/(R_1 + G)`
Where G = Resistance of galvanometer
∴ `R_1 + G = V/I_g`
`R_1 = V/(Ig) - G`
⇒ G = `V/(Ig) - R_1`
In the second case,
`I_g = V/(R_2 + G)`
R2 is the Resistance required to change the range from 0 - 2V.
`I_g = (2V)/(R_2 + G)`
`R_2 + G = (2V)/I_g`
`R_2 = (2V)/I_g - G`
⇒ R = `(2V)/I_g - R_2`
Hence, the resistance of the galvanometer is respectively `V/(Ig) - R_1` and `(2V)/(Ig) - R_2`.
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