A moving coil galvanometer, having a resistance G , produces full scale deflection when a current I G flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I o ( I

Question

A moving coil galvanometer, having a resistance G , produces full scale deflection when a current I G ​ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I o ​ ( I 0 ​ > I g ​ ) by connecting a shunt resistance R A ​ to it and (ii) into a voltmeter of range 0 to V ( V = G I 0 ​ ) by connecting a series resistance R V ​ to it. Then,

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For ammeter: ( I 0 ​ − I G ​ ) × R A ​ = I G ​ × G ⇒ I 0 ​ = I G ​ × R A ​ ( G + R A ​ ) ​ For voltmeter: V 0 ​ = I G ​ ( G + R V ​ ) ∵ V 0 ​ = I 0 ​ × G ⇒ I G ​ × ( G + R V ​ ) = I G ​ × R A ​ ( G + R A ​ ) × G ​ ⇒ R A ​ × G + R V ​ × R A ​ = G 2 + R A ​ × G ⇒ R V ​ R A ​ = G 2 Again, R V ​ R A ​ ​ = I 0 ​ − I G ​ I G ​ × G ​ × ( I 0 ​ − I G ​ ) × G I G ​ ​ = ( I 0 ​ − I G ​ ) 2 I G 2 ​ ​

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