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Two Parallel Currents

Q 15. State t...

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Q 15. State the principle of working of a galvanometer. A galvanometer of resistance G is converted into a voltmeter to measure up to V volts by connecting a resistance R₁ in series with the coil. If a resistance R₂ is connected in series with it, then it can measure up to V/2 volts. Find the resistance, in terms of R₁ and R₂ required to be connected to convert it into a voltmeter that can read up to 2V. Also, find thee resistance G of the galvanometer in terms of R₁ and R₂.

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Solution

Dear Student,

Galvanometer works on the principle of conversion of electrical energy into mechanical energy. When a current flows in a magnetic field it experiences a magnetic torque. If it is free to rotate under a controlling torque, it rotates through an angle proportional to the current flowing through it.

$l e t t h e m a x i m u m d e f l e c t i o n o f g a l v a n o m e t e r b e I . f i r I i t s h o w s f u l l s c a l e d e f l e c t o n . V = (G + R_{1}) I \frac{V}{2} = (G + R_{2}) I 2 = \frac{(G + R_{1})}{(G + R_{2})} 2 G + 2 R_{2} = (G + R_{1}) G = R_{1} - 2 R_{2} f o r 2 V l e t t a k e R r e q u i r e d . 2 V = (G + R) I 2 V = (G + R) (\frac{V}{(G + R_{1})}) 2 R_{1} - 4 R_{2} + 2 R_{1} = (R_{1} - 2 R_{2} + R) R = 3 R_{1} - 2 R_{2} R e g a r d s$

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