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A galvanometer of resistance G and figure of merit K produces full-scale deflection for n divisions. It is first converted into an ammeter of maximum range I using a shunt resistance S . The same galvanometer is then converted into a voltmeter of maximum range V using a series resistance R . The ratio of the maximum ranges V I is

Options

  1. A(G+S)(G+R) S
  2. BSR G+S
  3. CS(G+R) G
  4. DS(G+R) G+S

Correct answer

D. S(G+R) G+S

Step-by-step solution

The full-scale deflection current of the galvanometer is I_G = nK . When converted into an ammeter using a shunt resistance S , the maximum current range I is given by: I_G G = (I - I_G) S I = I_G G+S S When converted into a voltmeter using a series resistance R , the maximum voltage range V is given by: V = I_G (G+R) Dividing the expression for V by the expression for I , the term I_G cancels out: V I = I_G (G+R) I_G G+S S V I = S(G+R) G+S Answer: S(G+R) G+S

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