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JEE MainPhysicsCurrent Electricity

A galvanometer of resistance G and figure of merit K is converted into an ammeter using a shunt resistance S . A graph is plotted for the total measured current I against the number of deflections n shown by the galvanometer. If the graph is a straight line passing through the origin with slope m , the value of the shunt resistance S is

Options

  1. AmG K-m
  2. BKG m+K
  3. CKG m-K
  4. DKG m

Correct answer

C. KG m-K

Step-by-step solution

The current passing through the galvanometer for n deflections is I_G = nK . For an ammeter, the total current I is related to the galvanometer current by the parallel combination principle: I_G G = (I - I_G) S I = I_G G+S S Substituting I_G = nK , we get: I = nK G+S S The slope of the I versus n graph is m = I n . Therefore, m = K G+S S Solving for S : mS = KG + KS S(m - K) = KG S = KG m - K Answer: KG m-K

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