Two galvanometer which are identical are fitted with different coils. One has a coil of 500 turns and resistance $100 Ω$ while the other has 250 turns and resistance $550 Ω$ . Then ratio of the deflections when each is connected to a cell of e.m.f. 2.5 V and internal resistance $50 Ω$ is

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8 : 1

3 : 5

1 : 11

4 : 7

answer is C.

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Detailed Solution

τ = BiNA - -

$θ = \frac{BiNA}{C} \Rightarrow θ α i N$

$∴ θ_{1} : θ_{2} = i_{1} N_{1} : i_{2} N_{2}$

$i_{1} = \frac{v}{r + R_{1}} = \frac{2.5}{50 + 100} = \frac{2.5}{150} = \frac{1}{60}$

$i_{2} = \frac{v}{r_{1} + R_{2}} = \frac{2.5}{50 + 600} = \frac{2.5}{650} = \frac{1}{260}$

$θ_{1} : θ_{2} = (\frac{1}{60}) (500) : (\frac{1}{260}) (250)$

$= 8 : 1$

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