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Question

Full scale deflection current for a galvanometer is $$1mA$$. The value of shunt resistance (approximately) so that galvanometer shows half scale deflection is

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A
1.5 mΩ
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B
3 mΩ
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C
10 mΩ
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D
15 mΩ
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Solution

The correct option is A $$1.5$$ m$$\Omega$$
In the given part of circuit,
the full scale deflection current through galvanometer is
$$I_{fsd} = 10^{-3} A$$
When shunt resistance is introduced in the circuit galvanometer shows half scale deflection current
$$I_{hsd} = \dfrac {1}{2} 10^{-3} A$$
Therefore,
$$\dfrac{1}{2}10^{-3}(30)=S[10-\dfrac{1}{2}10^{-3}]$$
$$S = \dfrac {30\times 10^{-3}}{20 - 10^{-3}}$$
Hence,
$$S=\dfrac{30}{20000-1}\cong \dfrac{30}{20000}\cong1.5$$m$$\Omega .$$

Physics

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