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Q.

An electric current is measured by a tangent galvonometer, the current being proportional to the tangent to the angle of deflection. If the deflection is read as $45^{\circ}$ and an error of $1 %$ is made in reading it, the percentage error in the current is

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a

$\frac{π}{2}$

b

$\frac{π}{4}$

c

$π$

answer is B.

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Detailed Solution

$i \propto \tan θ θ = 45^{0} \frac{δ θ}{θ} \times 100 = 1 i = K \tan θ \Rightarrow \frac{δ θ}{\frac{π}{4}} \times 100 = 1 \log i = \log k + \log \tan θ \Rightarrow δ θ = \frac{π}{400} \log i = \log k + \log \tan θ \frac{1}{i} δ i = \frac{1}{\tan θ} \sec^{2} θ δ θ \frac{δ i}{i} \times 100 = \frac{2}{1} \times \frac{π}{400} \times 100 = \frac{π}{2}$

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