TS EAMCET · Maths · Application of Derivatives
Electric current (I) is measured by galvanometer, the current being proportional to the tangent of the angle \((\theta)\) 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
- A \(\pi\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad I \propto \tan \theta \\ & d I=\sec ^2 \theta d \theta \\ & \frac{\Delta I}{I} \times 100=\sec ^2 \theta \frac{\Delta \theta}{\theta} \times 100 \\ & \text { when } \theta=\frac{\pi}{4} \\ & \frac{\Delta \theta}{\theta} \times 100=\frac{\pi}{4} \times…
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