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Problem 39 Medium Difficulty
If a current $ I $ passes through a resistor with resistance $ R, $ Ohm's Law states that the voltage drop is $ V = RI. $ If $ V $ is constant and $ R $ is measured with a certain error, use differentials to show that the relative error in calculating $ I $ is approximately the same (in magnitude) as the relative error in $ R. $
Answer
$-\frac{d R}{R}$
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Video Transcript
Okay, The first thing, the nose, the eyes that could lead to the over our Therefore the derivative of I is negative v over R square. Do you are the relative error is changing? I over I In other words, d ie the derivative over I This is negative v over r squared d r over v over r, which is negative d r over our
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