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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 $R.$

$-\frac{d R}{R}$

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Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University

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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

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University

Lectures

Join Bootcamp