Problem

Solve the problems in related rates. A plane flyi…

Problem 12 Easy Difficulty

Solve the problems in related rates.
The voltage $V$ that produces a current $I$ (in $A$ ) in a wire of radius $r$ (in in.) is $V=0.030 I / r^{2} .$ If the current increases at $0.020 \mathrm{A} / \mathrm{s}$ in a wire of 0.040 in. radius, find the rate at which the voltage is increasing.

Answer

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Basic Technical Mathematics with Calculus

Chapter 24

Applications of the Derivative

Section 4

Related Rates

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Video Transcript

it is written in Chapter 29 problem 21. So it says, supposed the radius of the elastic Lupin problem 20 Increase constant rate the R D c for putting three centimeters per second. And we want to determine the e m of induced AT T equals our time t equals zero and that time T equals one second. Okay, so we know that the EU e meth induced could be given by equation 29 to a And since the field is uniform and perpendicular to the area, the flux is simply the field times the area. So we have methods. Affliction of time here is given by the time you're ever did with magnetic flux with respected time, but with a constant beef, The old we can pull the Byfield out there. Mrs what we get. Well, then, this becomes once we differentiate with Hector. Are we get to pie b r d r d t is our bollocks. That's a function of time. Look, we can also write what our area initially is Our pi r squared starts that are not is given as Michelle area over pies were routed. So this is our not which is radius at a time. Zero. So if we're looking for the E m s t equals zero and what this is is just too pie. Be are not the r e t. So this is to pie. And our Byfield was 0.28 Tesla are not was given as square. You're a hot over pie, but it came out well. We look back problem 20. It tells us at a 0.285 square meters over pi and lastly, it tells us our DRD t is 4.3 centimeters per second or report 43 0.0 forthe meters per second. So we can plug all this in and we get e m f at times zero is 23 mil evals Cool. Well, let's find it once again. Now. Well, this becomes roughly the same ring of two pi times Our deal in a week me to figure what ours what are not Plus he already two times time alarms. So what this becomes is square root of 285 over pi plus 0.0 for three times one second. But times once we could leave that off and we times all this time spent zero 43 units per second e. What we're left with is our answer. Enough of one time equals one second is 26 levels cool.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Problem

Solve the problems in related rates. A plane flyi…

Problem 12 Easy Difficulty

Solve the problems in related rates.
The voltage $V$ that produces a current $I$ (in $A$ ) in a wire of radius $r$ (in in.) is $V=0.030 I / r^{2} .$ If the current increases at $0.020 \mathrm{A} / \mathrm{s}$ in a wire of 0.040 in. radius, find the rate at which the voltage is increasing.

Answer

Related Courses

Basic Technical Mathematics with Calculus

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Discussion

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Watch More Solved Questions in Chapter 24

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus