(a) Suppose two resistors are connected in parallel with resistances Rị and R2 measured in Ohms (N). The totalresistance R is given by111RR1R2Suppose R1 is increasing at a rate of 1/4 2/s and R2 is increasing at a rate of 1/16 N/s. At what rate is R changingwhen R1 = 1/2 N and R2 = 1/4 N.(b) Car A is traveling North at a rate of 60 mi/hr, car B is traveling West at a rate of 45 mi/hr. The cars are onstraight roads approaching an intersection point. At what rate is the distance between the cars changing when Car Ais 3 miles from the intersection and Car B is 4 miles from the intersection.

When two resistors are connected in parallel, their equivalent resistance is given by; 1R=1R1+1R2 The rate of increase in the value of R1 dR1dt=14 Ω/s The rate of increase in the value of R2 dR2dt=116 Ω/s R1=12 Ω R2=14 ΩWe can write for parallel connection; 1R=1R1+1R2 Substituting the values; 1R=2+4 ∴R=16 ΩWe can write the equation for parallel connection; R-1=R1-1+R2-1 Differentiating this equation with respect to time; -R-2dRdt=-R1-2dR1dt-R2-2dR2dt ∴1R2dRdt=1R12dR1dt+1R22dR2dt Substituting the values; (6)2×dRdt=(2)2×14+(4)2×116 ∴dRdt=118 Ω/s Thus, the rate by which the equivalent resistance is changing is 118 Ω/s

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Physics

(a) Suppose two resistors are connected in parallel with resistances R1 and R2 measured in Ohms (N). The total resistance R is given by 1 1 + R1 1 R2 Suppose R1 is increasing at a rate of 1/4 N/s and R2 is increasing at a rate of 1/16 N/s. At what rate is R changing R when R1 = 1/2 N and R2 =1/4 N.

(a) Suppose two resistors are connected in parallel with resistances R1 and R2 measured in Ohms (N). The total resistance R is given by 1 1 + R1 1 R2 Suppose R1 is increasing at a rate of 1/4 N/s and R2 is increasing at a rate of 1/16 N/s. At what rate is R changing R when R1 = 1/2 N and R2 =1/4 N.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

(a) Suppose two resistors are connected in parallel with resistances Rị and R2 measured in Ohms (N). The total
resistance R is given by
1
1
1
R
R1
R2
Suppose R1 is increasing at a rate of 1/4 2/s and R2 is increasing at a rate of 1/16 N/s. At what rate is R changing
when R1 = 1/2 N and R2 = 1/4 N.
(b) Car A is traveling North at a rate of 60 mi/hr, car B is traveling West at a rate of 45 mi/hr. The cars are on
straight roads approaching an intersection point. At what rate is the distance between the cars changing when Car A
is 3 miles from the intersection and Car B is 4 miles from the intersection.

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