   Chapter 2.8, Problem 39E

Chapter
Section
Textbook Problem

# If two resistors with resistances R 1  and  R 2 are connected in parallel, as in the figure, then the total resistance R, measured in ohms ( Ω ) , is given by 1 R = 1 R 1 + 1 R 2 If R 1  and  R 2 are increasing at rates of 0.3 Ω / s and  0.2 Ω / s , respectively, how fast is R changing when R 1 = 80 Ω  and  R 2 = 100 Ω ? To determine

To find:

The rate at which R is changing.

Explanation

1. Concept:

Using parallel resistors with total resistance formula and differentiation, we can find the rate of change.

2. Formula:

i. Total resistance: 1R=1R1 +1R2

ii. Power rule of differentiation: ddxxn=n*xn-1

iii. Chain rule of differentiation: ddtfx=ddxfx*dxdt

3. Given:

i. dR1dt=0.3

ii. dR2dt=0.2

iii. R1=80 and R2=100

4. Calculations:

Consider the formula of total resistance 1R=1R1 +1R2

Substituting the values

1R=180+1100 =>

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